We consider the problem of deforming simultaneously a pair of givenView original: http://arxiv.org/abs/1202.2896
structures. We show that such deformations are governed by an L-infinity
algebra, which we construct explicitly. Our machinery is based on Th. Voronov's
derived bracket construction.
We consider algebraic and geometric applications, including the deformations
of morphisms of various kinds of algebras, of coisotropic submanifolds in
Poisson manifolds, and of twisted Poisson structures.