From 86080775224b75d052caca96ec22aaea2d8110c7 Mon Sep 17 00:00:00 2001 From: CDaut Date: Wed, 2 Nov 2022 12:36:41 +0100 Subject: [PATCH] mehr Beispiele zu Adjunktion --- chapters/nat_trafo.tex | 20 ++++++++++++++++++++ chapters/yoneda.tex | 0 main.pdf | Bin 352824 -> 354282 bytes 3 files changed, 20 insertions(+) create mode 100644 chapters/yoneda.tex diff --git a/chapters/nat_trafo.tex b/chapters/nat_trafo.tex index dcfdd5e..3e9478e 100644 --- a/chapters/nat_trafo.tex +++ b/chapters/nat_trafo.tex @@ -116,4 +116,24 @@ Funktoren.\\ Eine Adjunktion von $\mathcal{F}$ und $\mathcal{G}$ ist ein natürlicher Isomorphismus von\\ $\mor{\mathscr{D}}{\mathcal{F}(\_)}{\_}\mapsto\mor{\mathscr{C}}{\_}{\mathcal{G}(\_)}$. \end{definition} +\begin{example}{\glqq currying''\\} + Sei $V$ ein $\mathbb{K}$-VR. Die Funktoren $\mor{\mathbb{K}}{V}{\_}$ und $ \_\otimes V$ sind adjungiert.\\ + Es gilt also $\mor{\mathbb{K}}{W\otimes V}{X}\cong\mor{\mathbb{K}}{W}{\mor{\mathbb{K}}{V}{X}}$ + %TODO: Leonid fragen was das ist & besser erklären +\end{example} +\begin{example}{Weitere Beispiele\\} + % Keine Ahnung was das sein soll... + $\mathcal{F}: \cat{set}\mapsto\cat{K-VR}$\\ + $M\mapsto\mathcal{F}(M)$ freier VR und + $?: \cat{K-VR}\mapsto\cat{set}$\\ + $V\mapsto V$\\ + Dann sind $\mathcal{F}$ und $?$ adjungiert. Es gilt also + $\mor{\mathbb{K}}{\mathcal{F}(M)}{V}\cong\mor{\cat{set}}{M}{?(V)}$ mit + $\Phi\mapsto\Phi_M$ und $f\mapsto\left[\sum\lambda_m m\mapsto\sum\lambda_m f(m)\right]$ +\end{example} +\begin{example}{} + //Ausfüllen + %Verstehe das Beispiel nicht, kann es also nicht aufschreiben. +\end{example} +% Viele andere Beispiele, die Ich zu wenig verstehe um sie aufschreiben zu können... diff --git a/chapters/yoneda.tex b/chapters/yoneda.tex new file mode 100644 index 0000000..e69de29 diff --git a/main.pdf b/main.pdf index fb60d8bc53de85827f0ef8f347fccf0cbfa0b01a..559f6e060c306bbf05f726fda643eab444d90203 100644 GIT binary patch delta 39839 zcmdmSMD*2p(Fw{-W`@%pU0F5jTPNE3A2Hx*`~Hus|7^fyi}<~wFW;#+Y!BGT;Jjd` znRE1&*B^g-dRjC(Bz=-TUKeNm@B(9d?ZN+@*L@4OPG<91xOQ#BGmb@JD|jL%W#~9w zK9pSf|Jl4HTh}O^J*}wYdB

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