# HG changeset patch # User Kevin Walker # Date 1277913346 25200 # Node ID 14e3124a48e8ad5b723b395ebaec86071fe25159 # Parent 291f82fb79b59341f116aa705794606714544adf minor diff -r 291f82fb79b5 -r 14e3124a48e8 blob1.tex --- a/blob1.tex Mon Jun 28 10:03:13 2010 -0700 +++ b/blob1.tex Wed Jun 30 08:55:46 2010 -0700 @@ -16,7 +16,7 @@ \maketitle -[revision $\ge$ 393; $\ge$ 24 June 2010] +[revision $\ge$ 410; $\ge$ 30 June 2010] {\color[rgb]{.9,.5,.2} \large \textbf{Draft version, read with caution.}} We're in the midst of revising this, and hope to have a version on the arXiv soon. diff -r 291f82fb79b5 -r 14e3124a48e8 text/ncat.tex --- a/text/ncat.tex Mon Jun 28 10:03:13 2010 -0700 +++ b/text/ncat.tex Wed Jun 30 08:55:46 2010 -0700 @@ -1399,14 +1399,6 @@ We will define a more general self tensor product (categorified coend) below. -%\nn{what about self tensor products /coends ?} - -\nn{maybe ``tensor product" is not the best name?} - -%\nn{start with (less general) tensor products; maybe change this later} - - - \subsection{Morphisms of $A_\infty$ $1$-category modules} \label{ss:module-morphisms} @@ -1608,8 +1600,7 @@ $g((\bd \olD)\ot -)$ (where the $g((\bd_0 \olD)\ot -)$ part of $g((\bd \olD)\ot -)$ should be interpreted as above). -Define a {\it naive morphism} -\nn{should consider other names for this} +Define a {\it strong morphism} of modules to be a collection of {\it chain} maps \[ h_K : \cX(K)\to \cY(K) @@ -1623,7 +1614,7 @@ \ar[d]^{\gl} \\ \cX(K) \ar[r]^{h_{K}} & \cY(K) } \] -Given such an $h$ we can construct a non-naive morphism $g$, with $\bd g = 0$, as follows. +Given such an $h$ we can construct a morphism $g$, with $\bd g = 0$, as follows. Define $g(\olD\ot - ) = 0$ if the length/degree of $\olD$ is greater than 0. If $\olD$ consists of the single subdivision $K = I_0\cup\cdots\cup I_q$ then define \[