equal
deleted
inserted
replaced
447 boundary condition $c\in\cC(\bd X)$. |
447 boundary condition $c\in\cC(\bd X)$. |
448 |
448 |
449 The above construction can be extended to higher codimensions, assigning |
449 The above construction can be extended to higher codimensions, assigning |
450 a $k$-category $A(Y)$ to an $n{-}k$-manifold $Y$, for $0 \le k \le n$. |
450 a $k$-category $A(Y)$ to an $n{-}k$-manifold $Y$, for $0 \le k \le n$. |
451 These invariants fit together via actions and gluing formulas. |
451 These invariants fit together via actions and gluing formulas. |
452 We describe only the case $k=1$ below. |
452 We describe only the case $k=1$ below. We describe these extensions in the more general setting of the blob complex later, in particular in Examples \ref{ex:ncats-from-tqfts} and \ref{ex:blob-complexes-of-balls} and in \S \ref{sec:modules}. |
453 |
453 |
454 The construction of the $n{+}1$-dimensional part of the theory (the path integral) |
454 The construction of the $n{+}1$-dimensional part of the theory (the path integral) |
455 requires that the starting data (fields and local relations) satisfy additional |
455 requires that the starting data (fields and local relations) satisfy additional |
456 conditions. |
456 conditions. |
457 (Specifically, $A(X; c)$ is finite dimensional for all $n$-manifolds $X$ and the inner products |
457 (Specifically, $A(X; c)$ is finite dimensional for all $n$-manifolds $X$ and the inner products |