Stable Infinity Categories

Details Stable Infinity Categories Stable Infinity Categories

2006-08-09

arxiv.org/abs/math/0608228v5

Mathematics

Category Theory

73 Pages; corrected some minor typographical and mathematical errors 2/10/07: added material on filtered objects and spectral

Scientific paper

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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