Stable homotopy theories, i.e. pointed theories for which the suspension is an equivalence, are shown to form a reflective sub-2-category. Thus the stabilization T → StabT is characterized by a universal property. This permits a perspicuous proof of the existence of the coherent symmetric smash product in the standard stable homotopy theory. It is to be noted that spectra appear only in the proofs, not the statements of theorems.
Heller, A. (1997). Stable homotopy theories and stabilization. Journal of Pure and Applied Algebra, 115(2), 113–130. https://doi.org/10.1016/S0022-4049(96)00116-8