From 2b3cbd0d8361b9fa51c88750bb06ee8061e0028d Mon Sep 17 00:00:00 2001 From: CDaut Date: Sat, 15 Oct 2022 20:02:53 +0200 Subject: [PATCH] =?UTF-8?q?Kapitel=20=C3=BCber=20pullback=20angefangen?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- chapters/Kegel_und_Ko.tex | 40 ++++++++++++++++++++++++++++++++++++++ main.pdf | Bin 391303 -> 393492 bytes 2 files changed, 40 insertions(+) diff --git a/chapters/Kegel_und_Ko.tex b/chapters/Kegel_und_Ko.tex index ec90da6..9f52a18 100644 --- a/chapters/Kegel_und_Ko.tex +++ b/chapters/Kegel_und_Ko.tex @@ -410,3 +410,43 @@ aussehen können. \end{minipage} \end{center} \end{example} +\subsection{Pullback und Pushout} +\begin{definition}{Pullback\\} + Ein Pullback ist der Limes des Diagramms + \begin{tikzpicture}[baseline=0mm] + \node (A) at (0,0){$\cdot$}; + \node (B) at (1,0){$\cdot$}; + \node (C) at (1,1){$\cdot$}; + + \draw + (A) edge (B) + (C) edge (B) + ; + \end{tikzpicture} + also ein Limes $L$, sodass folgendes Diagramm kommutiert:\\ + \begin{figure}[h] + \begin{center} + \begin{tikzpicture} + \node (A) at (0,0){$\cdot$}; + \node (B) at (2,0){$\cdot$}; + \node (C) at (2,2){$\cdot$}; + \node[red] (L) at (0,2){$L$}; + \node[blue] (T) at (-1,3){$T$}; + + \draw + (A) edge (B) + (C) edge (B) + (L) edge[red] (A) + (L) edge[red] (C) + (T) edge[dotted] (L) + (T) edge[blue, bend right] (A) + (T) edge[blue, bend left] (C) + ; + \end{tikzpicture} + \end{center} + \caption{Das Kommutative Diagramm für einen Pullback} + \end{figure} +\end{definition} +\begin{example}{Pullback über der Kategorie \cat{K-VR}\\} + +\end{example} \ No newline at end of file diff --git a/main.pdf b/main.pdf index 2bfcfca8ede137f45b3dbfa9949c9bbc8ec33b9a..edc4412c53b9c54ab5f920c4f8d8fa3b9c1991ea 100644 GIT binary patch delta 24943 zcmZqwC_bf0VnYWblcnW!!Sk$|^>?S(`X4qBX#4(;tN)uo@_bqKxQQ98j4PeDbt#%C zZk?qTWM}o^b>XWeUzk~VLJpK%yZL?I=R2?z=&UxIW94Cr4s&ikp7ouJr!wK|mZJKj 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