proposition: Proposition set_conservative_moncat : conservative_moncat SET_monoidal_cat.
proof: 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.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Categories.HSET.All UniMath.CategoryTheory.EnrichedCats.Enrichment UniMath.CategoryTheory.EnrichedCats.EnrichmentFunctor UniMath.CategoryTheory.EnrichedCats.EnrichmentTransformation UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Monoidal.Examples.SetCartesianMonoidal