Background
Basic concepts
equivalences in/of $(\infty,1)$-categories
Universal constructions
Local presentation
Theorems
Extra stuff, structure, properties
Models
This entry provides a hyperlinked index for
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 $(\infty,1)$-categories of “stable objects”, i.e. of objects that behave like spectra in that for each object $X$ there not only its loop space object $\Omega X$ but also conversely, $X$ is the loop space object of another object $\Sigma X$.
The definition is very simple. The homotopy category of a stable $(\infty,1)$-category is shown to be a triangulated category: the comparatively complicated axioms of triangulated categories follow from the simple $(\infty,1)$-categorical axioms. Large chunks of homological algebra is then re-examined from the more natural point of view of stable $(\infty,1)$-categories.
Last revised on September 3, 2018 at 03:50:21. See the history of this page for a list of all contributions to it.