Enriched purity and presentability in Banach spaces
| Authors | |
|---|---|
| Year of publication | 2023 |
| Type | Article in Periodical |
| Magazine / Source | Communications in Algebra |
| MU Faculty or unit | |
| 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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