Bachuki Mesablishvili

On Rational Pairings of Functors

AbstractIn the theory of coalgebras C over a ring R, the rational functor relates the category

Descent theory for schemes

_{C^*}{mathbb{M}}

Pure Morphisms are Effective for Modules

of modules over the algebra C* (with convolution product) with the category

Descent in Locally Presentable Categories

^C{mathbb{M}}

Effective descent morphisms for Banach modules

of comodules over C. This is based on the pairing of the algebra C* with the coalgebra C provided by the evaluation map

Azumaya Monads and Comonads

{rm ev}:C^*otimes_R Cto R

Bimonads and Hopf monads on categories

. The (rationality) condition under consideration ensures that

Entwining structures in monoidal categories

^C{mathbb{M}}

Galois functors and entwining structures

becomes a coreflective full subcategory of

NOTES ON BIMONADS AND HOPF MONADS

_{C^*}{mathbb{M}}