Definition hcomp_bicat_hcomp (B : hcomp_bicat) (b₁ b₂ b₃ : pr11 B) : precategory_binproduct_data (hcomp_bicat_hom_cat B b₁ b₂) (hcomp_bicat_hom_cat B b₂ b₃) ⟶ hcomp_bicat_hom_cat B b₁ b₃. Proof. use make_functor. - use make_functor_data. + exact (λ fg, hb_comp1 (pr1 fg) (pr2 fg)). + exact (λ fg fg' α, hb_hcomp (pr1 α) (pr2 α)). - split. + intros f ; cbn in *. exact (pr1 (pr222 (pr222 B)) b₁ b₂ b₃ (pr1 f) (pr2 f)). + intros f g h α β ; cbn in *. exact (pr12 (pr222 (pr222 B)) b₁ b₂ b₃ _ _ _ _ _ _ (pr1 α) (pr2 α) (pr1 β) (pr2 β)). 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.PrecategoryBinProduct. Require Import UniMath.Bicategories.WkCatEnrichment.prebicategory. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.BicategoryLaws.