It is well known that Barr and Beck's definition of comonadic homology makes sense also with a functor of coefficients taking values in a semi-abelian category instead of an abelian one. The question arises whether such a homology theory has the same convenient properties as in the abelian case. Here we focus on independence of the chosen comonad: conditions for homology to depend on the induced class of projectives only.
Goedecke, J., & Van der Linden, T. (2007). A comparison theorem for simplicial resolutions. Journal of Homotopy and Related Structures, 2(1), 109-126. https://hdl.handle.net/2078.5/59940 (Original work published 2007)