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

TL;DR

This paper extends Masuoka's theorem into a bicategorical framework, providing a non-commutative generalization that relates invertible bimodules and cohomology in functor categories.

Contribution

It introduces a bicategorical version of Masuoka's theorem, broadening its applicability to non-commutative settings involving bimodules over functor categories.

Findings

Established a bicategorical analogue of Masuoka's theorem.

Connected invertible bimodules with Amitsur cohomology in a bicategorical context.

Extended classical results to non-commutative and categorical frameworks.

Abstract

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