The MV formalism for IBL-infinity and BV-infinity algebras

We introduce and study a category of algebras, which, on the one hand, contains such important categories as those of BV-infinity (homotopy Batalin-Vilkovisky) algebras, IBL-infinity (homotopy involutive Lie bi-) algebras and L-infinity (homotopy Lie) algebras, and on the other hand, is homotopically trivial, in particular allowing for a simple solution of the quantum master equation.