As stated earlier, an adjunction between categories C and D gives rise to a family of universal morphisms, one for each object in C and one for each object in D. Conversely, if there exists a universal morphism to a functor G : C → D from every object of D, then G has a left adjoint.
As stated earlier, an adjunction between categories C and D gives rise to a family of universal morphis:ms, one for each object in C and one for each object in D. Conversely, if there exists a universal morphism to a functor G  C → D from every object of D, then G has a left adjoint.