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Stable Infinity-Categories

Content

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

Introduction

Stable \infty-Categories

The Homotopy Category of a Stable \infty-Category

Properties of Stable \infty-Categories

Exact Functors

t-Structures and Localization

Boundedness and Completeness

Stabilization

The \infty-Category of Spectra

Excisive Functors

Filtered Objects and Spectral Sequences

The \infty-Categorical Dold-Kan Correspondence

Homological Algebra

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

Presentable Stable \infty-Categories

Accessible t-Structures

category: reference

Last revised on September 2, 2018 at 23:50:21. See the history of this page for a list of all contributions to it.