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inserted
replaced
982 \cC_{\cF,U}(B^k) & = \begin{cases}\cF(B) & \text{when $k<n$,} \\ \cF(B) / U(B) & \text{when $k=n$.}\end{cases} |
982 \cC_{\cF,U}(B^k) & = \begin{cases}\cF(B) & \text{when $k<n$,} \\ \cF(B) / U(B) & \text{when $k=n$.}\end{cases} |
983 \end{align*} |
983 \end{align*} |
984 This $n$-category can be thought of as the local part of the fields. |
984 This $n$-category can be thought of as the local part of the fields. |
985 Conversely, given a disk-like $n$-category we can construct a system of fields via |
985 Conversely, given a disk-like $n$-category we can construct a system of fields via |
986 a colimit construction; see \S \ref{ss:ncat_fields} below. |
986 a colimit construction; see \S \ref{ss:ncat_fields} below. |
|
987 |
|
988 \medskip |
987 |
989 |
988 In the $n$-category axioms above we have intermingled data and properties for expository reasons. |
990 In the $n$-category axioms above we have intermingled data and properties for expository reasons. |
989 Here's a summary of the definition which segregates the data from the properties. |
991 Here's a summary of the definition which segregates the data from the properties. |
990 |
992 |
991 An $n$-category consists of the following data: |
993 An $n$-category consists of the following data: |