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<title>Konstanter Funktor</title>

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<h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Konstanter Funktor</span></h1>

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<div id="mw-content-text" class="mw-body-content mw-content-ltr" lang="de" dir="ltr"><div class="mw-content-ltr mw-parser-output" lang="de" dir="ltr"><p>Der <b>konstante Funktor</b> ist ein Begriff aus dem <a href="Teilgebiete_der_Mathematik" title="Teilgebiete der Mathematik">mathematischen Teilgebiet</a> der <a href="Kategorientheorie" title="Kategorientheorie">Kategorientheorie</a>. Ein konstanter Funktor zwischen zwei Kategorien ist ein <a href="Funktor_(Mathematik)" title="Funktor (Mathematik)">Funktor</a>, der jedes Objekt auf ein festes Objekt der Zielkategorie und jeden <a href="Morphismus" title="Morphismus">Morphismus</a> auf die Identität dieses festen Objekts abbildet.

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<div class="mw-heading mw-heading2"><h2 id="Definition">Definition</h2></div>

<p>Seien <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {C}}}">

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<annotation encoding="application/x-tex">{\displaystyle {\mathcal {C}}}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/e7b3edab7022ca9e2976651bc59c489513ee9019.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.239ex; height:2.176ex;" alt="{\displaystyle {\mathcal {C}}}" loading="lazy"></span> und <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {D}}}">

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<annotation encoding="application/x-tex">{\displaystyle {\mathcal {D}}}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/3277962e1959c3241fb1b70c7f0ac6dcefebd966.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.792ex; height:2.176ex;" alt="{\displaystyle {\mathcal {D}}}" loading="lazy"></span> zwei Kategorien, <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D}">

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<annotation encoding="application/x-tex">{\displaystyle D}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/f34a0c600395e5d4345287e21fb26efd386990e6.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.924ex; height:2.176ex;" alt="{\displaystyle D}" loading="lazy"></span> sei ein Objekt in <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {D}}}">

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<annotation encoding="application/x-tex">{\displaystyle {\mathcal {D}}}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/3277962e1959c3241fb1b70c7f0ac6dcefebd966.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.792ex; height:2.176ex;" alt="{\displaystyle {\mathcal {D}}}" loading="lazy"></span>.

Die Zuordnungen

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<ul><li>Objekt aus <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {C}}\quad \mapsto \quad D}">

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<annotation encoding="application/x-tex">{\displaystyle {\mathcal {C}}\quad \mapsto \quad D}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/56413f2f1f358d35531db941254f75093fefa361.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:11.423ex; height:2.176ex;" alt="{\displaystyle {\mathcal {C}}\quad \mapsto \quad D}" loading="lazy"></span></li>

<li>Morphismus aus <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {C}}\quad \mapsto \quad 1_{D}}">

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<annotation encoding="application/x-tex">{\displaystyle {\mathcal {C}}\quad \mapsto \quad 1_{D}}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/72d5876b819541dd376a6791799609eacd4277f2.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.254ex; height:2.509ex;" alt="{\displaystyle {\mathcal {C}}\quad \mapsto \quad 1_{D}}" loading="lazy"></span></li></ul>

<p>bilden einen Funktor <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {C}}\rightarrow {\mathcal {D}}}">

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<annotation encoding="application/x-tex">{\displaystyle {\mathcal {C}}\rightarrow {\mathcal {D}}}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/e7092a67959086d75e18e842817bf90d41fbf987.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.645ex; height:2.176ex;" alt="{\displaystyle {\mathcal {C}}\rightarrow {\mathcal {D}}}" loading="lazy"></span>.

Man nennt diesen den konstanten Funktor mit Wert <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D}">

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<annotation encoding="application/x-tex">{\displaystyle D}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/f34a0c600395e5d4345287e21fb26efd386990e6.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.924ex; height:2.176ex;" alt="{\displaystyle D}" loading="lazy"></span> und bezeichnet ihn oft auch mit <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D}">

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<annotation encoding="application/x-tex">{\displaystyle D}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/f34a0c600395e5d4345287e21fb26efd386990e6.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.924ex; height:2.176ex;" alt="{\displaystyle D}" loading="lazy"></span>.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup>

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<div class="mw-heading mw-heading2"><h2 id="Bemerkungen">Bemerkungen</h2></div>

<ul><li>Dass es sich bei diesen Zuordnungen um einen Funktor handelt, ergibt sich direkt aus <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1_{D}\circ 1_{D}=1_{D}}">

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<annotation encoding="application/x-tex">{\displaystyle 1_{D}\circ 1_{D}=1_{D}}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/5decfa43ecd3eb5ca9dd72eaaedbeeecd39d96f8.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.559ex; height:2.509ex;" alt="{\displaystyle 1_{D}\circ 1_{D}=1_{D}}" loading="lazy"></span>.</li>

<li><a href="Kegel_(Kategorientheorie)" title="Kegel (Kategorientheorie)">Kegel und Kokegel</a> sind <a href="Nat%C3%BCrliche_Transformation" title="Natürliche Transformation">natürliche Transformationen</a> zwischen Funktoren auf <a href="Kleine_Kategorie" class="mw-redirect" title="Kleine Kategorie">kleinen Kategorien</a> konstanten Funktoren.</li></ul>

<div class="mw-heading mw-heading2"><h2 id="Der_Funktor_der_konstanten_Funktoren">Der Funktor der konstanten Funktoren</h2></div>

<p>Seien <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {C}}}">

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<annotation encoding="application/x-tex">{\displaystyle {\mathcal {C}}}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/e7b3edab7022ca9e2976651bc59c489513ee9019.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.239ex; height:2.176ex;" alt="{\displaystyle {\mathcal {C}}}" loading="lazy"></span> und <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {D}}}">

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<annotation encoding="application/x-tex">{\displaystyle {\mathcal {D}}}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/3277962e1959c3241fb1b70c7f0ac6dcefebd966.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.792ex; height:2.176ex;" alt="{\displaystyle {\mathcal {D}}}" loading="lazy"></span> zwei Kategorien, <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D_{1}}">

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<annotation encoding="application/x-tex">{\displaystyle D_{1}}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/e7714158afb63a98e7dbc6e885f70d9141c6923a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.979ex; height:2.509ex;" alt="{\displaystyle D_{1}}" loading="lazy"></span> und <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D_{2}}">

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<annotation encoding="application/x-tex">{\displaystyle D_{2}}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/41b3839c40bd06e3dfea10798dfab41a905af256.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.979ex; height:2.509ex;" alt="{\displaystyle D_{2}}" loading="lazy"></span> Objekte aus <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {D}}}">

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<annotation encoding="application/x-tex">{\displaystyle {\mathcal {D}}}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/3277962e1959c3241fb1b70c7f0ac6dcefebd966.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.792ex; height:2.176ex;" alt="{\displaystyle {\mathcal {D}}}" loading="lazy"></span>, die auch die durch sie gegebenen konstanten Funktoren bezeichnen.

Ist <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f\in \mathrm {Hom} _{\mathcal {D}}(D_{1},D_{2})}">

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<annotation encoding="application/x-tex">{\displaystyle f\in \mathrm {Hom} _{\mathcal {D}}(D_{1},D_{2})}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/40f916ffa51947050a7988c8003c0b850de2f82d.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:19.26ex; height:2.843ex;" alt="{\displaystyle f\in \mathrm {Hom} _{\mathcal {D}}(D_{1},D_{2})}" loading="lazy"></span> und <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha _{f}:=(\alpha _{C})_{C\in {\mathcal {C}}}}">

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<annotation encoding="application/x-tex">{\displaystyle \alpha _{f}:=(\alpha _{C})_{C\in {\mathcal {C}}}}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/7ebe08289ee69a03d699e4bd355670121ad34253.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:14.601ex; height:3.009ex;" alt="{\displaystyle \alpha _{f}:=(\alpha _{C})_{C\in {\mathcal {C}}}}" loading="lazy"></span> definiert durch <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha _{C}=f}">

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<annotation encoding="application/x-tex">{\displaystyle \alpha _{C}=f}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/9974c6f43a720faeb0e742e9d9539879f3a46aad.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.346ex; height:2.509ex;" alt="{\displaystyle \alpha _{C}=f}" loading="lazy"></span> für alle Objekte <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C\in {\mathcal {C}}}">

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<annotation encoding="application/x-tex">{\displaystyle C\in {\mathcal {C}}}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/c472ed9c4e8e46f94dcfc8a0c25f1bfb73f561ab.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.846ex; height:2.176ex;" alt="{\displaystyle C\in {\mathcal {C}}}" loading="lazy"></span>, so ist <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha _{f}}">

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<annotation encoding="application/x-tex">{\displaystyle \alpha _{f}}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/06946868f504d8dc48bce72a3e25b3e869fd3465.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.624ex; height:2.343ex;" alt="{\displaystyle \alpha _{f}}" loading="lazy"></span> eine natürliche Transformation <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D_{1}\rightarrow D_{2}}">

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<annotation encoding="application/x-tex">{\displaystyle D_{1}\rightarrow D_{2}}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/6a70f7741c54c5030cd05a0d70a4b934d63895b6.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.571ex; height:2.509ex;" alt="{\displaystyle D_{1}\rightarrow D_{2}}" loading="lazy"></span> zwischen den konstanten Funktoren.

Auf diese Weise erhält man einen Funktor <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle K_{{\mathcal {C}},{\mathcal {D}}}\colon {\mathcal {D}}\rightarrow {\mathcal {D}}^{\mathcal {C}}}">

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<annotation encoding="application/x-tex">{\displaystyle K_{{\mathcal {C}},{\mathcal {D}}}\colon {\mathcal {D}}\rightarrow {\mathcal {D}}^{\mathcal {C}}}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/164da528c65818260de3d0807b8a632a4991a8cc.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:14.146ex; height:3.343ex;" alt="{\displaystyle K_{{\mathcal {C}},{\mathcal {D}}}\colon {\mathcal {D}}\rightarrow {\mathcal {D}}^{\mathcal {C}}}" loading="lazy"></span> von <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {D}}}">

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<annotation encoding="application/x-tex">{\displaystyle {\mathcal {D}}}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/3277962e1959c3241fb1b70c7f0ac6dcefebd966.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.792ex; height:2.176ex;" alt="{\displaystyle {\mathcal {D}}}" loading="lazy"></span> in die <a href="Funktorkategorie" title="Funktorkategorie">Funktorkategorie</a> <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {D}}^{\mathcal {C}}}">

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<annotation encoding="application/x-tex">{\displaystyle {\mathcal {D}}^{\mathcal {C}}}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/756e35259944db0792a0ce5637c8f27b52f9799d.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.9ex; height:2.676ex;" alt="{\displaystyle {\mathcal {D}}^{\mathcal {C}}}" loading="lazy"></span>, der jedes Objekt <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D}">

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<annotation encoding="application/x-tex">{\displaystyle D}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/f34a0c600395e5d4345287e21fb26efd386990e6.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.924ex; height:2.176ex;" alt="{\displaystyle D}" loading="lazy"></span> auf den zugehörigen konstanten Funktor abbildet.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup>

Der Funktor <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle K_{{\mathcal {C}},{\mathcal {D}}}}">

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<annotation encoding="application/x-tex">{\displaystyle K_{{\mathcal {C}},{\mathcal {D}}}}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/c43a485ffca726da65db93163792165b98fcba92.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.806ex; height:2.843ex;" alt="{\displaystyle K_{{\mathcal {C}},{\mathcal {D}}}}" loading="lazy"></span> erhält sowohl <a href="Limes_(Kategorientheorie)" title="Limes (Kategorientheorie)">Limites</a> als auch <a href="Kolimes" title="Kolimes">Kolimites</a>.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup>

</p><p>Ist <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {C}}}">

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle {\mathcal {C}}}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/e7b3edab7022ca9e2976651bc59c489513ee9019.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.239ex; height:2.176ex;" alt="{\displaystyle {\mathcal {C}}}" loading="lazy"></span> eine kleine Kategorie und existieren in <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {D}}}">

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle {\mathcal {D}}}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/3277962e1959c3241fb1b70c7f0ac6dcefebd966.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.792ex; height:2.176ex;" alt="{\displaystyle {\mathcal {D}}}" loading="lazy"></span> alle Limites mit Indexkategorie <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {C}}}">

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle {\mathcal {C}}}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/e7b3edab7022ca9e2976651bc59c489513ee9019.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.239ex; height:2.176ex;" alt="{\displaystyle {\mathcal {C}}}" loading="lazy"></span>, so hat man eine <a href="Adjunktion_(Kategorientheorie)" title="Adjunktion (Kategorientheorie)">Adjunktion</a> <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle K_{{\mathcal {C}},{\mathcal {D}}}\dashv \lim _{\leftarrow {\mathcal {C}}}}">

<msub>

</mrow>

</mrow>

</msub>

</mrow>

</munder>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle K_{{\mathcal {C}},{\mathcal {D}}}\dashv \lim _{\leftarrow {\mathcal {C}}}}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/6a4d66188b32a5e8d2d0f55fe6799bc490f4407c.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:10.746ex; height:3.843ex;" alt="{\displaystyle K_{{\mathcal {C}},{\mathcal {D}}}\dashv \lim _{\leftarrow {\mathcal {C}}}}" loading="lazy"></span>.

Dabei bezeichnet <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lim _{\leftarrow {\mathcal {C}}}}">

</mrow>

</munder>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \lim _{\leftarrow {\mathcal {C}}}}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/589be7272db9ed35e6bf6dccc528691b82c7e219.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:3.23ex; height:3.843ex;" alt="{\displaystyle \lim _{\leftarrow {\mathcal {C}}}}" loading="lazy"></span> einen durch Wahlen von Limes-Objekten gebildeten Funktor <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {D}}^{\mathcal {C}}\rightarrow {\mathcal {D}}}">

<msup>

</mrow>

</mrow>

</msup>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle {\mathcal {D}}^{\mathcal {C}}\rightarrow {\mathcal {D}}}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/de6ecc90d389867de761d6c1a474e1e16285786f.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.306ex; height:2.676ex;" alt="{\displaystyle {\mathcal {D}}^{\mathcal {C}}\rightarrow {\mathcal {D}}}" loading="lazy"></span>.

</p><p>Ist <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {C}}}">

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle {\mathcal {C}}}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/e7b3edab7022ca9e2976651bc59c489513ee9019.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.239ex; height:2.176ex;" alt="{\displaystyle {\mathcal {C}}}" loading="lazy"></span> eine kleine Kategorie und existieren in <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {D}}}">

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle {\mathcal {D}}}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/3277962e1959c3241fb1b70c7f0ac6dcefebd966.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.792ex; height:2.176ex;" alt="{\displaystyle {\mathcal {D}}}" loading="lazy"></span> alle Kolimites mit Indexkategorie <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {C}}}">

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle {\mathcal {C}}}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/e7b3edab7022ca9e2976651bc59c489513ee9019.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.239ex; height:2.176ex;" alt="{\displaystyle {\mathcal {C}}}" loading="lazy"></span>, so hat man eine Adjunktion <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lim _{\rightarrow {\mathcal {C}}}\dashv K_{{\mathcal {C}},{\mathcal {D}}}}">

</mrow>

</munder>

<msub>

</mrow>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \lim _{\rightarrow {\mathcal {C}}}\dashv K_{{\mathcal {C}},{\mathcal {D}}}}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/0563a142587f137dd71c7e5f34d15f8035782d2b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:10.746ex; height:3.843ex;" alt="{\displaystyle \lim _{\rightarrow {\mathcal {C}}}\dashv K_{{\mathcal {C}},{\mathcal {D}}}}" loading="lazy"></span>.

Dabei bezeichnet <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lim _{{\mathcal {C}}\rightarrow }}">

</mrow>

</mrow>

</munder>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \lim _{{\mathcal {C}}\rightarrow }}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/306ad7dba88892f5ac0450ce891249a8b2ffa928.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:3.23ex; height:3.843ex;" alt="{\displaystyle \lim _{{\mathcal {C}}\rightarrow }}" loading="lazy"></span> einen durch Wahlen von Kolimes-Objekten gebildeten Funktor <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {D}}^{\mathcal {C}}\rightarrow {\mathcal {D}}}">

<msup>

</mrow>

</mrow>

</msup>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle {\mathcal {D}}^{\mathcal {C}}\rightarrow {\mathcal {D}}}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/de6ecc90d389867de761d6c1a474e1e16285786f.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.306ex; height:2.676ex;" alt="{\displaystyle {\mathcal {D}}^{\mathcal {C}}\rightarrow {\mathcal {D}}}" loading="lazy"></span>.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup>

</p><p>Trifft beides zu, erhält man die leicht einprägsame Formel (die Pfeile unter dem Limeszeichen in nachstehender Formel zeigen zur Mitte):

</p>

</mrow>

</mrow>

</munder>

<msub>

</mrow>

</mrow>

</msub>

</mrow>

</munder>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \lim _{{\mathcal {C}}\rightarrow }\dashv K_{{\mathcal {C}},{\mathcal {D}}}\dashv \lim _{\leftarrow {\mathcal {C}}}}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/e799e2d2e84f327786f6d1e58d0018fd6313e05a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:16.686ex; height:3.843ex;" alt="{\displaystyle \lim _{{\mathcal {C}}\rightarrow }\dashv K_{{\mathcal {C}},{\mathcal {D}}}\dashv \lim _{\leftarrow {\mathcal {C}}}}" loading="lazy"></span>.</dd></dl>

<div class="mw-heading mw-heading2"><h2 id="Einzelnachweise">Einzelnachweise</h2></div>

<li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text">Emily Riehl: <cite style="font-style:italic">Category Theory in Context</cite>. AMS Dover Publications, 2016, ISBN 978-0-486-80903-8, <span style="white-space:nowrap">Definition 3.1.1, S. 74</span>.<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rfr_id=info:sid/de.wikipedia.org:Konstanter+Funktor&rft.au=Emily+Riehl&rft.btitle=Category+Theory+in+Context&rft.date=2016&rft.genre=book&rft.isbn=9780486809038&rft.pub=AMS+Dover+Publications" style="display:none"> </span></span>

</li>

<li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text">Martin Brandenburg: <cite style="font-style:italic">Einführung in die Kategorientheorie</cite>. Springer, 2016, ISBN 978-3-662-53520-2, <span style="white-space:nowrap">Beispiel 3.2.21 2.</span>.<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rfr_id=info:sid/de.wikipedia.org:Konstanter+Funktor&rft.au=Martin+Brandenburg&rft.btitle=Einf%C3%BChrung+in+die+Kategorientheorie&rft.date=2016&rft.genre=book&rft.isbn=9783662535202&rft.pub=Springer" style="display:none"> </span></span>

</li>

<li id="cite_note-3"><span class="mw-cite-backlink"><a href="#cite_ref-3">↑</a></span> <span class="reference-text">Horst Herrlich, George E. Strecker: <cite style="font-style:italic">Category Theory</cite>. Allyn and Bacon Inc., 1972, ISBN 3-540-05634-3, <span style="white-space:nowrap">Beispiel 9.2 (4)</span>.<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rfr_id=info:sid/de.wikipedia.org:Konstanter+Funktor&rft.au=Horst+Herrlich%2C+George+E.+Strecker&rft.btitle=Category+Theory&rft.date=1972&rft.genre=book&rft.isbn=3540056343&rft.pub=Allyn+and+Bacon+Inc." style="display:none"> </span></span>

</li>

<li id="cite_note-4"><span class="mw-cite-backlink"><a href="#cite_ref-4">↑</a></span> <span class="reference-text">Horst Herrlich, George E. Strecker: <cite style="font-style:italic">Category Theory</cite>. Allyn and Bacon Inc., 1972, ISBN 3-540-05634-3, <span style="white-space:nowrap">15.8, S. 97</span>.<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rfr_id=info:sid/de.wikipedia.org:Konstanter+Funktor&rft.au=Horst+Herrlich%2C+George+E.+Strecker&rft.btitle=Category+Theory&rft.date=1972&rft.genre=book&rft.isbn=3540056343&rft.pub=Allyn+and+Bacon+Inc." style="display:none"> </span></span>

</li>

<li id="cite_note-5"><span class="mw-cite-backlink"><a href="#cite_ref-5">↑</a></span> <span class="reference-text">Horst Herrlich, George E. Strecker: <cite style="font-style:italic">Category Theory</cite>. Allyn and Bacon Inc., 1972, ISBN 3-540-05634-3, <span style="white-space:nowrap">Beispiel 24.4 (9), S. 168</span>.<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rfr_id=info:sid/de.wikipedia.org:Konstanter+Funktor&rft.au=Horst+Herrlich%2C+George+E.+Strecker&rft.btitle=Category+Theory&rft.date=1972&rft.genre=book&rft.isbn=3540056343&rft.pub=Allyn+and+Bacon+Inc." style="display:none"> </span></span>

</li>

<li id="cite_note-6"><span class="mw-cite-backlink"><a href="#cite_ref-6">↑</a></span> <span class="reference-text">Horst Herrlich, George E. Strecker: <cite style="font-style:italic">Category Theory</cite>. Allyn and Bacon Inc., 1972, ISBN 3-540-05634-3, <span style="white-space:nowrap">25.7, S. 199</span>.<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rfr_id=info:sid/de.wikipedia.org:Konstanter+Funktor&rft.au=Horst+Herrlich%2C+George+E.+Strecker&rft.btitle=Category+Theory&rft.date=1972&rft.genre=book&rft.isbn=3540056343&rft.pub=Allyn+and+Bacon+Inc." style="display:none"> </span></span>

</li>

</ol>

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<div class="klappleiste-kopf"><a href="Kategorientheorie" title="Kategorientheorie">Kategorientheorie</a><div class="erweiterte-navigationsleiste-quicklinks" style="float:left; font-weight:normal; font-size:75%; margin-left:1em; margin-right:2em; display:none;"><span title="Vorlage anzeigen">V</span> </div></div>

<td class="erw-nav-gruppe" style="white-space: nowrap;text-align: right;border: 1px solid transparent;border-top: 1px solid #FFF;border-bottom: 2px solid #FFF;padding: 0 1em;"><b>Einordnung</b>

</td>

<td class="erw-nav-gruppe" style="white-space: nowrap;text-align: right;border: 1px solid transparent;border-top: 1px solid #FFF;border-bottom: 2px solid #FFF;padding: 0 1em;"><b>Typen von Kategorien</b>

</td>

<p><a href="Duale_Kategorie" title="Duale Kategorie">dual</a> | <a href="Diskrete_Kategorie" title="Diskrete Kategorie">diskret</a> | <a href="Kleine_Kategorie" class="mw-redirect" title="Kleine Kategorie">klein</a> | <a href="Lokal_kleine_Kategorie" title="Lokal kleine Kategorie">lokal klein</a> | <a href="Monoidale_Kategorie" title="Monoidale Kategorie">monoidal</a> | <a href="Symmetrische_monoidale_Kategorie" title="Symmetrische monoidale Kategorie">symmetrisch monoidal</a> | <a href="Angereicherte_Kategorie" title="Angereicherte Kategorie">angereichert</a> | <a href="Ausgeglichene_Kategorie" title="Ausgeglichene Kategorie">ausgeglichen</a> | <a href="Erreichbare_Kategorie" title="Erreichbare Kategorie">erreichbar</a> | <a href="Vollst%C3%A4ndige_Kategorie" title="Vollständige Kategorie">vollständig</a> | <a href="Kovollst%C3%A4ndige_Kategorie" class="mw-redirect" title="Kovollständige Kategorie">kovollständig</a>

</p>

</td></tr>

<tr>

<td class="erw-nav-gruppe" style="white-space: nowrap;text-align: right;border: 1px solid transparent;border-top: 1px solid #FFF;border-bottom: 2px solid #FFF;padding: 0 1em;"><b>Typen von Objekten</b>

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<p><a href="Anfangsobjekt%2C_Endobjekt_und_Nullobjekt" title="Anfangsobjekt, Endobjekt und Nullobjekt">initial</a> | <a href="Anfangsobjekt%2C_Endobjekt_und_Nullobjekt" title="Anfangsobjekt, Endobjekt und Nullobjekt">terminal</a> | <a href="Anfangsobjekt%2C_Endobjekt_und_Nullobjekt" title="Anfangsobjekt, Endobjekt und Nullobjekt">null</a> | <a href="Injektives_Objekt" title="Injektives Objekt">injektiv</a> | <a href="Projektives_Objekt" title="Projektives Objekt">projektiv</a> | <a href="Generator_und_Kogenerator" title="Generator und Kogenerator">Generator</a> | <a href="Kogenerator" class="mw-redirect" title="Kogenerator">Kogenerator</a> | <a href="Ind-Objekte_und_Pro-Objekte" title="Ind-Objekte und Pro-Objekte">Pro</a> | <a href="Ind-Objekte_und_Pro-Objekte" title="Ind-Objekte und Pro-Objekte">Ind</a> | <a href="Gruppenobjekt" title="Gruppenobjekt">Gruppe</a> | <a href="Monoid-Objekt" title="Monoid-Objekt">Monoid</a> | <a href="Exponentiales_Objekt" title="Exponentiales Objekt">exponential</a> | <a href="Freies_Objekt" title="Freies Objekt">frei</a> | <a href="Kompaktes_Objekt" title="Kompaktes Objekt">kompakt</a>

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<td class="erw-nav-gruppe" style="white-space: nowrap;text-align: right;border: 1px solid transparent;border-top: 1px solid #FFF;border-bottom: 2px solid #FFF;padding: 0 1em;"><b>Typen von Morphismen</b>

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<p><a href="Monomorphismus" title="Monomorphismus">Mono</a> | <a href="Epimorphismus" title="Epimorphismus">Epi</a> | <a href="Bimorphismus" title="Bimorphismus">Bi</a> | <a href="Retraktion_und_Koretraktion" title="Retraktion und Koretraktion">Retraktion</a> | <a href="Koretraktion" class="mw-redirect" title="Koretraktion">Koretraktion</a> | <a href="Injektive_Aufl%C3%B6sung" title="Injektive Auflösung">Injektive Auflösung</a> | <a href="Projektive_Aufl%C3%B6sung" title="Projektive Auflösung">Projektive Auflösung</a>

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<td class="erw-nav-gruppe" style="white-space: nowrap;text-align: right;border: 1px solid transparent;border-top: 1px solid #FFF;border-bottom: 1px solid #FFF;padding: 0 1em;"><b>Typen von Funktoren</b>

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<p><a class="mw-selflink selflink">konstant</a> | <a href="Voller_Funktor" class="mw-redirect" title="Voller Funktor">voll</a> | <a href="Treuer_Funktor" title="Treuer Funktor">treu</a> | <a href="Volltreuer_Funktor" class="mw-redirect" title="Volltreuer Funktor">volltreu</a> | <a href="Additiver_Funktor" title="Additiver Funktor">additiv</a> | <a href="Exakter_Funktor" title="Exakter Funktor">exakt</a> | <a href="Abgeleiteter_Funktor" title="Abgeleiteter Funktor">abgeleitet</a> | <a href="Glatter_Funktor" title="Glatter Funktor">glatt</a>

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<td class="erw-nav-gruppe" style="white-space: nowrap;text-align: right;border: 1px solid transparent;border-top: 1px solid #FFF;border-bottom: 2px solid #FFF;padding: 0 1em;"><b>Konstruktionen</b>

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<td class="erw-nav-gruppe" style="white-space: nowrap;text-align: right;border: 1px solid transparent;border-top: 1px solid #FFF;border-bottom: 2px solid #FFF;padding: 0 1em;"><b><a href="Limes_(Kategorientheorie)" title="Limes (Kategorientheorie)">Limes</a></b>

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<p><a href="Produkt_und_Koprodukt" title="Produkt und Koprodukt">Produkt</a> | <a href="Differenzkern" title="Differenzkern">Differenzkern</a> | <a href="Faserprodukt" title="Faserprodukt">Faserprodukt</a> | <a href="Ende_(Kategorientheorie)" title="Ende (Kategorientheorie)">Ende</a>

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<td class="erw-nav-gruppe" style="white-space: nowrap;text-align: right;border: 1px solid transparent;border-top: 1px solid #FFF;border-bottom: 1px solid #FFF;padding: 0 1em;"><b><a href="Kolimes" title="Kolimes">Kolimes</a></b>

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<p><a href="Filtrierter_Kolimes" title="Filtrierter Kolimes">Filtrierter Kolimes</a> | <a href="Koprodukt" class="mw-redirect" title="Koprodukt">Koprodukt</a> | <a href="Differenzkokern" title="Differenzkokern">Differenzkokern</a> | <a href="Kofaserprodukt" class="mw-redirect" title="Kofaserprodukt">Kofaserprodukt</a>

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</tbody></table>

<p><a href="Kan-Erweiterung" title="Kan-Erweiterung">Kan-Erweiterung</a> | <a href="Monade_(Kategorientheorie)" title="Monade (Kategorientheorie)">Monade</a> | <a href="Komonade" title="Komonade">Komonade</a> | <a href="Kategorie_der_Elemente" title="Kategorie der Elemente">Kategorie der Elemente</a> | <a href="Kommakategorie" title="Kommakategorie">Kommakategorie</a> | <a href="Pfeilkategorie" title="Pfeilkategorie">Pfeilkategorie</a> | <a href="Homotopie-Kategorie" title="Homotopie-Kategorie">Homotopie-Kategorie</a>

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<td class="erw-nav-gruppe" style="white-space: nowrap;text-align: right;border: 1px solid transparent;border-top: 1px solid #FFF;border-bottom: 2px solid #FFF;padding: 0 1em;"><b>Resultate</b>

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<p><a href="Lemma_von_Yoneda" title="Lemma von Yoneda">Lemma von Yoneda</a> | <a href="Fixpunktsatz_von_Lawvere" title="Fixpunktsatz von Lawvere">Fixpunktsatz von Lawvere</a> | <a href="Einbettungssatz_von_Mitchell" title="Einbettungssatz von Mitchell">Einbettungssatz von Mitchell</a>

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<td class="erw-nav-gruppe" style="white-space: nowrap;text-align: right;border: 1px solid transparent;border-top: 1px solid #FFF;border-bottom: 1px solid #FFF;padding: 0 1em;"><b>Spezielle Funktoren</b>

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<p><a href="Hom-Funktor" title="Hom-Funktor">Hom-Funktor</a> | <a href="Potenzmengenfunktor" title="Potenzmengenfunktor">Potenzmengenfunktor</a> | <a href="Diagonalfunktor" title="Diagonalfunktor">Diagonalfunktor</a> | <a href="Ext-Funktor" class="mw-redirect" title="Ext-Funktor">Ext</a> | <a href="Tor-Funktor" class="mw-redirect" title="Tor-Funktor">Tor</a>

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