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authorKarl Berry <karl@freefriends.org>2010-10-12 00:13:11 +0000
committerKarl Berry <karl@freefriends.org>2010-10-12 00:13:11 +0000
commit324e3ca487267e4d60094b29bda9e562fa489803 (patch)
treedbd69d6b00ea2a4e15e9635522b20b6cb9aeae7b /Master/texmf-dist/doc/latex/math-e/10-01-4.ltxps
parent308e7e96ccb036e76b8e07e4e980394f50977580 (diff)
new doc package math-e (11oct10)
git-svn-id: svn://tug.org/texlive/trunk@20062 c570f23f-e606-0410-a88d-b1316a301751
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+%%
+%% An UIT Edition example
+%%
+%% Example 10-01-4 on page 199.
+%%
+%% Copyright (C) 2010 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{375.57637pt}
+\usepackage[utf8]{inputenc}
+\AtBeginDocument{\setlength\parindent{0pt}}
+\StartShownPreambleCommands
+\usepackage{amsmath,amssymb,amsopn,pst-node}
+\DeclareMathOperator{\Hom}{Hom}
+\DeclareMathOperator{\Mod}{Mod}
+\DeclareMathOperator{\obj}{obj}
+\StopShownPreambleCommands
+\begin{document}
+Let $\mathcal{C}:=\mathcal{D}:=\Mod_A$, $M\in
+ \obj(\Mod_A)$ be fixed,
+\begin{align*}
+ F:=\square\otimes_A M : \Mod_A &\rightarrow \Mod_A, \\
+ G:=\Hom_A(M,\square) : \Mod_A &\rightarrow \Mod_A.
+\end{align*}
+These two functors are adjoint, by
+$h(X,Y)(\phi)(x)(m)\rightarrow\phi(x\otimes m)$:\\[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}