Lemma transportf_make_ob {A : PreShv (∫ X)} {I : C} {x y} (e : x = y) (u : pr1 (pr1 A (make_ob I x))) : transportf (λ x, pr1 (pr1 A (make_ob I x))) e u = transportf (λ x, pr1 (pr1 A x)) (maponpaths (make_ob I) e) u. 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.