Shifted double Lie-Rinehart algebras

Abstract: We generalize the notions of shifted double Poisson and shifted double Lie-Rinehart structures, defined by Van den Bergh in [VdB08a, VdB08b], to monoids in a symmetric monoidal abelian category. The main result is that an n-shifted double Lie-Rinehart structure on a pair (A, M) is equivalent to a non-shifted double Lie-Rinehart structure on the pair (A, M [--n]).