We prove that the free algebra functor associated to a symmetric, pseudo commutative 2-monad, from the underlying symmetric monoidal 2-category to the 2-category of algebras and pseudo maps over the 2-monad can be enhanced to a multifunctor. Furthermore, we prove that this multifunctor is pseudo symmetric. Our proof implies coherence results for both symmetric and non-symmetric pseudo commutative 2-monads conjectured by Hyland and Power.
Keywords: Multicategories, Coherence, 2-monads
2020 MSC: Primary: 18N15, 18M65; Secondary: 18N10, 18F25
Theory and Applications of Categories, Vol. 45, 2026, No. 40, pp 1683-1731.
Published 2026-06-23.
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