262 \label{sec:example:traditional-n-categories(fields)} |
262 \label{sec:example:traditional-n-categories(fields)} |
263 We now describe in more detail Example \ref{ex:traditional-n-categories(fields)}, |
263 We now describe in more detail Example \ref{ex:traditional-n-categories(fields)}, |
264 systems of fields coming from embedded cell complexes labeled |
264 systems of fields coming from embedded cell complexes labeled |
265 by $n$-category morphisms. |
265 by $n$-category morphisms. |
266 |
266 |
267 Given an $n$-category $C$ with the right sort of duality |
267 Given an $n$-category $C$ with the right sort of duality, |
268 (e.g. a pivotal 2-category, *-1-category), |
268 e.g., a *-1-category (that is, a 1-category with an involution of the morphisms |
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269 reversing source and target) or a pivotal 2-category, |
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270 (\cite{MR1686423, 0908.3347,1009.0186}), |
269 we can construct a system of fields as follows. |
271 we can construct a system of fields as follows. |
270 Roughly speaking, $\cC(X)$ will the set of all embedded cell complexes in $X$ |
272 Roughly speaking, $\cC(X)$ will the set of all embedded cell complexes in $X$ |
271 with codimension $i$ cells labeled by $i$-morphisms of $C$. |
273 with codimension $i$ cells labeled by $i$-morphisms of $C$. |
272 We'll spell this out for $n=1,2$ and then describe the general case. |
274 We'll spell this out for $n=1,2$ and then describe the general case. |
273 |
275 |