Anfang Kolimes Kokegel Koprodukt
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@ -260,4 +260,27 @@ aussehen können.
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$\Rightarrow\varphi\circ\tilde{\varphi}=id_L$\\
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Analog: $\tilde{\varphi}\circ\varphi=id_{\tilde{L}}$
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\qed
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\end{lemma}
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\end{lemma}
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\subsection{Kokegel, Kolimes und Koprodukt}
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\begin{definition}{Kokegel \& Kolimes\\}
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Sei $D:I\mapsto\mathscr{C}$ ein Diagramm.\\
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Kokegel:
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\begin{tikzpicture}[baseline=5mm]
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\node[blue] (K) at (0, 0){$K$};
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\node (P1) at (-1, 1){$\cdot$};
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\node (P2) at (1, 1){$\cdot$};
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\node (center) at (0,1){};
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\draw
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(P1) edge (P2)
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(P1) edge[blue] (K)
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(P2) edge[blue] (K)
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;
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\draw (center) ellipse (1.25 and 0.25);
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\end{tikzpicture}
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Ein Objekt $K$ aus $\mathscr{C}$, sodass von jedem Objekt aus $\mathscr{C}$
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Morphismen auf $K$ existieren und alle Dreiecke kommutieren.\\
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Ein Kolimes ist ein universeller Kokegel:
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\end{definition}
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