On the uniqueness of infinity-categorical enhancements of triangulated categories

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.

Updates and corrections to Section 8; discussion of recent results of Canonaco, Neeman, and Stellari

References in corpus (2)

• Higher Topos Theory
• A note on K-theory and triangulated derivators

Cited by in corpus (1)

• A derived Gabriel-Popescu theorem for t-structures via derived injectives