Definition functor_tensorunit_composition {F : functor C D} {G : functor D E} (FF : functor_tensorunit_disp_cat TC TD IC ID F) (GG : functor_tensorunit_disp_cat TD TE ID IE G) : functor_tensorunit_disp_cat TC TE IC IE (functor_composite F G). Proof. exists (functor_tensor_composition (pr1 FF) (pr1 GG)). exact (functor_unit_composition (pr2 FF) (pr2 GG)). 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.