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Stable Infinity Categories

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arxiv math/0608228 v5 pith:QMWCMK2M submitted 2006-08-09 math.CT math.AT

classification math.CTmath.AT
keywords categoryinfinitystablecategorieshomotopyabelianaccountcharacterize
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This paper is an expository account of the theory of stable infinity categories. We prove that the homotopy category of a stable infinity category is triangulated, and that the collection of stable infinity categories is closed under a variety of constructions. We also explain how to construct the derived category of an abelian category (with enough projective objects) as the homotopy category of a suitable stable infinity category; moreover, we characterize this stable infinity category by a universal mapping property.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The category of necklaces is a test category

    math.CT 2026-07 accept novelty 6.0 of 10

    The category of necklaces is a test category, so its presheaf category is a model for homotopy types.

  2. The $S_\bullet$-construction as an equivalence between 2-Segal spaces and stable augmented double Segal spaces

    math.AT 2024-12 conditional novelty 2.0 of 10

    An expository note restating the proven equivalence between 2-Segal spaces and stable augmented double Segal spaces via path and S-constructions, with proof sketches that defer to the original papers.

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