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999 |
999 |
1000 \medskip |
1000 \medskip |
1001 |
1001 |
1002 In the $n$-category axioms above we have intermingled data and properties for expository reasons. |
1002 In the $n$-category axioms above we have intermingled data and properties for expository reasons. |
1003 Here's a summary of the definition which segregates the data from the properties. |
1003 Here's a summary of the definition which segregates the data from the properties. |
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1004 We also remind the reader of the inductive nature of the definition: All the data for $k{-}1$-morphisms must be in place |
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1005 before we can describe the data for $k$-morphisms. |
1004 |
1006 |
1005 A disk-like $n$-category consists of the following data: |
1007 A disk-like $n$-category consists of the following data: |
1006 \begin{itemize} |
1008 \begin{itemize} |
1007 \item functors $\cC_k$ from $k$-balls to sets, $0\le k\le n$ (Axiom \ref{axiom:morphisms}); |
1009 \item functors $\cC_k$ from $k$-balls to sets, $0\le k\le n$ (Axiom \ref{axiom:morphisms}); |
1008 \item boundary natural transformations $\cC_k \to \cl{\cC}_{k-1} \circ \bd$ (Axiom \ref{nca-boundary}); |
1010 \item boundary natural transformations $\cC_k \to \cl{\cC}_{k-1} \circ \bd$ (Axiom \ref{nca-boundary}); |