Lemma η_slice_ok {Γ: HSET_over_sort} (a: pr1 (pr1 Γ)) : sort_in (η_slice(Γ:=Γ) a) = (pr2 Γ) a. Proof. unfold η_slice. set (H1 := pr2 ((Monads.η T) Γ)). simpl in H1. apply toforallpaths in H1. now rewrite H1. Qed.
Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Limits.BinCoproducts. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Monads.Monads. Require Import UniMath.CategoryTheory.Categories.HSET.Core. Require Import UniMath.CategoryTheory.Categories.HSET.Colimits. Require Import UniMath.CategoryTheory.Categories.HSET.Limits. Require Import UniMath.CategoryTheory.Categories.HSET.Slice. Require Import UniMath.CategoryTheory.slicecat.