
diff -r c06a899bd1f0 -r d3b05641e7ca text/hochschild.tex
--- a/text/hochschild.tex	Sun Jul 04 13:15:03 2010 -0600
+++ b/text/hochschild.tex	Sun Jul 04 23:32:48 2010 -0600
@@ -107,7 +107,7 @@
 quasi-isomorphic to its $0$-th homology (which in turn, by \ref{item:hochschild-coinvariants}
 above, is just $C$) via the quotient map $\HC_0 \onto \HH_0$.
 \end{enumerate}
-(Together, these just say that Hochschild homology is `the derived functor of coinvariants'.)
+(Together, these just say that Hochschild homology is ``the derived functor of coinvariants".)
 We'll first recall why these properties are characteristic.
 
 Take some $C$-$C$ bimodule $M$, and choose a free resolution
@@ -130,8 +130,8 @@
 \cP_*(F_j) & \xrightarrow{\cP_0(F_j) \onto H_0(\cP_*(F_j))} \coinv(F_j).
 \end{align*}
 The cone of each chain map is acyclic.
-In the first case, this is because the `rows' indexed by $i$ are acyclic since $\cP_i$ is exact.
-In the second case, this is because the `columns' indexed by $j$ are acyclic, since $F_j$ is free.
+In the first case, this is because the ``rows" indexed by $i$ are acyclic since $\cP_i$ is exact.
+In the second case, this is because the ``columns" indexed by $j$ are acyclic, since $F_j$ is free.
 Because the cones are acyclic, the chain maps are quasi-isomorphisms.
 Composing one with the inverse of the other, we obtain the desired quasi-isomorphism
 $$\cP_*(M) \quismto \coinv(F_*).$$




