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Tuesday, November 12, 2019

**Abstract:** Symmetric monoidal categories have (at least) two allures to homotopy theorists: they describe the algebraic structure appearing in many categories of interest, and they effectively model all connective spectra. Equivariantly, both of these tasks become more interesting, as the category of (connective) genuine equivariant spectra is significantly more subtle. In this talk, I introduce a new model for equivariant symmetric monoidal categories which both describes the algebraic structure in equivariant categories and has a K-theory functor to genuine G-spectra. I will give several examples and applications, including comparisons to many previously proposed models of genuine symmetric monoidal categories and equivariant algebra.