Proposition set_conservative_moncat : conservative_moncat SET_monoidal_cat. Proof. intros X Y f Hf. use (hset_equiv_is_z_iso _ _ (_ ,, _)). use isweq_iso. - exact (λ y, invmap (_ ,, Hf) (λ _, y) tt). - abstract (intros x ; exact (eqtohomot (homotinvweqweq (_ ,, Hf) (λ _, x)) tt)). - abstract (intros y ; exact (eqtohomot (homotweqinvweq (_ ,, Hf) (λ _, y)) tt)). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Categories.HSET.All. Require Import UniMath.CategoryTheory.EnrichedCats.Enrichment. Require Import UniMath.CategoryTheory.EnrichedCats.EnrichmentFunctor. Require Import UniMath.CategoryTheory.EnrichedCats.EnrichmentTransformation. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Examples.SetCartesianMonoidal. Import MonoidalNotations.