Categories of relations including Weinstein's (linear) symplectic category are known to provide semantics convenient for quantum theory. We apply this philosophy to quantum L-infinity algebras, which give a homotopy algebraic framework for perturbative quantum field theories. Using homological perturbation theory to formalize a finite-dimensional incarnation of Batalin-Vilkovisky path integrals, we introduce a categorical perspective on quantum L-infinity algebras generalizing the minimal model theorem. No knowledge of QFT, symplectic geometry or homological perturbation theory will be assumed. This is a joint work with Ján Pulmann and Branislav Jur?o in progress.