Mario Román


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Endocells of a map pseudomonoid are duoidal

Last updated Sep 8, 2023

Proposition. Let $(𝔸,m,u,d,e)$ be an adjoint pseudomonoid. The endomaps, $\operatorname{End}(𝔸)$, form a duoidal category with composition and convolution.

Example. In the monoidal bicategory of profunctors, any monoidal category $(𝔸,⊗,I)$ induces a duoidal structure on its endoprofunctors, given by composition and Day convolution.


Tags: Map pseudomonoid, duoidal category, Compositional dependencies with duoidals.

This results appears in Section 9.1 of Commutativity (Garner, Lopez Franco, 2015), which in turn cites Proposition 4 of Monoidal Bicategories and Hopf Algebroids (Day, Street, 1997).