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authorNorbert Preining <norbert@preining.info>2019-09-02 13:46:59 +0900
committerNorbert Preining <norbert@preining.info>2019-09-02 13:46:59 +0900
commite0c6872cf40896c7be36b11dcc744620f10adf1d (patch)
tree60335e10d2f4354b0674ec22d7b53f0f8abee672 /info/examples/Math/10-01-4.ltxps
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+%%
+%% Ein Beispiel der DANTE-Edition
+%% Mathematiksatz mit LaTeX
+%% 2. Auflage
+%%
+%% Beispiel 10-01-4 auf Seite 213.
+%%
+%% Copyright (C) 2012 Herbert Voss
+%%
+%% It may be distributed and/or modified under the conditions
+%% of the LaTeX Project Public License, either version 1.3
+%% of this license or (at your option) any later version.
+%%
+%% See http://www.latex-project.org/lppl.txt for details.
+%%
+%%
+%% ====
+% Show page(s) 1
+%%
+%%
+\documentclass[]{exaarticle}
+\pagestyle{empty}
+\setlength\textwidth{352.81416pt}
+\usepackage[utf8]{inputenc}
+\AtBeginDocument{\setlength\parindent{0pt}}
+\StartShownPreambleCommands
+\usepackage{amsmath,amssymb,pst-node} \DeclareMathOperator{\Hom}{Hom}
+\DeclareMathOperator{\Mod}{Mod} \DeclareMathOperator{\obj}{obj}
+\StopShownPreambleCommands
+\begin{document}
+Seien $\mathcal{C}:=\mathcal{D}:=\Mod_A$, $M\in \obj(\Mod_A)$ fixiert,
+\begin{align*}
+ F:=\square\otimes_A M : \Mod_A &\rightarrow \Mod_A, \\
+ G:=\Hom_A(M,\square) : \Mod_A &\rightarrow \Mod_A.
+\end{align*}
+Diese beiden Funktoren sind adjungiert, mittels
+$h(X,Y)(\phi)(x)(m)\rightarrow\phi(x\otimes m)$:\\[10pt]
+$\begin{psmatrix}[colsep=-0.3cm, rowsep=0pt]
+ \quad\phi{\;} & & {\;} h(X,Y)(\phi)\quad\\
+ \Hom_A(M \otimes_A X, Y) & & \Hom_A(X, \Hom_A(M, Y)) \\[1.5cm]
+ & L_A^2(M, X; Y)
+\end{psmatrix}$
+\ncline{|->}{1,1}{1,3}
+\ncline[doubleline=true]{2,1}{2,3}\nbput{h(X,Y)}
+\naput[nrot=:U,labelsep=0pt]{$\sim$}
+\ncline[doubleline=true]{2,1}{3,2}\naput[nrot=:U,labelsep=0pt]{$\sim$}
+\ncline[doubleline=true]{3,2}{2,3}\naput[nrot=:U,labelsep=0pt]{$\sim$}
+\end{document}