proposition: Lemma functor_op_of_precomp_functor_factorizes_through_functorcatofopp_is_nat_z_iso : is_nat_z_iso functor_op_of_precomp_functor_factorizes_through_functorcatofopp_as_nat_trans.
proof: Proof. intro G. use make_is_z_isomorphism. - use make_nat_trans. + intro ; apply identity. + abstract (intro ; intros ; apply (id_right _ @ ! id_left _)). - abstract (split ; (use nat_trans_eq ; [ apply homset_property | intro ; apply id_right ])). Defined.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.OppositeCategory.Core UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.Equivalences.Core UniMath.CategoryTheory.whiskering