Proposition conservative_weq_covyoneda_conservative (V : monoidal_cat) : conservative_moncat V ≃ conservative (covyoneda V (I_{V})). 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.
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.covyoneda. Require Import UniMath.CategoryTheory.Categories.HSET.All. Require Import UniMath.CategoryTheory.Monoidal.Categories. Import MonoidalNotations.