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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 $e$.) |
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263 |
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264 For lack of a better name, we'll call elements of $P$ cone-product polyhedra, |
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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 |