Lemma transportf_make_ob_eq {I J} (f : C⟦J,I⟧) {a b} (e : make_ob J a = make_ob J b) : transportf (λ x : ∫ X, C⟦pr1 x,I⟧) e f = transportf (λ x, C⟦x,I⟧) (base_paths _ _ e) f. Proof. now induction e. Qed.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.Categories.HSET.Core. Require Import UniMath.CategoryTheory.opp_precat. Require Import UniMath.CategoryTheory.Presheaf.