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https://hdl.handle.net/10316/113614
Title: | Artin glueings of toposes as adjoint split extensions | Authors: | Faul, Peter F. Manuell, Graham Siqueira, José |
Keywords: | Gluing; Artin-Wraith glueing; Topoi; Left-exact functor; Weakly Schreier; Baer sum | Issue Date: | 9-Dec-2020 | Publisher: | Elsevier | Project: | Coordenação de Aperfeiçoamento de Pessoal de Nível Superior -Brasil (CAPES), which supported the CAPES scholar José Siqueira (process n◦88881.128278/2016-01) | Serial title, monograph or event: | Journal of Pure and Applied Algebra | Volume: | 227 | Issue: | 5 | Abstract: | Artin glueings of frames correspond to adjoint split extensions in the category of frames and finite-meet-preserving maps. We extend these ideas to the setting of toposes and show that Artin glueings of toposes correspond to a 2-categorical notion of adjoint split extensions in the 2-category of toposes, finite-limit-preserving functors and natural transformations. A notion of morphism between these split extensions is introduced, which allows the category Ext(H,N) to be constructed. We show that Ext(H,N) is contravariantly equivalent to Hom(H,N), and moreover, that this can be extended to a 2-natural contravariant equivalence between the Hom 2-functor and a naturally defined Ext 2-functor. | Description: | 41 pages. Fixed minor errors and improved clarity. Includes some proofs we had to remove from the published version | URI: | https://hdl.handle.net/10316/113614 | ISSN: | 00224049 | DOI: | 10.1016/j.jpaa.2022.107273 | Rights: | openAccess |
Appears in Collections: | I&D CMUC - Artigos em Revistas Internacionais |
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Artin glueings of toposes as adjoint split extensions.pdf | 614.66 kB | Adobe PDF | View/Open |
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