2023/04/28 by Andrew Slattery, Slattery, Andrew · 2 citations
Computer Science · Mathematics · #18A05 #18M65 (Secondary) #18N15 (Primary) 18D65 #Advanced Algebra and Logic #Advanced Topology and Set Theory #Category Theory (math.CT) #FOS: Mathematics #Logic, Reasoning, and Knowledge
paper · pdf · doi:10.48550/arxiv.2304.14788
openalex publication_date 2023/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We extend the classical work of Kock on strong and commutative monads, as well as the work of Hyland and Power for 2-monads, in order to define strong and pseudocommutative relative pseudomonads. In order to achieve this, we work in the more general setting of 2-multicategories rather than monoidal 2-categories. We prove analogous implications to the classical work: that a strong relative pseudomonad is a pseudo-multifunctor, and that a pseudocommutative relative pseudomonad is a multicategorical pseudomonad. Furthermore, we extend the work of López Franco with a proof that a lax-idempotent strong relative pseudomonad is pseudocommutative. We apply the results of this paper to the example of the presheaf relative pseudomonad.