Enriched purity and presentability in Banach spaces
Abstract
The category $Ban$ of Banach spaces and linear maps of norm $\leq 1$ is locally $\aleph_1$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 to sets of morphisms having finitedimensional domains and separable codomains.
 Publication:

arXiv eprints
 Pub Date:
 June 2022
 arXiv:
 arXiv:2206.08546
 Bibcode:
 2022arXiv220608546R
 Keywords:

 Mathematics  Category Theory;
 Mathematics  Functional Analysis
 EPrint:
 24 pages