Definition hcomp_bicat_hom_cat (B : hcomp_bicat) (b₁ b₂ : B) : category. Proof. use make_category. - use make_precategory. + use make_precategory_data. * use make_precategory_ob_mor. ** exact (hb_mor b₁ b₂). ** exact (λ f g, hb_cell f g). * exact (λ f, hb_id2 f). * exact (λ _ _ _ f g, hb_vcomp f g). + repeat split ; simpl ; cbn. * exact (pr12 B b₁ b₂). * exact (pr122 B b₁ b₂). * exact (pr1 (pr222 B) b₁ b₂). * exact (pr12 (pr222 B) b₁ b₂). - exact (pr122 (pr222 B) b₁ b₂). 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.