...
--- a/text/kw_macros.tex Thu Dec 17 04:37:12 2009 +0000
+++ b/text/kw_macros.tex Fri Dec 18 06:06:43 2009 +0000
@@ -24,6 +24,8 @@
\def\ot{\otimes}
\def\inv{^{-1}}
+\def\spl{_\pitchfork}
+
%\def\nn#1{{{\it \small [#1]}}}
\def\nn#1{{{\color[rgb]{.2,.5,.6} \small [#1]}}}
\long\def\noop#1{}
--- a/text/ncat.tex Thu Dec 17 04:37:12 2009 +0000
+++ b/text/ncat.tex Fri Dec 18 06:06:43 2009 +0000
@@ -213,6 +213,8 @@
$$\mathfig{.65}{tempkw/blah6}$$
\caption{An example of strict associativity}\label{blah6}\end{figure}
+\nn{figure \ref{blah6} (blah6) needs a dotted line in the south split ball}
+
Notation: $a\bullet b \deq \gl_Y(a, b)$ and/or $a\cup b \deq \gl_Y(a, b)$.
In the other direction, we will call the projection from $\cC(B)_E$ to $\cC(B_i)_E$
a {\it restriction} map and write $\res_{B_i}(a)$ for $a\in \cC(B)_E$.
@@ -220,11 +222,13 @@
For example, if $B$ is a $k$-ball and $Y\sub \bd B$ is a $k{-}1$-ball, there is a
restriction map from $\cC(B)_{\bd Y}$ to $\cC(Y)$.
-%More notation and terminology:
-%We will call the projection from $\cC(B)_E$ to $\cC(B_i)_E$ a {\it restriction}
-%map
+We will write $\cC(B)_Y$ for the image of $\gl_Y$ in $\cC(B)$.
+We will call $\cC(B)_Y$ morphisms which are splittable along $Y$ or transverse to $Y$.
+We have $\cC(B)_Y \sub \cC(B)_E \sub \cC(B)$.
-The above two axioms are equivalent to the following axiom,
+More generally, if $X$ is a sphere or ball subdivided \nn{...}
+
+The above two composition axioms are equivalent to the following one,
which we state in slightly vague form.
\xxpar{Multi-composition:}