Corings and Comodules

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The Tilting–Cotilting Correspondence (2017, background): “ver general coalgebras. Let A be an associative ring and Cbe an A-A-bimodule endowed with a coassociative, counital coring structure with the comultiplication map ∆: C −→C⊗A C and the counit map C−→A [19], [58, Section 1.1], [63, Section 2.5]. Assume that C is a ﬂat right A-module; then the category”
On Categories of Monoids, Comonoids, and Bimonoids (2008, unknown): “[4]).”
Derived equivalences and stable equivalences of Morita type, I (2008, background): “An extension B ↪→ A of algebras is a Frobenius extension if and only if BA is a finitely generated projective module and HomB(BA,B) A as A-B-bimodules (see, for example, [9], 40.”
MONADS AND COMONADS ON MODULE CATEGORIES (2008, background): “In the particular case of a left D-comodule N , it reduces to the usual notion of a D-Galois left comodule in [8] by putting A = C = EndD(N).”
Partial (Co)Actions of Hopf Algebras and Partial Hopf-Galois Theory (2006, background): “The Galois theory of Dokuchaev et al. (2007) can then be considered as a special case of the Galois theory of corings (see Brzeziński, 2002; Brzeziński and Wisbauer, 2003; Caenepeel, 2004; Wisbauer, 2004).”