Abstract
We show that the BRST Lagrangian double copy construction of (Formula presented.) supergravity as the 'square' of Yang-Mills theory finds a natural interpretation in terms of homotopy algebras. We significantly expand on our previous work arguing the validity of the double copy at the loop level, and we give a detailed derivation of the double-copied Lagrangian and BRST operator.
Our constructions are very general and can be applied to a vast set of examples.