Monoid (category theory)

In category theory, a monoid (or monoid object) (M, μ, η) in a monoidal category (C, ⊗, I) is an object M together with two morphisms

such that the pentagon diagram

and the unitor diagram

commute. In the above notations, 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.