Stefan Schwede and Brooke Shipley, in their article “A uniqueness theorem for stable homotopy theory” announced the Uniqueness Theorem, which have multiple applications, mainly it is useful for proving the first step of rigidity by constructing the Quillen functor. In my talk, I will announce the theorem, explain the technical terms: Spectra, Quillen functor pair, model category structure….
Furthermore, if I have enough time, I will talk about the rigidity question.