  We develop a set of tools for doing computations in and of (partially)
wrapped Fukaya categories. In particular, we prove (1) a descent (cosheaf)
property for the wrapped Fukaya category with respect to so-called Weinstein
sectorial coverings and (2) that the partially wrapped Fukaya category of a
Weinstein manifold with respect to a mostly Legendrian stop is generated by the
cocores of the critical handles and the linking disks to the stop. We also
prove (3) a `stop removal equals localization' result, and (4) that the
Fukaya--Seidel category of a Lefschetz fibration with Liouville fiber is
generated by the Lefschetz thimbles. These results are derived from three main
ingredients, also of independent use: (5) a K\"unneth formula (6) an exact
triangle in the Fukaya category associated to wrapping a Lagrangian through a
Legendrian stop at infinity and (7) a geometric criterion for when a
pushforward functor between wrapped Fukaya categories of Liouville sectors is
fully faithful.
