text/ncat.tex
changeset 260 971234b03c4a
parent 259 db18f7c32abe
child 261 1c408505c9f5
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259:db18f7c32abe 260:971234b03c4a
  1179 where $({_\cC\cN}(J\setmin K))^*$ denotes the (linear) dual of the chain complex associated
  1179 where $({_\cC\cN}(J\setmin K))^*$ denotes the (linear) dual of the chain complex associated
  1180 to the right-marked interval $J\setmin K$.
  1180 to the right-marked interval $J\setmin K$.
  1181 This extends to a functor from all left-marked intervals (not just those contained in $J$).
  1181 This extends to a functor from all left-marked intervals (not just those contained in $J$).
  1182 It's easy to verify the remaining module axioms.
  1182 It's easy to verify the remaining module axioms.
  1183 
  1183 
  1184 Now re reinterpret $(\cM_\cC\ot {_\cC\cN})^*$
  1184 Now we reinterpret $(\cM_\cC\ot {_\cC\cN})^*$
  1185 as some sort of morphism $\cM_\cC \to (_\cC\cN)^*$.
  1185 as some sort of morphism $\cM_\cC \to (_\cC\cN)^*$.
       
  1186 Let $f\in (\cM_\cC\ot {_\cC\cN})^*$.
       
  1187 Let $\olD$ be a chain of subdivisions with $D_0 = [J = I_1\cup\cdots\cup I_m]$, and let
       
  1188 $m\ot \cbar \in \cM(I_1)\ot\cC(I_2)\ot\cdots\ot\cC(I_{m-1})$.
       
  1189 
       
  1190 
       
  1191 
       
  1192 
       
  1193 
       
  1194 
  1186 
  1195 
  1187 \nn{...}
  1196 \nn{...}
  1188 
  1197 
  1189 
  1198 
  1190 
  1199