The MV formalism for IBL _∞ - and BV _∞ -algebras

We develop a new formalism for the quantum master equation Δ e^{S / ħ}= 0 and the category of IBL _∞-algebras and simplify some homotopical algebra arising in the context of oriented surfaces with boundary. We introduce and study a category of MV-algebras, which, on the one hand, contains such important categories as those of IBL _∞-algebras and L_∞-algebras and, on the other hand, is homotopically trivial, in particular allowing for a simple solution of the quantum master equation. We also present geometric interpretation of our results.