Thick Subcategory

A thick subcategory of a triangulated category is a full triangulated subcategory closed under retracts. The thick subcategory generated by specified objects is their closure under equivalences, finite direct sums, integer shifts, cofiber sequences, and retracts. It does not include arbitrary infinite sums or tensoring with arbitrary objects unless separately required. For example, the sphere spectrum generates the finite spectra as a thick subcategory of the stable homotopy category. The Hahn-Wilson conjecture uses ordinary thick closure in the category of -complete spectra.