x y z g f : mor_of _ _ (f o g) = mor_of y z f o mor_of x y g. Proof. simpl. erewrite IsInitialMorphism_property_morphism_unique; [ reflexivity | ]. rewrite ?. repeat try_associativity_quick rewrite IsInitialMorphism_property_morphism_property. reflexivity. Qed.
Require Import Category.Core Functor.Core NaturalTransformation.Core. Require Import Functor.Identity Functor.Composition.Core. Require Import Functor.Dual Category.Dual. Require Import Adjoint.Core Adjoint.UnitCounit Adjoint.UnitCounitCoercions Adjoint.Dual. Import Comma.Core. Require Import UniversalProperties Comma.Dual InitialTerminalCategory.Core InitialTerminalCategory.Functors.