We define homotopy Lie-Rinehart pairs and the associated homotopy Rinehart algebra in the context of coalgebras. We define homotopy Lie-Rinehart resolutions and present conditions under which the associated homotopy Rinehart algebra is a cohomological model for the Rinehart algebra of the resolved Lie-Rinehart pair.
"Homotopy Rinehart cohomology of homotopy Lie-Rinehart pairs." Homology Homotopy Appl. 3 (1) 139 - 163, 2001.