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Monday, April 5, 2021

**Abstract:** Following the work of Guillou, May, Merling, and Osorno, we give a (very) broad overview of the (2-)algebraic input that goes into their proof of the multiplicative equivariant Barratt-Priddy-Quillen theorem. Although it is not explicitly invoked, an underlying point we wish to make is the presence of bicategorical enrichment over the 2-category of categories internal to G-spaces when G is a finite group, where bicategorical enrichment is meant in the sense of e.g. Garner--Shulman, Franco, or Lack. This also opens up a pathway to concepts like enriched analogues of bicategorical concepts, less celebrated structures such as double multi or poly categories, and other devices which are related to the usual celebrities in formal category theory, which we might discuss existing or hoped applications for, time permitting. This talk is intended to be accessible with hardly any knowledge of homotopy theory. Please email vb8 at illinois dot edu for the zoom details.