We show, for an arbitrary adjunction F U : B â†’ A with B Cauchy complete, that the functor F is comonadic if and only if the monad T on A induced by the adjunction is of effective descent type,â€¦ (More)

Interpreting entwining structures as special instances of J. Beckâ€™s distributive law, the concept of entwining module can be generalized for the setting of arbitrary monoidal category. In this paper,â€¦ (More)

Galois comodules over a coring can be characterised by properties of the relative injective comodules. They motivated the definition of Galois functors over some comonad (or monad) on any categoryâ€¦ (More)

One reason for the universal interest in Frobenius algebras is that their characterisation can be formulated in arbitrary categories: a functor K : A â†’ B between categories is Frobenius if thereâ€¦ (More)

We give a complete characterization of the class of quasi-compact morphisms of schemes that are stable effective descent morphisms for the SCHEMESindexed category given by quasi-coherent sheaves ofâ€¦ (More)

In the theory of coalgebras C over a ring R, the rational functor relates the category Câˆ—M of modules over the algebra Câˆ— (with convolution product) with the category CM of comodules over C. This isâ€¦ (More)

We prove that pure morphisms of commutative rings are effective Adescent morphisms where A is a (COMMUTATIVE RINGS)-indexed category given by (i) finitely generated modules, or (ii) flat modules, orâ€¦ (More)

For a generalisation of the classical theory of Hopf algebra over fields, A. BruguiÃ¨res and A. Virelizier study opmonoidal monads on monoidal categories (which they called bimonads). In a recentâ€¦ (More)