nLab co-unitality

Redirected from "counitality".
Contents

Contents

Idea

The formal dual of unitality:

An object in a monoidal category which is equipped with a comultiplication map which satisfies both co-unitality and co-associativity is called a co-monoid.

Definition

Given a monoidal category (𝒞,)(\mathcal{C}, \otimes) and an object AA in 𝒞\mathcal{C} equipped with a morphism (“co-multiplication”) Δ:AAA\Delta \colon A \longrightarrow A \otimes A, and a morphism ϵ:AI\epsilon \colon A \longrightarrow I, ϵ\epsilon is called a counit if the following diagrams commute

where II is the unit of the monoidal category and λ,ρ\lambda, \rho are the left and right unitors respectively.

Last revised on May 11, 2024 at 19:36:15. See the history of this page for a list of all contributions to it.