Definition functor_ass_disp_cat : disp_cat (functor_tensorunit_cat TC TD IC ID). Proof. use disp_full_sub. intros [F [FT FU]]. exact (∏ (x y z : C), pr1 FT (x, y) #⊗_D id (pr1 F(z)) · pr1 FT (x ⊗_C y, z) · #(pr1 F) (αC ((x, y), z)) = αD ((pr1 F x, pr1 F y), pr1 F z) · id (pr1 F x) #⊗_D pr1 FT (y, z) · pr1 FT (x, y ⊗_C z)). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalCategoriesTensored.