--- a/text/appendixes/misc_appendices.tex	Wed Jun 02 08:43:12 2010 -0700
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
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-%!TEX root = ../../blob1.tex
-
-
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-%\section{Morphisms and duals of topological $A_\infty$ modules}
-%\label{sec:A-infty-hom-and-duals}%
-%
-%\begin{defn}
-%If $\cM$ and $\cN$ are topological $A_\infty$ left modules over a topological $A_\infty$ category $\cC$, then a morphism $f: \cM \to \cN$ consists of a chain map $f:\cM(J,p;b) \to \cN(J,p;b)$ for each right marked interval $(J,p)$ with a boundary condition $b$, such that  for each interval $J'$ the diagram
-%\begin{equation*}
-%\xymatrix{
-%\cC(J';a,b) \tensor \cM(J,p;b) \ar[r]^{\text{gl}} \ar[d]^{\id \tensor f} & \cM(J' cup J,a) \ar[d]^f \\
-%\cC(J';a,b) \tensor \cN(J,p;b) \ar[r]^{\text{gl}}                                & \cN(J' cup J,a) 
-%}
-%\end{equation*}
-%commutes on the nose, and the diagram
-%\begin{equation*}
-%\xymatrix{
-%\CD{(J,p) \to (J',p')} \tensor \cM(J,p;a) \ar[r]^{\text{ev}} \ar[d]^{\id \tensor f} & \cM(J',p';a) \ar[d]^f \\
-%\CD{(J,p) \to (J',p')} \tensor \cN(J,p;a) \ar[r]^{\text{ev}}  & \cN(J',p';a) \\
-%}
-%\end{equation*}
-%commutes up to a weakly unique homotopy.
-%\end{defn}
-
-%The variations required for right modules and bimodules should be obvious.
-
-%\todo{duals}
-%\todo{ the functors $\hom_{\lmod{\cC}}\left(\cM \to -\right)$ and $\cM^* \tensor_{\cC} -$ from $\lmod{\cC}$ to $\Vect$ are naturally isomorphic}
-