 Spelled out, this means that for each object formula_30 in formula_28, 
there exists an object formula_49 in formula_22 and a morphism formula_51 such that for every object formula_21 in formula_22 
and every morphism formula_33 there exists a unique morphism formula_32 with formula_56.Again, this formula_15 can be uniquely turned into a functor formula_20 such that formula_59 for formula_60 a morphism in formula_28; formula_13 is then called a right adjoint to formula_15.It is true, as the terminology implies, that formula_15 is left adjoint to formula_13 if and only if formula_13 is right adjoint to formula_15.