The BV complex provides homological tools to handle the quotient of the critical locus of a functional by the symmetries of the system. However the usual construction is algebraic, and the underlying geometric idea is not clear from it. My goal is to explain how, in the context of derived geometry, we can define BV as a homotopy quotient of the critical locus together with a Lagrangian correspondence that makes BV look like the symplectic reduction of the critical locus, and recover the classical construction from it.