Derived completion for comodules

On Corings and Comodules

It is shown that the categories of R-coalgebras for a commutative unital ring R and the category of A-corings for some R-algebra A as well as their respective categories of comodules are locally presentable.

Model theory of comodules

Flat Connections and Comodules

This is the text of a talk given at the Isaac Newton Institute in Cambridge on 4th August, 2006. This talk is motivated by a recent paper [A Kaygun and M Khalkhali, Hopf modules and noncommutative differential geometry, Lett. Math. Phys. 76 (2006), 77–91] in which Hopf modules appearing as coefficients in Hopf-cyclic cohomology are interpreted as modules with flat connections. We start by descr...

Fundamental Constructions for Coalgebras, Corings, and Comodules

We study the various categories of corings, coalgebras, and comodules from a categorical perspective. Emphesis is given to the question which properties of these categories can be seen as instances of general categorical resp. algebraic results. We obtain new results concerning the existence of limits and of factorizations of morphisms. MSC 2000: Primary 16W30, Secondary 18C05

On Galois Comodules

Generalising the notion of Galois corings, Galois comodules were introduced as comodules P over an A-coring C for which PA is finitely generated and projective and the evaluation map μC : Hom (P, C) ⊗S P → C is an isomorphism (of corings) where S = End(P ). It was observed that for such comodules the functors HomA(P,−)⊗S P and −⊗A C from the category of right A-modules to the category of right ...