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arXiv · 2509.15101

Coherence for Pseudo Commutative Monads

Diego Manco
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Abstract

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.

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Diego Manco. 2025-09-18. Coherence for Pseudo Commutative Monads. https://arxiv.org/abs/2509.15101

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