The Structure of Corings: Induction Functors, Maschke-Type Theorem, and Frobenius and Galois-Type Properties

By Tomasz Brzezinski. 2000

178 citations recorded by the source corpus.

Given a ring A and an A-coring C, we study when the forgetful functor from the category of right C-comodules to the category of right A-modules and its right adjoint −⊗AC are separable. We then proceed to study when the induction functor −⊗AC is also the left adjoint of the forgetful functor. This question is closely related to the problem when A→ AHom(C,A) is a Frobenius extension. We introduce the notion of a Galois coring and analyse when the tensor functor over the subring of A fixed under the coaction of C is an equivalence. We also comment on possible dualisation of the notion of a coring.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c3c68a60ffbb78dadedd7599623cae6da80d5f04

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In Algebra and Number Theory

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Citations in the corpus

Morita theory for corings and cleft entwining structures (2002, background): “Recall that x ∈C is called grouplike if ΔC(x) = x ⊗A x and eC(x) = 1. G(C) is the set of all grouplike elements inC . We have the following interpretations of G(C) (see e.g. [12, Sec 4.8], [ 6 ]).”
Galois theory for comatrix corings: Descent theory, Morita theory, Frobenius and separability properties (2004, background): “This was discussed by Brzezi´nski in [ 6 ].”
Homological algebra of semimodules and semicontramodules. Semi-infinite homological algebra of assoc (2007, background): “An important particular case of the above construction of semialgebras was considered in [15].”