Definition is_nat_trans_slice_to_fam_mor {a b : slice X} (f : a --> b) : is_nat_trans (s_to_f a : functor (discrete X) HSET) (s_to_f b : functor (discrete X) HSET) (slice_to_fam_mor_fun f) := is_nat_trans_discrete_precategory (slice_to_fam_mor_fun f).
Require Import UniMath.Foundations.Sets. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Categories.HSET.Core. Require Import UniMath.CategoryTheory.Categories.HSET.MonoEpiIso. Require Import UniMath.CategoryTheory.Categories.HSET.Univalence. Require Import UniMath.CategoryTheory.Categories.HSET.Slice. Require Import UniMath.CategoryTheory.slicecat. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.Groupoids. Require Import UniMath.CategoryTheory.Categories.StandardCategories.