Comatrix Corings and Galois Comodules over Firm Rings

Constructing Infinite Comatrix Corings from Colimits

“…The natural framework needed to introduce infinite comatrix corings was proposed recently by Gómez Torrecillas and the third author in [12]. The philosophy is the following.…”

Morita Theory for Comodules Over Corings

“…By [19,Lemma 5.10], the combined isomorphism End A ′ (P ) ⊗ A A ∼ = A means exactly that A is a left ideal in End A ′ (P ). The other claim follows symmetrically.…”

“…Unit and counit of the adjunction (2.8) are given explicitly by (2.10) for N ∈ M R and M ∈ M C . In any case when R⊗ R Σ is an R-C bicomodule that is R-firmly projective as a right A-module, the theory developed in [19] can be applied to it. (We refer to [29, Section 4.2.5] for a more detailed treatment of structure theorems.)…”

“…Without this finiteness property it may have a dual only in a larger bicategory. In [19] it was assumed that a bimodule has a dual in the bicategory of firm bimodules over firm rings and a Galois theory in this setting was developed.…”

“…If R is a left T -module such that ι is left T -linear with respect to this action, then we will call R a left ideal for T , even if ι is not necessarily injective. In particular, [19,Lemma 5.10] applies to this situation.…”