proposition: Lemma identity_of Y : mor_of Y Y 1 = 1.
proof: Proof. simpl. erewrite IsInitialMorphism_property_morphism_unique; [ reflexivity | ]. rewrite ?identity_of, ?left_identity, ?right_identity. reflexivity. Qed.
imports: Category.Core Functor.Core NaturalTransformation.Core Functor.Identity Functor.Composition.Core Functor.Dual Category.Dual Adjoint.Core Adjoint.UnitCounit Adjoint.UnitCounitCoercions Adjoint.Dual UniversalProperties Comma.Dual InitialTerminalCategory.Core InitialTerminalCategory.Functors