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A coherence theorem for pseudo symmetric multifunctors

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Diego Manco

Donald Yau defined the notion of pseudo symmetric Cat-enriched multifunctor between Cat-enriched multicategories and proved that Mandell's inverse K-theory multifunctor is pseudo symmetric. We prove a coherence theorem for pseudo symmetric Cat-enriched multifunctors. As an application we prove that pseudo symmetric Cat-enriched multifunctors, and in particular Mandell's inverse K-theory, preserve Σ-free E_n-algebras (n=1,2,...,∞), at the cost of changing the parameterizing Σ-free E_n-operad O for the Σ-free E_n-operad O x EΣ_*.

Keywords:
Multicategories, K-theory

2020 MSC:
Primary 18M65, 19D23; Secondary 55P47, 55P43.

*Theory and Applications of Categories,*
Vol. 41, 2024,
No. 47, pp 1644-1678.

Published 2024-10-29.

http://www.tac.mta.ca/tac/volumes/41/47/41-47.pdf

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