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 

   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: