Let be the category with objects all commutative rings with identity and morphisms all ring homomorphisms

Let ℓ  be the category with objects all commutative rings with identity and morphisms all ring homomorphisms ∫: R → S such that ∫{1_R) = 1_s. Then the polynomial ring Z[x₁, ... , x_n] is a free object on the set {x₁, ... , x_n} in the category ℓ.