Definition make_psfunctor_data {C D : bicat} (F₀ : C → D) (F₁ : ∏ {a b : C}, C⟦a,b⟧ → D⟦F₀ a, F₀ b⟧) (F₂ : ∏ {a b : C} {f g : C⟦a,b⟧}, f ==> g → F₁ f ==> F₁ g) (Fid : ∏ (a : C), identity (F₀ a) ==> F₁ (identity a)) (Fcomp : (∏ (a b c : C) (f : a --> b) (g : b --> c), F₁ f · F₁ g ==> F₁ (f · g))) : psfunctor_data C D. Proof. exact ((F₀ ,, F₁) ,, (F₂ ,, Fid ,, Fcomp)). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.Equivalences.FullyFaithful. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Examples.BicatOfUnivCats. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Core.EquivToAdjequiv. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Require Import UniMath.Bicategories.PseudoFunctors.Display.Base. Require Import UniMath.Bicategories.PseudoFunctors.Display.Map1Cells. Require Import UniMath.Bicategories.PseudoFunctors.Display.Map2Cells. Require Import UniMath.Bicategories.PseudoFunctors.Display.Identitor. Require Import UniMath.Bicategories.PseudoFunctors.Display.Compositor. Require Import UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat.