  This expository paper describes sewing conditions in two-dimensional
open/closed topological field theory. We include a description of the
G-equivariant case, where G is a finite group. We determine the category of
boundary conditions in the case that the closed string algebra is semisimple.
In this case we find that sewing constraints -- the most primitive form of
worldsheet locality -- already imply that D-branes are (G-twisted) vector
bundles on spacetime. We comment on extensions to cochain-valued theories and
various applications. Finally, we give uniform proofs of all relevant sewing
theorems using Morse theory.
