Definition bicat_to_hcomp_bicat_data (B : bicat) : hcomp_bicat_data. Proof. simple refine (_ ,, _ ,, _ ,, _ ,, _ ,, _ ,, _ ,, _ ,, _ ,, _ ,, _ ,, _ ,, _ ,, _). - exact B. - exact (λ x y, x --> y). - exact (λ _ _ f g, f ==> g). - exact (λ x, id₁ _). - exact (λ _ _ _ f g, f · g). - exact (λ _ _ f, id2 f). - exact (λ _ _ _ _ _ α β, α • β). - exact (λ _ _ f, runitor f). - exact (λ _ _ f, rinvunitor f). - exact (λ _ _ f, lunitor f). - exact (λ _ _ f, linvunitor f). - exact (λ _ _ _ _ f g h, rassociator f g h). - exact (λ _ _ _ _ f g h, lassociator f g h). - exact (λ _ _ _ _ _ _ _ α β, β ⋆⋆ α). 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.