From 0d8cd2eeaeec98eee28a2f6050a3030c641e0132 Mon Sep 17 00:00:00 2001 From: CDaut Date: Sun, 16 Oct 2022 21:57:39 +0200 Subject: [PATCH] Kokern Definition --- chapters/Kegel_und_Ko.tex | 33 ++++++++++++++++++++++++++++++++- main.pdf | Bin 317486 -> 319038 bytes 2 files changed, 32 insertions(+), 1 deletion(-) diff --git a/chapters/Kegel_und_Ko.tex b/chapters/Kegel_und_Ko.tex index d3fa26d..4093ac4 100644 --- a/chapters/Kegel_und_Ko.tex +++ b/chapters/Kegel_und_Ko.tex @@ -582,7 +582,7 @@ aussehen können. $0_{A,B}\in\mor{\mathscr{C}}{A}{B}$ ist dabei so definiert, dass für jeden Morphismus $f\in\mor{\mathscr{C}}{A}{B}$ $0_{A,B}+f=f=f+0_{A,B}$ gilt. Nicht in jeder Kategorie existiert solch eine Abbildung.\\ - Gesucht ist also ein Kegel $K$ und eine Abbildung $\iota$, sodass folgendes Diagramm + Gesucht ist also ein Limes $K$ und eine Abbildung $\iota$, sodass folgendes Diagramm kommutiert und $0\circ\iota=f\circ\iota$ gilt:\\ \begin{figure}[h] \begin{center} @@ -625,4 +625,35 @@ aussehen können. \end{tikzpicture} \end{center} Wobei $Kern(f):=\{v\in V|f(v)=0\}$ und $\varphi(t)=g(t)$ +\end{example} +\begin{example}{Kokern\\} + Ein Kokern ist der Kolimes über dem Diagramm + \begin{tikzpicture}[baseline=-1mm] + \node (L) at (0,0){$\bullet$}; + \node (R) at (1,0){$\bullet$}; + + \draw + (L) edge node[above]{$0$} (R) + (L) edge[bend right] (R) + ; + \end{tikzpicture}. Gesucht ist also ein Kolimes, sodass folgendes Diagramm kommutiert: + \begin{figure}[h] + \begin{center} + \begin{tikzpicture} + \node (L) at (0,0){$\bullet$}; + \node (R) at (2,0){$\bullet$}; + \node[red] (KK) at (4,0){$\bullet$}; + \node[blue] (Keg) at (4,1.5){$\bullet$}; + + \draw + (L) edge node[above]{$0$} (R) + (L) edge[bend right] node[below]{$f$} (R) + (R) edge[red] (KK) + (R) edge[blue] node[above]{$g$} (Keg) + (KK) edge[dotted] (Keg) + ; + \end{tikzpicture} + \end{center} + \caption{Das Kommutative Diagramm für einen Kokern} + \end{figure} \end{example} \ No newline at end of file diff --git a/main.pdf b/main.pdf index 76280708b21b54c6b68793eb29e29d4d419c87ad..a3f520773303978204ae7792876e56d4f61e7f4d 100644 GIT binary patch delta 11805 zcmZ3tL3rOD;SJ{*SxWa=dr!X17+L?e)z_|nnO;?(*-x|XNjrLvF$RA-WGmV;UrEUD zWTU@?&?5bYH_a^^Jk#X_4OTr~qTw6up20cMRKovG#Dx22*|X*Dv$gDYxK~ z+^an&FYnU0t+>HMH1xm6dc~*e_ll?fIQ*t>`TU(PlM)jpa4Be1pYH71$=^@NDu}|4qZVeaELi4l6VnMN}G| 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