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309 Put another way, the cell decompositions we consider are dual to standard cell |
309 Put another way, the cell decompositions we consider are dual to standard cell |
310 decompositions of $X$. |
310 decompositions of $X$. |
311 |
311 |
312 We will always assume that our $n$-categories have linear $n$-morphisms. |
312 We will always assume that our $n$-categories have linear $n$-morphisms. |
313 |
313 |
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314 \nn{need to replace ``cell decomposition" below with something looser. not sure what to call it. |
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315 maybe ``nice stratification"?? the link of each piece of each stratum should be a cell decomposition of |
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316 a sphere, but that's probably all we need. or maybe refineable to a cell decomp?} |
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317 |
314 For $n=1$, a field on a 0-manifold $P$ is a labeling of each point of $P$ with |
318 For $n=1$, a field on a 0-manifold $P$ is a labeling of each point of $P$ with |
315 an object (0-morphism) of the 1-category $C$. |
319 an object (0-morphism) of the 1-category $C$. |
316 A field on a 1-manifold $S$ consists of |
320 A field on a 1-manifold $S$ consists of |
317 \begin{itemize} |
321 \begin{itemize} |
318 \item a cell decomposition of $S$ (equivalently, a finite collection |
322 \item a cell decomposition of $S$ (equivalently, a finite collection |