We develop a new formalism for the Quantum Master Equation $\Delta e^{ S/\hbar} = 0$ and the category of ${ \rm IBL}_\infty$-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 ${ \rm IBL}_\infty$-algebras and ${ \rm L}_\infty$-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.
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