  We introduce a class of Liouville manifolds with boundary which we call
Liouville sectors. We define the wrapped Fukaya category, symplectic
cohomology, and the open-closed map for Liouville sectors, and we show that
these invariants are covariantly functorial with respect to inclusions of
Liouville sectors. From this foundational setup, a local-to-global principle
for Abouzaid's generation criterion follows.
