Definition disp_cat_of_fibers_assoc {B C : category} (F : functor C B) : ∏ (b0 b1 b2 b3 : B) (f1 : b0 --> b1) (f2 : b1 --> b2) (f3 : b2 --> b3) (c0 : disp_cat_of_fibers_ob F b0) (c1 : disp_cat_of_fibers_ob F b1) (c2 : disp_cat_of_fibers_ob F b2) (c3 : disp_cat_of_fibers_ob F b3) (g1 : disp_cat_of_fibers_mor' c0 c1 f1) (g2 : disp_cat_of_fibers_mor' c1 c2 f2) (g3 : disp_cat_of_fibers_mor' c2 c3 f3), disp_cat_of_fibers_comp' g1 (disp_cat_of_fibers_comp' g2 g3) = transportb _ (assoc _ _ _) (disp_cat_of_fibers_comp' (disp_cat_of_fibers_comp' g1 g2) g3).
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.