  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.
