Stable ∞-category

Summary

A stable ∞-category is an (∞,1)-category with a zero object and with fibers and cofibers of all morphisms. In it, fiber sequences and cofiber sequences coincide. Its homotopy category is a triangulated category in a natural way. Stable ∞-categories give a well-behaved replacement for triangulated categories: cones are functorial, and all finite limits and finite colimits exist. Main examples are the ∞-category of spectra and the derived ∞-category of a ring.