text/blobdef.tex
changeset 542 3baa4e4d395e
parent 515 9e44c1469918
child 544 24be062a87a1
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   258 For example, a diagram of $k$ strictly nested blobs corresponds to a $k$-simplex, while
   258 For example, a diagram of $k$ strictly nested blobs corresponds to a $k$-simplex, while
   259 a diagram of $k$ disjoint blobs corresponds to a $k$-cube.
   259 a diagram of $k$ disjoint blobs corresponds to a $k$-cube.
   260 (When the fields come from an $n$-category, this correspondence works best if we think of each twig label $u_i$ as having the form
   260 (When the fields come from an $n$-category, this correspondence works best if we think of each twig label $u_i$ as having the form
   261 $x - s(e(x))$, where $x$ is an arbitrary field on $B_i$, $e: \cF(B_i) \to C$ is the evaluation map, 
   261 $x - s(e(x))$, where $x$ is an arbitrary field on $B_i$, $e: \cF(B_i) \to C$ is the evaluation map, 
   262 and $s:C \to \cF(B_i)$ is some fixed section of $e$.)
   262 and $s:C \to \cF(B_i)$ is some fixed section of $e$.)
       
   263 
       
   264 For lack of a better name, we'll call elements of $P$ cone-product polyhedra, 
       
   265 and say that blob diagrams have the structure of a cone-product set (analogous to simplicial set).
   263 \end{remark}
   266 \end{remark}
   264 
   267