  We give criteria for the existence of a Serre functor on the derived category
of a gauged Landau-Ginzburg model. This is used to provide a general theorem on
the existence of an admissible (fractional) Calabi-Yau subcategory of a gauged
Landau-Ginzburg model and a geometric context for crepant categorical
resolutions. We explicitly describe our framework in the toric setting. As a
consequence, we generalize several theorems and examples of Orlov and
Kuznetsov, ending with new examples of semi-orthogonal decompositions
containing (fractional) Calabi-Yau categories.
