  We define enumerative invariants associated to a hybrid Gauged Linear Sigma
Model. We prove that in the relevant special cases, these invariants recover
both the Gromov-Witten type invariants defined by Chang-Li and Fan-Jarvis-Ruan
using cosection localization as well as the FJRW type invariants constructed by
Polishchuk-Vaintrob. The invariants are defined by constructing a "fundamental
factorization" supported on the moduli space of Landau-Ginzburg maps to a
convex hybrid model. This gives the kernel of a Fourier-Mukai transform; the
associated map on Hochschild homology defines our theory.
