Accessibility and presentability in 2-categories

0559514 - MÚ 2024 RIV NL eng J - Článek v odborném periodiku
Di Liberti, Ivan - Loregian, F.
Accessibility and presentability in 2-categories.
Journal of Pure and Applied Algebra. Roč. 227, č. 1 (2023), č. článku 107155. ISSN 0022-4049. E-ISSN 1873-1376
Grant CEP: GA ČR(CZ) GX20-31529X
Institucionální podpora: RVO:67985840
Klíčová slova: higher category theory * homotopy theory
Obor OECD: Pure mathematics
Impakt faktor: 0.8, rok: 2022
Způsob publikování: Omezený přístup
https://doi.org/10.1016/j.jpaa.2022.107155

We outline a definition of accessible and presentable objects in a 2-category K endowed with a “KZ context”, that is to say a pair of lax-idempotent monads interacting in a prescribed way, this perspective suggests a unified treatment of many “Gabriel-Ulmer like” theorems, asserting how presentable objects arise as reflections of generating ones. We outline the notion of (Gabriel-Ulmer) envelope for a KZ context, sufficient to concoct Gabriel-Ulmer duality. We end the paper with a roundup of examples, involving classical (set-based and enriched), low dimensional category theory, and a perspective for future work, rooted in higher category theory and homotopy theory.
Trvalý link: https://hdl.handle.net/11104/0332790