Definition arrow_category_equiv_comma_category_unit : functor_identity _ ⟹ arrow_category_to_comma_category ∙ comma_category_to_arrow_category. Proof. use make_nat_trans. - exact arrow_category_equiv_comma_category_unit_data. - exact arrow_category_equiv_comma_category_unit_is_nat_trans. 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.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.CommaCategories. Require Import UniMath.CategoryTheory.Adjunctions.Core.