Quantum Frobenius Heisenberg categorification

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