Definition indexed_cat_id {C : category} (F : indexed_cat_data C) (x : C) : functor_identity _ ⟹ (F $ identity x) := pr122 F x.
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.