In the category of abelian groups, show that the group A 1 X A 2 ,

In the category α  of abelian groups, show that the group· A₁ X A₂, together with the homomorphisms L₁ : A₁ → A₁ X A₂ and L₂ : A₂ → A₁ X A₂ (as in the Example preceding Definition 2.2) is a coproduct for { A₁,A₂}.