group cohomology, nonabelian group cohomology, Lie group cohomology
cohomology with constant coefficients / with a local system of coefficients
differential cohomology
symmetric monoidal (∞,1)-category of spectra
Higher monadic descent is the generalization of the notion of monadic descent from category theory to higher category theory. It relates to the descent of ∞-stacks as ordinary monad descent relates to stacks.
See also cohomological descent.
For a homomorphism of suitable monoids, there is the corresponding pull-push adjunction (extension of scalars restriction of scalars) on categories of modules
The bar construction of the corresponding monad is the corresponding Amitsur complex.
(e.g. Hess 10, section 6)
A pseudomonadicity theorem for pseudomonads is proved in Theorem 3.6 of:
and sharpened in Theorem A.2 of:
(see Remark A.3 for a comparison with the work of Creurer et al.).
More generally, this paper discusses a notion of 2-fibered categories, originally defined in Gray’s work, and then again introduced and discussed at length in this paper. The appendix also discusses a 2-categorical version of Beck-Chevalley condition needed for a comparison with 2-monadic descent.
A comprehensive treatment in the context of (∞,1)-category-theory, general theory of (∞,1)-monads and their monadicity theorem is in
later absorbed as
Unfortunately, Kontsevich‘s monadicity theorem (July 2004) which is in the setup of A-∞-categories, still remains unpublished. The triangulated version is in Rosenberg’s lectures
Its proof is based on Verdier's abelianization functor.
See also, for another point of view,
Discussion of monadic descent for simplicially enriched categories is in
and for quasi-categories in
Last revised on April 5, 2023 at 20:57:15. See the history of this page for a list of all contributions to it.