A COHERENCE THEOREM FOR PSEUDO SYMMETRIC MULTIFUNCTORS

Donald Yau defined the notion of pseudo symmetric Cat- enriched multifunctor between Cat- enriched multicategories and proved that Mandell's inverse Ktheory 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 Sigma-free E-n-algebras (n = 1, 2, ..., infinity ), at the cost of changing the parameterizing Sigma-free E-n-operad O for the Sigma-free E-n-operad O x E Sigma(& lowast;).