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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 ...

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 ...

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 $\bot$ on ...

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 $X$, $\text{Vect}_G(X)$, ...