Definition make_indexed_cat_data {C : category} (F₀ : C → univalent_category) (F₁ : ∏ (x y : C), x --> y → F₀ x ⟶ F₀ y) (Fid : ∏ (x : C), functor_identity _ ⟹ F₁ x x (identity x)) (Fcomp : ∏ (x y z : C) (f : x --> y) (g : y --> z), F₁ x y f ∙ F₁ y z g ⟹ F₁ x z (f · g)) : indexed_cat_data C := F₀ ,, F₁ ,, Fid ,, Fcomp.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations.