Definition disp_cat_of_fibers_id_left {B C : category} (F : functor C B) : ∏ (b b' : B) (f : b --> b') (c : disp_cat_of_fibers_ob F b) (c' : disp_cat_of_fibers_ob F b') (g : disp_cat_of_fibers_mor' c c' f), disp_cat_of_fibers_comp' (disp_cat_of_fibers_id F _ _) g = transportb _ (id_left _) g.
Require Import UniMath.Foundations.Sets. 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.Core.Functors. Require Import UniMath.CategoryTheory.Categories.HSET.Core. Require Import UniMath.CategoryTheory.Categories.HSET.MonoEpiIso. Require Import UniMath.CategoryTheory.Categories.HSET.Univalence. Require Import UniMath.CategoryTheory.Limits.Pullbacks. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.opp_precat. Require Import UniMath.CategoryTheory.Presheaf. Require Import UniMath.CategoryTheory.Core.TransportMorphisms. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.CategoryTheory.DisplayedCats.Fibrations. Require Import UniMath.Foundations.All. Require Import UniMath.CategoryTheory.DisplayedCats.MoreFibrations.Prefibrations. Require Import UniMath.CategoryTheory.DisplayedCats.MoreFibrations.CartesiannessOfComposites.