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On the uniqueness of infinity-categorical enhancements of triangulated categories

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arxiv 1812.01526 v3 pith:ROI6DFJ4 submitted 2018-12-04 math.AG math.AT

Benjamin Antieau This is my paper · ORCID
classification math.AGmath.AT
keywords categoriesinfinity-categoriestheorytriangulatedenhancementsgiveinfinity-categoricalprestable
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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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  1. The derived $\infty$-category of Frobenius modules

    math.AG 2025-10 conditional novelty 6.0 of 10

    For any quasi-compact F_p-scheme with affine diagonal, the derived ∞-category of Frobenius modules is t-exactly equivalent to Frobenius modules on the derived ∞-category, and both satisfy Zariski descent.

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