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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]).
@article{TAC_2020_35_a16, author = {Johan Leray}, title = {Shifted double {Lie-Rinehart} algebras}, journal = {Theory and applications of categories}, pages = {594--621}, publisher = {mathdoc}, volume = {35}, year = {2020}, language = {en}, url = {http://geodesic.mathdoc.fr/item/TAC_2020_35_a16/} }
Johan Leray. Shifted double Lie-Rinehart algebras. Theory and applications of categories, Tome 35 (2020), pp. 594-621. http://geodesic.mathdoc.fr/item/TAC_2020_35_a16/