diff -r ef8fac44a8aa -r 6e23226d1cca text/ncat.tex --- a/text/ncat.tex Mon May 31 23:42:37 2010 -0700 +++ b/text/ncat.tex Tue Jun 01 11:34:03 2010 -0700 @@ -74,7 +74,7 @@ We will concentrate on the case of PL unoriented manifolds. (The ambitious reader may want to keep in mind two other classes of balls. -The first is balls equipped with a map to some other space $Y$. +The first is balls equipped with a map to some other space $Y$. \todo{cite something of Teichner's?} This will be used below to describe the blob complex of a fiber bundle with base space $Y$. The second is balls equipped with a section of the the tangent bundle, or the frame @@ -107,7 +107,7 @@ homeomorphisms to the category of sets and bijections. \end{prop} -We postpone the proof of this result until after we've actually given all the axioms. Note that defining this functor for some $k$ only requires the data described in Axiom \ref{axiom:morphisms} at level $k$, along with the data described in other Axioms at lower levels. +We postpone the proof of this result until after we've actually given all the axioms. Note that defining this functor for some $k$ only requires the data described in Axiom \ref{axiom:morphisms} at level $k$, along with the data described in the other Axioms at lower levels. %In fact, the functors for spheres are entirely determined by the functors for balls and the subsequent axioms. (In particular, $\cC(S^k)$ is the colimit of $\cC$ applied to decompositions of $S^k$ into balls.) However, it is easiest to think of it as additional data at this point.