If the domains of formula_181 are equal, then the diagram which defines morphisms in formula_182 with formula_183 is identical to the diagram which defines a natural transformation formula_184. The difference between the two notions is that a natural transformation is a particular collection of morphisms of type of the form formula_185, while objects of the comma category contains "all" morphisms of type of such form. A functor to the comma category selects that particular collection of morphisms. This is described succinctly by an observation by S.A. Huq that a natural transformation formula_186, with formula_187, corresponds to a functor formula_188 which maps each object formula_9 to formula_190 and maps each morphism formula_191 to formula_17. This is a bijective correspondence between natural transformations formula_184 and functors formula_188 which are sections of both forgetful functors from formula_182.