The BV formalism for L_∞ -algebras

Functorial properties of the correspondence between commutative BV _∞-algebras and L_∞-algebras are investigated. The category of L_∞-algebras with L_∞-morphisms is characterized as a certain category of pureBV _∞-algebras with pureBV _∞-morphisms. The functor assigning to a commutative BV _∞-algebra the L_∞-algebra given by higher derived brackets is also shown to have a left adjoint. Cieliebak-Fukaya-Latschev’s machinery of IBL _∞- and BV _∞-morphisms is further developed with introducing the logarithm of a map.