symmetric monoidal (∞,1)-category of spectra
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.
This approach has been studied by, in particular, Michael Barr and Jon Beck. In addition to their work there is the monograph:
Last revised on August 20, 2022 at 10:44:55. See the history of this page for a list of all contributions to it.