stable homotopy theory
loop space object
suspension object
stable (∞,1)-category
stabilization
triangulated category
stable (∞,1)-category of spectra
spectrum
stable homotopy category
smash product of spectra
symmetric monoidal smash product of spectra
A-∞ ring
E-∞ ring
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The stable homotopy category is the homotopy category of the stable (infinity,1)-category of spectra.
This is the category studied in stable homotopy theory.