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Stable Infinity-Categories

Context

(,1)(\infty,1)-Category theory

Stable Homotopy theory

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on stable homotopy theory in terms of stable ∞-categories.

Based on the theory of (∞,1)-categories as developed in his book Higher Topos Theory, the author studies here (,1)(\infty,1)-categories of “stable objects”, i.e. of objects that behave like spectra in that for each object XX there not only its loop space object ΩX\Omega X but also conversely, XX is the loop space object of another object ΣX\Sigma X.

The definition is very simple. The homotopy category of a stable (,1)(\infty,1)-category is shown to be a triangulated category: the comparatively complicated axioms of triangulated categories follow from the simple (,1)(\infty,1)-categorical axioms. Large chunks of homological algebra is then re-examined from the more natural point of view of stable (,1)(\infty,1)-categories.

Content

1 Introduction

2 Stable \infty-Categories

3 The Homotopy Category of a Stable \infty-Category

4 Properties of Stable \infty-Categories

5 Exact Functors

6 t-Structures and Localization

7 Boundedness and Completeness

8 Stabilization

9 The \infty-Category of Spectra

10 Excisive Functors

11 Filtered Objects and Spectral Sequences

12 The \infty-Categorical Dold-Kan Correspondence

13 Homological Algebra

14 The Universal Property of D (A)D^-(A)

15 Presentable Stable \infty-Categories

16 Accessible t-Structures

category: reference

Revised on September 3, 2012 22:10:30 by Urs Schreiber (131.174.188.82)