proposition: Proposition faithful_weq_covyoneda_faithful (V : monoidal_cat) : faithful_moncat V ≃ faithful (covyoneda V (I_{V})).
proof: Proof. use weqimplimpl. - intros HV x y f. use invproofirrelevance. intros φ₁ φ₂. use subtypePath. { intro. apply homset_property. } apply HV. intros g. exact (eqtohomot (pr2 φ₁ @ !(pr2 φ₂)) g). - intros HV x y f g H. use (invmaponpathsincl _ (HV x y) f g). use funextsec. exact H. - apply isaprop_faithful_moncat. - apply isaprop_faithful. 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