We generalize the notions of shifted double Poisson and shifted double Lie-Rinehart structures 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]).
Keywords: Noncommutative geometry, Double Poisson algebra, Double Lie-Rinehart algebra
2020 MSC: 14A22, 18M85, 18M05
Theory and Applications of Categories, Vol. 35, 2020, No. 17, pp 594-621.