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Hopf-Galois extensions for monoidal Hom-Hopf algebras

Yuanyuan Chen, Liangyun Zhang (2016)

Colloquium Mathematicae

Hopf-Galois extensions for monoidal Hom-Hopf algebras are investigated. As the main result, Schneider's affineness theorem in the case of monoidal Hom-Hopf algebras is shown in terms of total integrals and Hopf-Galois extensions. In addition, we obtain an affineness criterion for relative Hom-Hopf modules which is associated with faithfully flat Hopf-Galois extensions of monoidal Hom-Hopf algebras.

How algebraic is algebra?

Adámek, Jiří, Lawvere, F.W., Rosický, Jiří (2001)

Theory and Applications of Categories [electronic only]

How to construct a Hovey triple from two cotorsion pairs

James Gillespie (2015)

Fundamenta Mathematicae

Let be an abelian category, or more generally a weakly idempotent complete exact category, and suppose we have two complete hereditary cotorsion pairs ( , ˜ ) and ( ˜ , ) in satisfying ˜ and ˜ = ˜ . We show how to construct a (necessarily unique) abelian model structure on with (resp. ˜ ) as the class of cofibrant (resp. trivially cofibrant) objects, and (resp. ˜ ) as the class of fibrant (resp. trivially fibrant) objects.

Hu's Primal Algebra Theorem revisited

Hans-Eberhard Porst (2000)

Commentationes Mathematicae Universitatis Carolinae

It is shown how Lawvere's one-to-one translation between Birkhoff's description of varieties and the categorical one (see [6]) turns Hu's theorem on varieties generated by a primal algebra (see [4], [5]) into a simple reformulation of the classical representation theorem of finite Boolean algebras as powerset algebras.

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