Definition ps_base_data : prebicat_data. Proof. use build_prebicat_data. - exact (ob C → ob D). - exact (λ f g, ∏ (x : C), f x --> g x). - exact (λ f g α β, ∏ (x : C), α x ==> β x). - exact (λ f x, id₁ (f x)). - exact (λ f g h α β x, α x · β x). - exact (λ f g α x, id₂ (α x)). - exact (λ f g α β γ m₁ m₂ x, m₁ x • m₂ x). - exact (λ f g h α β γ m x, α x ◃ m x). - exact (λ f g h α β γ m x, m x ▹ γ x). - exact (λ f g α x, lunitor (α x)). - exact (λ f g α x, linvunitor (α x)). - exact (λ f g α x, runitor (α x)). - exact (λ f g α x, rinvunitor (α x)). - exact (λ f₁ f₂ f₃ f₄ α β γ x, lassociator (α x) (β x) (γ x)). - exact (λ f₁ f₂ f₃ f₄ α β γ x, rassociator (α x) (β x) (γ x)). 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.PrecategoryBinProduct. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.AdjointUnique.