proposition: Lemma fourth_iso_nat_in_F: is_nat_trans Fun3 precomp_prod_functor (λ F, make_nat_trans (pr1 (Fun3 F)) _ (fourth_iso_on_sets F) (fourth_iso_nat_in_x F)).
proof: Proof. intros X Y f. apply (nat_trans_eq has_homsets_HSET); intro. apply funextsec; intros g. apply idpath. Qed.
imports: UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.exponentials UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.RightKanExtension UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.yoneda UniMath.CategoryTheory.YonedaBinproducts UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.Categories.HSET.Limits UniMath.CategoryTheory.Categories.HSET.Structures UniMath.CategoryTheory.Categories.HSET.MonoEpiIso UniMath.CategoryTheory.Limits.Graphs.Limits UniMath.CategoryTheory.Presheaf