Abstract
We study in this article the concept of algebra up to homotopy for a structure defined by two operations . Important examples of such structure are those of pre-Gerstenhaber and pre-Poisson algebras. Given a structure of pre-commutative and pre-Lie algebra for two shifts of degree given by a and b, we define the structure of a pre-(a, b)-algebra and we give an explicit construction of the associated algebra up to homotopy.
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