# Enriched purity and presentability in Banach spaces

@inproceedings{Rosicky2022EnrichedPA, title={Enriched purity and presentability in Banach spaces}, author={Jivr'i Rosick'y}, year={2022} }

. The category Ban of Banach spaces and linear maps of norm ≤ 1 is locally ℵ 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 ﬁnite-dimensional domains and separable codomains. prove that pure morphisms of Banach spaces…

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