DubTop Seminar: the inverse K-theory multifunctor

Thirty years ago, Thomason showed that Segal’s K-theory functor is an equivalence between a stable homotopy category of symmetric monoidal categories and the stable homotopy category of connective spectra, passing through certain category-valued functors. We will present Mandell’s alternate proof of this result exhibiting an explicit inverse K-theory functor, reviewing the necessary (multi)categorical background, as well as Elmendorf and Johnson-Yau’s proofs that this functor also preserves multiplicative data. Finally, as is the custom and my true motivation, we conjecture how this may be generalized equivariantly.