# HG changeset patch # User Kevin Walker # Date 1310837998 21600 # Node ID 1e4bb652812d1ede431914e855c2b1d19a25df6c # Parent 870d6fac54207d92a8905385130a10fb09425c7a typos from ref rpt diff -r 870d6fac5420 -r 1e4bb652812d RefereeReport.pdf Binary file RefereeReport.pdf has changed diff -r 870d6fac5420 -r 1e4bb652812d text/appendixes/comparing_defs.tex --- a/text/appendixes/comparing_defs.tex Fri Jul 15 15:03:22 2011 -0700 +++ b/text/appendixes/comparing_defs.tex Sat Jul 16 11:39:58 2011 -0600 @@ -126,7 +126,7 @@ We will construct from $\cC$ a traditional pivotal 2-category. (The ``pivotal" corresponds to our assumption of strong duality for $\cC$.) -We will try to describe the construction in such a way the the generalization to $n>2$ is clear, +We will try to describe the construction in such a way that the generalization to $n>2$ is clear, though this will make the $n=2$ case a little more complicated than necessary. Before proceeding, we must decide whether the 2-morphisms of our @@ -586,7 +586,7 @@ ($\cC$ applied to the standard interval with boundary labeled by $x$ and $y$). For simplicity we will now assume there is only one object and suppress it from the notation. -A choice of homeomorphism $I\cup I \to I$ induces a chain map $m_2: A\times A\to A$. +A choice of homeomorphism $I\cup I \to I$ induces a chain map $m_2: A\otimes A\to A$. We now have two different homeomorphisms $I\cup I\cup I \to I$, but they are isotopic. Choose a specific 1-parameter family of homeomorphisms connecting them; this induces a degree 1 chain homotopy $m_3:A\ot A\ot A\to A$. diff -r 870d6fac5420 -r 1e4bb652812d text/deligne.tex --- a/text/deligne.tex Fri Jul 15 15:03:22 2011 -0700 +++ b/text/deligne.tex Sat Jul 16 11:39:58 2011 -0600 @@ -110,7 +110,7 @@ (\ldots, N_{i-1}, N_i, N_{i+1}, \ldots) &\to& (\ldots, N_{i-1}, N'_i, N''_i, N_{i+1}, \ldots) \\ (\ldots, R_{i-1}, R_i, R_{i+1}, \ldots) &\to& (\ldots, R_{i-1}, R_i\cup M''_i, R_i\cup N'_i, R_{i+1}, \ldots) \\ - (\ldots, f_{i-1}, f_i, \ldots) &\to& (\ldots, f_{i-1}, \rm{id}, f_i, \ldots) . + (\ldots, f_{i-1}, f_i, \ldots) &\to& (\ldots, f_{i-1}, {\rm{id}}, f_i, \ldots) . \end{eqnarray*} (See Figure \ref{xdfig1}.) \begin{figure}[t]