English

Stable Infinity Categories

Category Theory 2009-05-08 v5 Algebraic Topology

Abstract

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.

Keywords

Cite

@article{arxiv.math/0608228,
  title  = {Stable Infinity Categories},
  author = {Jacob Lurie},
  journal= {arXiv preprint arXiv:math/0608228},
  year   = {2009}
}

Comments

73 Pages; corrected some minor typographical and mathematical errors 2/10/07: added material on filtered objects and spectral sequences. 9/19/07: various minor changes. 5/8/9: Some of the material on constructing stabilizations has been made more explicit