  Yau defines the notion of pseudo symmetric $\mathbf{Cat}$-enriched
multifunctor between $\mathbf{Cat}$-enriched multicategories and proves that
Mandell's inverse $K$-theory multifunctor is pseudo symmetric. We prove a
coherence theorem for pseudo symmetric $\mathbf{Cat}$-enriched multifunctors.
As an application, we prove that pseudo symmetric $\mathbf{Cat}$-enriched
multifunctors, and in particular Mandell's inverse $K$-theory, preserve
$E_n$-algebras ($n=1,2,...,\infty$), at the cost of changing the parameterizing
$E_n$-operad.
