# HG changeset patch
# User Kevin Walker <kevin@canyon23.net>
# Date 1323394902 28800
# Node ID 04079a7aeaeff0b91f4ac373f5fa0c318f87ce74
# Parent  e3c5c55d901d31a7c6016493b3abfcf2b042cee7
minor - Section 4

diff -r e3c5c55d901d -r 04079a7aeaef text/hochschild.tex
--- a/text/hochschild.tex	Thu Dec 08 15:57:34 2011 -0800
+++ b/text/hochschild.tex	Thu Dec 08 17:41:42 2011 -0800
@@ -212,7 +212,7 @@
 (a) the point * is not on the boundary of any blob or
 (b) there are no labeled points or blob boundaries within distance $\ep$ of *,
 other than blob boundaries at * itself.
-Note that all blob diagrams are in $F_*^\ep$ for $\ep$ sufficiently small.
+Note that all blob diagrams are in some $F_*^\ep$ for $\ep$ sufficiently small.
 Let $b$ be a blob diagram in $F_*^\ep$.
 Define $f(b)$ to be the result of moving any blob boundary points which lie on *
 to distance $\ep$ from *.
@@ -228,6 +228,7 @@
 Otherwise, define $s(y)$ to be the result of adding a label 1 (identity morphism) at *.
 Extending linearly, we get the desired map $s: J_* \to K_*(C)$.
 It is easy to check that $s$ is a chain map and $s \circ i = \id$.
+What remains is to show that $i \circ s$ is homotopic to the identity.
 
 Let $N_\ep$ denote the ball of radius $\ep$ around *.
 Let $L_*^\ep \sub J_*$ be the subcomplex