Definition arrow_category_to_comma_category : arrow_category C ⟶ comma (functor_identity C) (functor_identity C). Proof. use make_functor. - exact arrow_category_to_comma_category_data. - exact arrow_category_to_comma_category_is_functor. 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.