2016/10/04 by José Gómez-Torrecillas, Gómez-Torrecillas, J., Bachuki Mesablishvili +1
Mathematics · #16D20 #16T15 #18D05 #18D10 #18G30 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.1610.00905
openalex publication_date 2016/10/04 · openalex created_date 2016/10/14 · openalex updated_date 2026/07/28
We prove that the classical result asserting that the relative Picard group of a faithfully flat extension of commutative rings is isomorphic to the first Amitsur cohomology group stills valid in the realm of symmetric monoidal categories. To this end, we built some group exact sequences from an adjunction in a bicategory, which are of independent interest. As a particular byproduct of the evolving theory, we prove a version of Hilbert's theorem 90 for cocommutatvie coalgebra coextensions (=surjective homomorphisms).