One of these classical theories is based on a finite group, and for that we can apply the finite path integrals of §\[sec:5\] (in the generalized form for 2-groupoids) to construct the quantum theory. In §\[sec:cs6\] we start at the other end of the theory, that is, with points rather than 4-manifolds. We describe two braided tensor categories which may be attached to a point in the anomaly theory ${\mathscr{A}}$; they are Morita equivalent, so both define ${\mathscr{A}}$. In \[subsec:c6.2\] we introduce a finite (lattice) approximation of the continuous version of the anomaly theory, and so obtain many more Morita equivalent braided tensor categories which define that theory (Proposition \[morita\]). Finally, in \[cs9.2\] we spell out what the anomaly theory assigns to manifolds of various dimensions from $0$ to $4$.

The Chern-Simons theory proper is described in \[sec:c9\]; see Theorem \[thm:9.1\]. The tables in \[subsec:c9.3\] are helpful in organizing the motley characters who play a part in our story. Our account here emphasizes 0-manifolds as that is the new element.

We begin in §\[sec:1\] with a discussion of the 1-dimensional case to set down some basic notions. Here the gauge group is an arbitrary compact Lie group $G$, and the 