 Cotriple homology

In algebra, given a category "C" with a cotriple, the "n"-th cotriple homology of an object "X" in "C" with coefficients in a functor "E" is the "n"-th homotopy group of the "E" of the augmented simplicial object induced from "X" by the cotriple.The term "homology" is because in the abelian case, by the Dold–Kan correspondence, the homotopy groups are the homology of the corresponding chain complex.