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Mathematics > Algebraic Geometry

arXiv:1812.01526 (math)
[Submitted on 4 Dec 2018 (v1), last revised 18 Mar 2021 (this version, v3)]

Title:On the uniqueness of infinity-categorical enhancements of triangulated categories

Authors:Benjamin Antieau
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Abstract:We study the problem of when triangulated categories admit unique infinity-categorical enhancements. Our results use Lurie's theory of prestable infinity-categories to give conceptual proofs of, and in many cases strengthen, previous work on the subject by Lunts--Orlov and Canonaco--Stellari. We also give a wide range of examples involving quasi-coherent sheaves, categories of almost modules, and local cohomology to illustrate the theory of prestable infinity-categories. Finally, we propose a theory of stable $n$-categories which would interpolate between triangulated categories and stable infinity-categories.
Comments: Updates and corrections to Section 8; discussion of recent results of Canonaco, Neeman, and Stellari
Subjects: Algebraic Geometry (math.AG); Algebraic Topology (math.AT)
MSC classes: 14A30, 14F08, 18E05, 18E10, 18G80
Cite as: arXiv:1812.01526 [math.AG]
  (or arXiv:1812.01526v3 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1812.01526

Submission history

From: Benjamin Antieau [view email]
[v1] Tue, 4 Dec 2018 17:01:39 UTC (42 KB)
[v2] Thu, 20 Dec 2018 18:10:22 UTC (48 KB)
[v3] Thu, 18 Mar 2021 13:27:10 UTC (47 KB)
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