Mario Román


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Map pseudomonoid

Last updated Sep 8, 2023

# Definition

In a monoidal bicategory, a monoid and a comonoid may be related by two adjunctions. An adjoint monoid is a monoid-comonoid pair where the multiplication is left adjoint to the comultiplication and the unit is left adjoint to the counit.

Definition. Let $𝔹$ be a monoidal bicategory. An adjoint monoid $M ∈ 𝔹$ is both a 2-monoid $(M,m,u)$ and a 2-comonoid $(M,d,e)$ such that the multiplication is adjoint to the comultiplication, $m \dashv d$ and the unit is adjoint to the counit, $u \dashv e$.


Tags: pseudomonoid, Handbook of Categorical Algebra (Borceux). #aug21