diff -r 19e58f33cdc3 -r 96ec10a46ee1 text/ncat.tex --- a/text/ncat.tex Mon Aug 30 13:19:05 2010 -0700 +++ b/text/ncat.tex Tue Aug 31 11:18:26 2010 -0700 @@ -17,14 +17,14 @@ The definitions presented below tie the categories more closely to the topology and avoid combinatorial questions about, for example, the minimal sufficient collections of generalized associativity axioms; we prefer maximal sets of axioms to minimal sets. -For examples of topological origin +It is easy to show that examples of topological origin (e.g.\ categories whose morphisms are maps into spaces or decorated balls), -it is easy to show that they satisfy our axioms. For examples of a more purely algebraic origin, one would typically need the combinatorial results that we have avoided here. -\nn{Say something explicit about Lurie's work here? It seems like this was something that Dan Freed wanted explaining when we talked to him in Aspen} +%\nn{Say something explicit about Lurie's work here? +%It seems like this was something that Dan Freed wanted explaining when we talked to him in Aspen} \medskip @@ -190,7 +190,8 @@ \caption{Combining two balls to get a full boundary.}\label{blah3}\end{figure} Note that we insist on injectivity above. -The lemma follows from Definition \ref{def:colim-fields} and Lemma \ref{lem:colim-injective}. \nn{we might want a more official looking proof...} +The lemma follows from Definition \ref{def:colim-fields} and Lemma \ref{lem:colim-injective}. +%\nn{we might want a more official looking proof...} Let $\cl{\cC}(S)_E$ denote the image of $\gl_E$. We will refer to elements of $\cl{\cC}(S)_E$ as ``splittable along $E$" or ``transverse to $E$". @@ -890,12 +891,12 @@ The remaining data for the $A_\infty$ $n$-category --- composition and $\Diff(X\to X')$ action --- also comes from the $\cE\cB_n$ action on $A$. -\nn{should we spell this out?} +%\nn{should we spell this out?} Conversely, one can show that a topological $A_\infty$ $n$-category $\cC$, where the $k$-morphisms $\cC(X)$ are trivial (single point) for $k