diff -r 8f488e576afd -r 8aca80203f9d text/ncat.tex --- a/text/ncat.tex Sun Jul 11 14:31:56 2010 -0600 +++ b/text/ncat.tex Sun Jul 11 14:38:48 2010 -0600 @@ -97,7 +97,7 @@ $1\le k \le n$. At first it might seem that we need another axiom for this, but in fact once we have all the axioms in this subsection for $0$ through $k-1$ we can use a colimit -construction, as described in Subsection \ref{ss:ncat-coend} below, to extend $\cC_{k-1}$ +construction, as described in \S\ref{ss:ncat-coend} below, to extend $\cC_{k-1}$ to spheres (and any other manifolds): \begin{lem} @@ -746,7 +746,7 @@ to be the set of all $C$-labeled embedded cell complexes of $X\times F$. Define $\cC(X; c)$, for $X$ an $n$-ball, to be the dual Hilbert space $A(X\times F; c)$. -(See Subsection \ref{sec:constructing-a-tqft}.) +(See \S\ref{sec:constructing-a-tqft}.) \end{example} \noop{ @@ -1508,7 +1508,7 @@ \label{ss:module-morphisms} In order to state and prove our version of the higher dimensional Deligne conjecture -(Section \ref{sec:deligne}), +(\S\ref{sec:deligne}), we need to define morphisms of $A_\infty$ $1$-category modules and establish some of their elementary properties. @@ -1877,7 +1877,7 @@ of these points labeled by $n$-categories $\cA_i$ ($0\le i\le l$) and the marked points labeled by $\cA_i$-$\cA_{i+1}$ bimodules $\cM_i$. (See Figure \ref{feb21c}.) -To this data we can apply the coend construction as in Subsection \ref{moddecss} above +To this data we can apply the coend construction as in \S\ref{moddecss} above to obtain an $\cA_0$-$\cA_l$ $0$-sphere module and, forgetfully, an $n{-}1$-category. This amounts to a definition of taking tensor products of $0$-sphere module over $n$-categories.