proposition: Proposition conservative_weq_covyoneda_conservative (V : monoidal_cat) : conservative_moncat V ≃ conservative (covyoneda V (I_{V})).
proof: Proof. use weqimplimpl. - intros HV x y f Hf. apply HV. exact (hset_z_iso_is_equiv _ _ (_ ,, Hf)). - intros HV x y f Hf. apply HV. use (hset_equiv_is_z_iso _ _ (_ ,, _)). exact Hf. - apply isaprop_conservative_moncat. - apply isaprop_conservative. Qed.
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.covyoneda UniMath.CategoryTheory.Categories.HSET.All UniMath.CategoryTheory.Monoidal.Categories