Lemma idtoiso_functorcat_compute_pointwise' (C : precategory_data) (D : category) (F G : ob [C, D]) (p : F = G) (a : ob C) : functor_z_iso_pointwise_if_z_iso' C D F G (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. apply idpath. Qed.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Adjunctions.Core.