English

Enriched Locally Generated Categories

Category Theory 2025-10-16 v2

Abstract

We introduce the notion of M\mathcal{M}-locally generated category for a factorization system (E,M)(\mathcal{E},\mathcal{M}) and study its properties. We offer a Gabriel-Ulmer duality for these categories, introducing the notion of nest. We develop this theory also from an enriched point of view. We apply this technology to Banach spaces showing that it is equivalent to the category of models of the nest of finite-dimensional Banach spaces.

Keywords

Cite

@article{arxiv.2009.10980,
  title  = {Enriched Locally Generated Categories},
  author = {Ivan Di Liberti and Jiří Rosický},
  journal= {arXiv preprint arXiv:2009.10980},
  year   = {2025}
}

Comments

Comments are welcome! v2: very mild update. 2.9 and 2.10 are new examples

R2 v1 2026-06-23T18:44:15.148Z