Monoid (category theory)
commute. In the above notation, 1 is the identity morphism of M, I is the unit element and α, λ and ρ are respectively the associativity, the left identity and the right identity of the monoidal category C.
Dually, a comonoid in a monoidal category C is a monoid in the dual category Cop.
Suppose that the monoidal category C has a symmetry γ. A monoid M in C is commutative when μ o γ = μ.
Given two monoids (M, μ, η) and (M', μ', η') in a monoidal category C, a morphism f : M → M ' is a morphism of monoids when
The category of monoids in C and their monoid morphisms is written MonC.