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.
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