The Brauer and Brauer-Taylor groups of a symmetric monoidal category

Enrico M. Vitale

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Constructing quantales and their modules from monoidal categories

Susan B. Niefield (1996)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

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Galois H-objects with a normal basis in closed categories. A cohomological interpretation.

José N. Alonso Alvarez, José Manuel Fernández Vilaboa (1993)

Publicacions Matemàtiques

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In this paper, for a cocommutative Hopf algebra H in a symmetric closed category C with basic object K, we get an isomorphism between the group of isomorphism classes of Galois H-objects with a normal basis and the second cohomology group H²(H,K) of H with coefficients in K. Using this result, we obtain a direct sum decomposition for the Brauer group of H-module Azumaya monoids with inner action: BM_inn(C,H) ≅ B(C) ⊕ H^2...