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Pseudo symmetric multifunctors and application to K-theory

Diego Manco Berrio, University of Oregon
Thursday, October 19, 2023 - 3:30pm to 4:30pm
PDL C-401
Diego Manco Berrio

Multicategories have been used by Mandell and Elmendorf to encode multiplicative structures in the multicategory of permutative categories. They defined \(K\)-theory as a symmetric multifunctor from permutative categories to connective spectra and showed that it preserves the encoded multiplicative structures. Yau has shown that Mandell’s inverse \(K\)-theory multifunctor from \(\Gamma\)-categories to permutative categories preserves the action of the symmetric group by permuting factors only up to coherent isomorphisms, i.e., it is pseudo symmetric rather than symmetric, so it is not immediate that it preserves symmetric multiplicative structures. In this talk, we introduce pseudo symmetric multifunctors, including a new definition equivalent to the original one given by Yau, and show some examples and applications that imply that pseudo symmetric multifunctors, and in particular Mandell’s inverse -theory multifunctor, preserve certain symmetric multiplicative structures, like \(E_n\)-algebras.

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