A bicategorical version of Masuoka's theorem. Applications to bimodules over functor categories and to firm bimodules

2008/08/19 by José Gómez-Torrecillas, Gómez-Torrecillas, J., Bachuki Mesablishvili +1
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Rings, Modules, and Algebras #Algebraic structures and combinatorial models

paper · pdf · doi:10.48550/arxiv.0808.2553

Abstract

We give a bicategorical version of the main result of A. Masuoka (Corings and invertible bimodules, \em Tsukuba J. Math. 13 (1989), 353--362) which proposes a non-commutative version of the fact that for a faithfully flat extension of commutative rings R ⊆ S, the relative Picard group Pic(S/R) is isomorphic to the Amitsur 1--cohomology group H¹(S/R,U) with coefficients in the units functor U.

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