Background
Basic concepts
equivalences in/of -categories
Universal constructions
Local presentation
Theorems
Extra stuff, structure, properties
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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 -categories of “stable objects”, i.e. of objects that behave like spectra in that for each object there not only its loop space object but also conversely, is the loop space object of another object .
The definition is very simple. The homotopy category of a stable -category is shown to be a triangulated category: the comparatively complicated axioms of triangulated categories follow from the simple -categorical axioms. Large chunks of homological algebra is then re-examined from the more natural point of view of stable -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.