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https://hdl.handle.net/10316/114837
Title: | On presheaf submonads of quantale-enriched categories | Authors: | Clementino, Maria Manuel Fitas, Carlos |
Keywords: | Quantale; V -category; distributor; laxidempotent monad; presheaf monad; free cocompletion monad; Ballmonad; Lawvere-Cauchy completion monad | Issue Date: | 2023 | Publisher: | Taylor & Francis | Project: | UIDB/00324/2020 FCTPh.D.grant SFRH/BD/150460/2019 |
Serial title, monograph or event: | Quaestiones Mathematicae | Volume: | 46 | Issue: | 10 | Abstract: | This paper focuses on the presheaf monad, or the free cocompletion monad, and its submonads on the realm of V-categories, for a quantale V. First we present two characterisations of presheaf submonads, both using V-distributors: one based on admissible classes of V-distributors, and other using Beck-Chevalley conditions on V-distributors. Further we prove that lax idempotency for 2-monads on V-Cat can be characterized via such a Beck-Chevalley condition. Then we focus on the study of the Eilenberg-Moore categories of algebras for our monads, having as main examples the formal ball monad and the Lawvere-Cauchy completion monad. | URI: | https://hdl.handle.net/10316/114837 | ISSN: | 1607-3606 1727-933X |
DOI: | 10.2989/16073606.2022.2144532 | Rights: | openAccess |
Appears in Collections: | I&D CMUC - Artigos em Revistas Internacionais FCTUC Matemática - Artigos em Revistas Internacionais |
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On presheaf submonads of quantale-enriched categories.pdf | 749.1 kB | Adobe PDF | View/Open |
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