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arXiv · 1812.01526

On the uniqueness of infinity-categorical enhancements of triangulated categories

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.

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Benjamin Antieau. 2018-12-04. On the uniqueness of infinity-categorical enhancements of triangulated categories. https://arxiv.org/abs/1812.01526

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