proposition: Lemma iso_exp_precomp_prod_functor : @z_iso [PreShv C, PreShv C] precomp_prod_functor (exp (Yon c)).
proof: Proof. use z_iso_inv_from_z_iso. use (z_iso_comp first_iso_on_functors). use (z_iso_comp second_iso_on_functors). use (z_iso_comp third_iso_on_functors). use fourth_iso_on_functors. Defined.
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