Lemma idtoiso_functorcat_compute_pointwise (C : precategory_data) (D : precategory) (hs: has_homsets D) (F G : ob [C, D, hs]) (p : F = G) (a : ob C) : functor_z_iso_pointwise_if_z_iso C D _ F G (idtoiso p) (pr2 (idtoiso p)) a = idtoiso (toforallpaths (λ _ : ob C, D) (pr1 (pr1 F)) (pr1 (pr1 G)) (base_paths (pr1 F) (pr1 G) (base_paths F G p)) a). Proof. induction p. apply (z_iso_eq(C:=D,,hs)). apply idpath. Qed.
Require Import UniMath.Foundations.Propositions. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.MoreFoundations.Univalence. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.TransportMorphisms. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence.