We describe a simplified categorical approach to Galois descent theory. It is well known that Galois descent is a special case of Grothendieck descent, and that under mild additional conditions the category of Grothendieck descent data coincides with the Eilenberg-Moore category of algebras over a suitable monad. This also suggests using monads directly, and our monadic approach to Galois desce...

We describe a simplified categorical approach to Galois descent theory. It is well known that Galois descent is a special case of Grothendieck descent, and that under mild additional conditions the category of Grothendieck descent data coincides with the Eilenberg-Moore category of algebras over a suitable monad. This also suggests using monads directly, and our monadic approach to Galois desce...

In this paper, we introduce the notion of Grothendieck enriched categories for over a sufficiently nice monoidal category $$\mathcal {V}$$ , generalizing classical categories. Then establish Gabriel-Popescu type theorem We also prove that property being is preserved under change base by right adjoint functor. particular, if take as complexes abelian groups, obtain dg As an application main resu...

This problem was solved in the negative by Bridson and Grunewald in [6] who produced many examples of groups G, and proper subgroups H for which û an isomorphism. The method of proof of [6] was a far reaching generalization of an example of Platonov and Tavgen [33] that produced finitely generated examples that answered Grothendieck’s problem in the negative (see also [5]). Henceforth, we will ...