proposition: Lemma isaprop_Initial : isaprop (Initial C).
proof: Proof. apply invproofirrelevance. intros O O'. apply (total2_paths_f (isotoid _ H (ziso_Initials O O')) ). apply proofirrelevance. unfold isInitial. apply impred. intro t ; apply isapropiscontr. Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.Tactics UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.Epis UniMath.CategoryTheory.Limits.Coproducts