  Starting with a k-linear or DG category admitting a (homotopy) Serre functor,
we construct a k-linear or DG 2-category categorifying the Heisenberg algebra
of the numerical K-group of the original category. We also define a
2-categorical analogue of the Fock space representation of the Heisenberg
algebra. Our construction generalises and unifies various categorical
Heisenberg algebra actions appearing in the literature. In particular, we give
a full categorical enhancement of the action on derived categories of symmetric
quotient stacks introduced by Krug, which itself categorifies a Heisenberg
algebra action proposed by Grojnowski.

Algebraic Geometry;Category Theory;Representation Theory