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Mathematics > Category Theory

arXiv:1804.08710 (math)
[Submitted on 23 Apr 2018 (v1), last revised 25 May 2022 (this version, v6)]

Title:Accessibility and presentability in 2-categories

Authors:Ivan Di Liberti, Fosco Loregian
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Abstract:We outline a definition of accessible and presentable objects in a 2-category $\mathcal K$ 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.
Comments: Final version, accepted for publication on JPAA
Subjects: Category Theory (math.CT)
MSC classes: 18A05 18D05
Cite as: arXiv:1804.08710 [math.CT]
  (or arXiv:1804.08710v6 [math.CT] for this version)
  https://doi.org/10.48550/arXiv.1804.08710

Submission history

From: Fosco Loregian G. [view email]
[v1] Mon, 23 Apr 2018 20:11:29 UTC (32 KB)
[v2] Sat, 5 May 2018 12:44:00 UTC (35 KB)
[v3] Tue, 5 Jun 2018 13:46:40 UTC (45 KB)
[v4] Mon, 28 Jan 2019 10:25:08 UTC (37 KB)
[v5] Sat, 23 Jan 2021 17:13:15 UTC (31 KB)
[v6] Wed, 25 May 2022 08:57:34 UTC (42 KB)
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