Some exact sequences associated with adjunctions in bicategories. Applications
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- by J. Gómez-Torrecillas and B. Mesablishvili PDF
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Abstract:
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 still is valid in the realm of symmetric monoidal categories. To this end, we build 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 cocommutative coalgebra coextensions (=surjective homomorphisms).References
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Additional Information
- J. Gómez-Torrecillas
- Affiliation: Departament of Algebra and CITIC, Universidad de Granada, E18071 Granada, Spain
- Email: gomezj@ugr.es
- B. Mesablishvili
- Affiliation: I. Javakhishvili Tbilisi State University, Faculty of Exact and Natural Sciences, Department of Mathematics, 2 University St., 0186, Tbilisi, Georgia
- MR Author ID: 249211
- Email: bachi@rmi.ge
- Received by editor(s): October 4, 2016
- Received by editor(s) in revised form: March 23, 2017
- Published electronically: February 14, 2019
- Additional Notes: This research partially supported by grant MTM2013-41992-P from the Ministerio de Economía y Competitividad of the Spanish Government and from FEDER
The second named author was supported by Shota Rustaveli National Science Foundation Grants DI/18/5- 113/13 and FR/189/5- 113/14 - © Copyright 2019 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 371 (2019), 8255-8295
- MSC (2010): Primary 16D20, 16T15, 18D05, 18D10, 18G30
- DOI: https://doi.org/10.1090/tran/7625
- MathSciNet review: 3955547