The Batalin-Vikovisky construction, as opposed to BV-algebras, has enjoyed a resurgence of interest recently, with radically different settings, though all involve `The Classical master equation´. Here I review some ancient history and then attempt to establish the underlying homological algebra corresponding to the phrase ``derived critical locus with symmetries´´, without going into detail about the applications in Lagrangian physics with symmetries or in algebraic geometry.