proposition: Lemma is_precategory_ptd : is_precategory ptd_precategory_data.
proof: Proof. repeat split; simpl; intros. - apply (invmap (eq_ptd_mor _ _ )). apply (@id_left (functor_category C C)). - apply (invmap (eq_ptd_mor _ _ )). apply (@id_right (functor_category _ _)). - apply (invmap (eq_ptd_mor _ _ )). apply (@assoc (functor_category _ _)). - apply (invmap (eq_ptd_mor _ _ )). apply (@assoc' (functor_category _ _)). Qed.
imports: UniMath.Foundations.PartD UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.FunctorCategory