F' a' (m : morphism D a a') (T : NaturalTransformation F' F) : Functor (F / a) (F' / a') := comma_category_induced_functor (s := (F, !a)) (d := (F', !a')) (T, @slice_category_induced_functor_nt a a' m).
Require Import Category.Core Functor.Core NaturalTransformation.Core. Require Import Category.Dual. Require Import Category.Prod. Require Import NaturalTransformation.Identity. Require Import FunctorCategory.Core Cat.Core. Require Import InitialTerminalCategory.Core InitialTerminalCategory.Functors. Import Comma.Core. Require Import HoTT.Tactics. Require Import Basics.Tactics.