Definition disp_hcomp {D : disp_prebicat} {b₁ b₂ b₃ : C} {f₁ f₂ : b₁ --> b₂} {g₁ g₂ : b₂ --> b₃} {α : f₁ ==> f₂} {β : g₁ ==> g₂} {bb₁ : D b₁} {bb₂ : D b₂} {bb₃ : D b₃} {ff₁ : bb₁ -->[ f₁ ] bb₂} {ff₂ : bb₁ -->[ f₂ ] bb₂} {gg₁ : bb₂ -->[ g₁ ] bb₃} {gg₂ : bb₂ -->[ g₂ ] bb₃} (αα : ff₁ ==>[ α ] ff₂) (ββ : gg₁ ==>[ β ] gg₂) : ff₁ ;; gg₁ ==>[ β ⋆⋆ α ] ff₂ ;; gg₂ := (αα ▹▹ gg₁) •• (ff₂ ◃◃ ββ).
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Core.Univalence.