From 61473d76b7fb4dd27f1c47aa76f8974de6428ad4 Mon Sep 17 00:00:00 2001 From: CDaut Date: Sun, 16 Oct 2022 00:38:27 +0200 Subject: [PATCH] =?UTF-8?q?Pushout=20=C3=BCber=20KVR?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- chapters/Kegel_und_Ko.tex | 30 ++++++++++++++++++++++++++++-- chapters/deckblatt.tex | 2 +- main.pdf | Bin 397194 -> 314065 bytes main.tex | 2 +- 4 files changed, 30 insertions(+), 4 deletions(-) diff --git a/chapters/Kegel_und_Ko.tex b/chapters/Kegel_und_Ko.tex index 126f515..46ab2ea 100644 --- a/chapters/Kegel_und_Ko.tex +++ b/chapters/Kegel_und_Ko.tex @@ -535,9 +535,35 @@ aussehen können. (W) edge[blue, bend left] (T) (P) edge[dotted] (T) ; - + \end{tikzpicture} \end{center} \caption{Das kommutative Diagramm für einen Pushout.} \end{figure} -\end{definition} \ No newline at end of file +\end{definition} +\begin{example}{Pushout über \cat{K-VR}\\} + Betrachte folgendes kommutatives Diagramm: + \begin{center} + \begin{tikzpicture} + \node (X) at (0,0){$X$}; + \node (V) at (0,-2){$V$}; + \node (W) at (2,0){$W$}; + \node[red] (P) at (2,-2){$V\coprod_X W$}; + \node[blue] (T) at (3,-3){$T$}; + + \draw + (X) edge node[left]{$f_V$} (V) + (X) edge node[above]{$f_W$}(W) + (V) edge[red] (P) + (W) edge[red] (P) + (V) edge[blue, bend right] node[below]{$g_V$} (T) + (W) edge[blue, bend left] node[right]{$g_W$}(T) + (P) edge[dotted] node[above]{$\varphi$} (T) + ; + + \end{tikzpicture} + \end{center} + Wobei $V\coprod_X W:=\{(v,w)\in V\times W\}_{/U}$ mit $U=\{(-f_V(x),f_W(x))|x\in X\}$\\ + $V\mapsto V\coprod_X W$ ist definiert als $v\mapsto [(v,0)]$ und\\ + $\varphi: V\coprod_X W\mapsto T$ ist definiert als $[(v,w)]\mapsto g_V(v)+g_W(w)$ +\end{example} \ No newline at end of file diff --git a/chapters/deckblatt.tex b/chapters/deckblatt.tex index 8b030cd..5e15d9e 100644 --- a/chapters/deckblatt.tex +++ b/chapters/deckblatt.tex @@ -5,7 +5,7 @@ \huge Eine Einführung in die Kategorientheorie\\ \vspace{15mm} \Large - Nach einem Vortrag von Leonid Grau am 26.09.2022\\ + Nach einem Vortrag von Leonid Grau vom 26.09.2022\\ \vspace{30mm} Fassung vom \today \end{center} diff --git a/main.pdf b/main.pdf index c882bf3c676ebef2f86ad82a7877529fb217ebb6..58a4e61c53e88895c7739b08fdb8165ff6ddc9db 100644 GIT binary patch delta 232036 zcmeC0FL80I@C0RMQwxR3f$AFdtrKni4;u)yegD@b{Z_HP_Mcbyl5Ii?5*-l>nicbs z7OH9Z{`_lkqlB^ZW!(Id^Tpd(OB52e3;nJcFLf0ZFL)P)~ zA>-;lAM{UI#!VD_Bk^1&Z>Pzb^9!YyOR(+B&l5V$$hl?OnM14AxHwB`EuPSGYD2xR zj1$|E5|5a>{?8YlUTg8>*0B%MQ{DyN-l!U16SVl!G%HK0=Dhe3Qx-@IGv7o*|vIg5jiG&cozF zkI&2OlzDT%CfMr?o$U2l$ zF0Z`iuTso^sY0&YwBnYX>F<`t3&_R)+Z4>wt9hkfGwH@W3C~AWkJHPGe76Uje7a}) 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