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9 votes
5 answers
1k views

English Reference for the Bénabou-Roubaud theorem

The Bénabou-Roubaud theorem links fibrational descent theory with monadicity. Particularly, it says that given a bifibration satisfying the Beck-Chevalley condition w.r.t some arrow p in the base ...
Arrow's user avatar
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30 votes
2 answers
3k views

Why are monadicity and descent related?

This question is probably too vague for experts, but I really don't know how to avoid it. I've read in several places that under mild conditions, a morphism is an effective descent morphism iff the ...
Arrow's user avatar
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6 votes
1 answer
560 views

Higher descent cohomology

Descent cohomology for a comonad is defined at degrees 0 and 1 by Mesablishvili in his paper "On Descent Cohomology" (as well as by many other authors in many other contexts). For a comonad on ...
Jonathan Beardsley's user avatar
21 votes
0 answers
1k views

Can we describe equivariant vector bundles of free group action in terms of descent theory (Barr-Beck theorem)?

It is well known that for a compact topological group G acts (say, from the right) freely on a compact space X. Then the category of equivariant complex vector bundles on X, VectG(X), ...
Zhaoting Wei's user avatar
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