Enriched Locally Generated Categories

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Authors

DI LIBERTI Ivan ROSICKÝ Jiří

Year of publication 2022
Type Article in Periodical
Magazine / Source Theory and Applications of Categories
MU Faculty or unit

Faculty of Science

Citation
Web http://www.tac.mta.ca/tac/volumes/38/17/38-17abs.html
Keywords locally generated category; nest; Gabriel-Ulmer duality; enriched category; metric spaces; Banach spaces; accessible monad
Description We introduce the notion of M-locally generated category for a factorization system (E,M) and study its properties. We offer a Gabriel-Ulmer duality for these categories, introducing the notion of nest. We develop this theory also from an enriched point of view. We apply this technology to Banach spaces showing that it is equivalent to the category of models of the nest of finite-dimensional Banach spaces.
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