Quantum Frobenius Heisenberg categorification

Abstract We associate a diagrammatic monoidal category Heis k ( A ; z , t ) , which we call the quantum Frobenius Heisenberg category, to a symmetric Frobenius superalgebra A, a central charge k ∈ Z , and invertible parameters z , t in some ground ring. When A is trivial, i.e. it equals the ground ring, these categories recover the quantum Heisenberg categories introduced in our previous work, and when the central charge k is zero they yield generalizations of the affine HOMFLY-PT skein category. By exploiting some natural categorical actions of Heis k ( A ; z , t ) on generalized cyclotomic quotients, we prove a basis theorem for morphism spaces.