diff -r 091c36b943e7 -r 6cc92b273d44 text/a_inf_blob.tex --- a/text/a_inf_blob.tex Wed Jun 02 12:52:08 2010 -0700 +++ b/text/a_inf_blob.tex Wed Jun 02 16:51:40 2010 -0700 @@ -235,7 +235,7 @@ \[ F \to E \to Y . \] -We outline two approaches. +We outline one approach here and a second in Subsection xxxx. We can generalize the definition of a $k$-category by replacing the categories of $j$-balls ($j\le k$) with categories of $j$-balls $D$ equipped with a map $p:D\to Y$. @@ -254,6 +254,7 @@ +\nn{put this later} \nn{The second approach: Choose a decomposition $Y = \cup X_i$ such that the restriction of $E$ to $X_i$ is a product $F\times X_i$. @@ -275,7 +276,6 @@ Let $X$ be a closed $k$-manifold with a splitting $X = X'_1\cup_Y X'_2$. We will need an explicit collar on $Y$, so rewrite this as $X = X_1\cup (Y\times J) \cup X_2$. -\nn{need figure} Given this data we have: \nn{need refs to above for these} \begin{itemize} \item An $A_\infty$ $n{-}k$-category $\bc(X)$, which assigns to an $m$-ball