• Corpus ID: 249848103

Enriched purity and presentability in Banach spaces

  title={Enriched purity and presentability in Banach spaces},
  author={Jivr'i Rosick'y},
. 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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