# HG changeset patch # User Kevin Walker # Date 1319344260 21600 # Node ID e8e234aeb266d5ec33328be4efaac0f05a98553a # Parent db365e67adf6f984040f26ce98d4817fa6f2b2b2 begin to incorporate recent n-cat axiom changes into the module axioms diff -r db365e67adf6 -r e8e234aeb266 text/ncat.tex --- a/text/ncat.tex Sat Oct 22 18:07:32 2011 -0600 +++ b/text/ncat.tex Sat Oct 22 22:31:00 2011 -0600 @@ -1842,7 +1842,7 @@ In our example, $\cl\cM(H) = \cD(H\times\bd W \cup \bd H\times W)$. -\begin{module-axiom}[Module boundaries (maps)] +\begin{module-axiom}[Module boundaries] {For each marked $k$-ball $M$ we have a map of sets $\bd: \cM(M)\to \cl\cM(\bd M)$. These maps, for various $M$, comprise a natural transformation of functors.} \end{module-axiom} @@ -1950,10 +1950,7 @@ \] which is natural with respect to the actions of homeomorphisms, and also compatible with restrictions to the intersection of the boundaries of $M$ and $M_i$. -If $k < n$, -or if $k=n$ and we are in the $A_\infty$ case, -we require that $\gl_Y$ is injective. -(For $k=n$ in the ordinary (non-$A_\infty$) case, see below.)} +If $k < n$ we require that $\gl_Y$ is injective.} \end{module-axiom} @@ -1974,10 +1971,7 @@ \] which is natural with respect to the actions of homeomorphisms, and also compatible with restrictions to the intersection of the boundaries of $X$ and $M'$. -If $k < n$, -or if $k=n$ and we are in the $A_\infty$ case, -we require that $\gl_Y$ is injective. -(For $k=n$ in the ordinary (non-$A_\infty$) case, see below.)} +If $k < n$ we require that $\gl_Y$ is injective.} \end{module-axiom} \begin{module-axiom}[Strict associativity]