Enriched purity and presentability in Banach spaces

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Authors

ROSICKÝ Jiří

Year of publication 2023
Type Article in Periodical
Magazine / Source Communications in Algebra
MU Faculty or unit

Faculty of Science

Citation
Web https://doi.org/10.1080/00927872.2023.2228412
Doi http://dx.doi.org/10.1080/00927872.2023.2228412
Keywords Banach spaces; linear maps; finite-dimensional; separable codomains; metric spaces
Description The category Ban of Banach spaces and linear maps of norm ?1 is locally ?1-presentable but not locally finitely presentable. We prove, however, that Ban is locally finitely presentable in the enriched sense over complete metric spaces. Moreover, in this sense, pure morphisms are just ideals of Banach spaces. We characterize classes of Banach spaces approximately injective with respect to sets of morphisms having finite-dimensional domains and separable codomains.
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