nLab monadic cohomology

Idea

Every monad induces an augmented cosimplicial endofunctor; in an additive category we can produce a cochain complex out of any such cosimplicial endofunctor when applied to any particular object. Taking the cohomology of that complex yields monadic cohomology, see at canonical resolution.

References

This approach has been studied by, in particular, Michael Barr and Jon Beck. In addition to their work there is the monograph:

• John Duskin, Simplicial methods and the interpretation of “triple” cohomology“ Memoirs of the AMS 163, Amer. Math. Soc. (1975) [ISBN:978-1-4704-0645-5]