Definition indexed_functor_data {C : category} (Φ Ψ : indexed_cat C) : UU := ∑ (τ₀ : ∏ (x : C), Φ x ⟶ Ψ x), ∏ (x y : C) (f : x --> y), nat_z_iso (τ₀ x ∙ (Ψ $ f)) ((Φ $ f) ∙ τ₀ y).
Require Import UniMath.Foundations.All. 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. Require Import UniMath.CategoryTheory.IndexedCategories.IndexedCategory.