diff -r b8f7de7a4206 -r 0cbef0258d72 text/ncat.tex --- a/text/ncat.tex Mon Jan 10 14:18:52 2011 -0800 +++ b/text/ncat.tex Mon Jan 10 15:25:53 2011 -0800 @@ -678,12 +678,12 @@ An $n$-category consists of the following data: \begin{itemize} -\item Functors $\cC_k$ from $k$-balls to sets, $0\le k\le n$ (Axiom \ref{axiom:morphisms}) -\item Boundary natural transformations $\cC_k \to \cl{\cC}_{k-1} \circ \bd$ (Axiom \ref{nca-boundary}) -\item Composition/gluing maps $\gl_Y : \cC(B_1)_E \times_{\cC(Y)} \cC(B_2)_E \to \cC(B_1\cup_Y B_2)_E$ (Axiom \ref{axiom:composition}) -\item Product/identity maps $\pi^*:\cC(X)\to \cC(E)$ for each pinched product $\pi:E\to X$ (Axiom \ref{axiom:product}) -\item If enriching in an auxiliary category, additional structure on $\cC_n(X; c)$ -\item In the $A_\infty$ case, an action of $C_*(\Homeo_\bd(X))$, and similarly for families of collar maps (Axiom \ref{axiom:families}) +\item Functors $\cC_k$ from $k$-balls to sets, $0\le k\le n$ (Axiom \ref{axiom:morphisms}). +\item Boundary natural transformations $\cC_k \to \cl{\cC}_{k-1} \circ \bd$ (Axiom \ref{nca-boundary}). +\item Composition/gluing maps $\gl_Y : \cC(B_1)_E \times_{\cC(Y)} \cC(B_2)_E \to \cC(B_1\cup_Y B_2)_E$ (Axiom \ref{axiom:composition}). +\item Product/identity maps $\pi^*:\cC(X)\to \cC(E)$ for each pinched product $\pi:E\to X$ (Axiom \ref{axiom:product}). +\item If enriching in an auxiliary category, additional structure on $\cC_n(X; c)$. +\item In the $A_\infty$ case, an action of $C_*(\Homeo_\bd(X))$, and similarly for families of collar maps (Axiom \ref{axiom:families}). \end{itemize} The above data must satisfy the following conditions: \begin{itemize}