Coherence for Pseudo Commutative Monads
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914046080450560 |
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| author | Manco, Diego |
| author_facet | Manco, Diego |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_15101 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Coherence for Pseudo Commutative Monads Manco, Diego Category Theory 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. |
| title | Coherence for Pseudo Commutative Monads |
| topic | Category Theory |
| url | https://arxiv.org/abs/2509.15101 |