Categories in category theory | Objects (category theory) | Monoidal categories
Monoid (category theory)
In category theory, a branch of mathematics, a monoid (or monoid object, or internal monoid, or algebra) (M, μ, η) in a monoidal category (C, ⊗, I) is an object M together with two morphisms * μ: M ⊗ M → M called multiplication, * η: I → M called unit, such that the pentagon diagram and the unitor diagram 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. (Wikipedia).
