equivalences in/of $(\infty,1)$-categories
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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 $(\infty,1)$-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.