@@ -1245,15 +1245,15 @@ variable {C : Type u₁} [Category.{v₁} C]
12451245/-- `FullyFaithful.homEquiv` as a natural isomorphism. -/
12461246@[simps!]
12471247def homNatIso {D : Type u₂} [Category.{v₂} D] {F : C ⥤ D} (hF : F.FullyFaithful) (X : C) :
1248- F.op ⋙ uliftYoneda.obj. {v₁} (F.obj X) ≅ uliftYoneda.obj. {v₂} X :=
1248+ F.op ⋙ uliftYoneda.{v₁}.obj (F.obj X) ≅ uliftYoneda.{v₂}.obj X :=
12491249 NatIso.ofComponents
12501250 (fun Y => Equiv.toIso (Equiv.ulift.trans <| hF.homEquiv.symm.trans Equiv.ulift.symm))
12511251 (fun f => by ext; exact Equiv.ulift.injective (hF.map_injective (by simp)))
12521252
12531253/-- `FullyFaithful.homEquiv` as a natural isomorphism. -/
12541254@[simps!, deprecated homNatIso (since := " 2025-10-28" )]
12551255def homNatIsoMaxRight {D : Type u₂} [Category.{max v₁ v₂} D] {F : C ⥤ D} (hF : F.FullyFaithful)
1256- (X : C) : F.op ⋙ yoneda.obj (F.obj X) ≅ uliftYoneda.obj. {v₂} X :=
1256+ (X : C) : F.op ⋙ yoneda.obj (F.obj X) ≅ uliftYoneda.{v₂}.obj X :=
12571257 isoWhiskerLeft F.op (uliftYonedaIsoYoneda.symm.app _) ≪≫ hF.homNatIso _ ≪≫
12581258 NatIso.ofComponents (fun _ => Equiv.toIso (Equiv.ulift.trans Equiv.ulift.symm))
12591259
@@ -1273,15 +1273,15 @@ def compUliftYonedaCompWhiskeringLeft {D : Type u₂} [Category.{v₂} D] {F : C
12731273@[simps!, deprecated compUliftYonedaCompWhiskeringLeft (since := " 2025-10-28" )]
12741274def compYonedaCompWhiskeringLeftMaxRight {D : Type u₂} [Category.{max v₁ v₂} D] {F : C ⥤ D}
12751275 (hF : F.FullyFaithful) : F ⋙ yoneda ⋙ (whiskeringLeft _ _ _).obj F.op ≅ uliftYoneda.{v₂} := by
1276- refine isoWhiskerLeft F (isoWhiskerRight uliftYonedaIsoYoneda.symm. {v₁} _) ≪≫
1276+ refine isoWhiskerLeft F (isoWhiskerRight uliftYonedaIsoYoneda.{v₁}.symm _) ≪≫
12771277 hF.compUliftYonedaCompWhiskeringLeft ≪≫
12781278 NatIso.ofComponents (fun _ => NatIso.ofComponents
12791279 (fun _ => Equiv.toIso (Equiv.ulift.trans Equiv.ulift.symm)))
12801280
12811281/-- `FullyFaithful.homEquiv` as a natural isomorphism, using coyoneda. -/
12821282@[simps!]
12831283def homNatIso' {D : Type u₂} [Category.{v₂} D] {F : C ⥤ D} (hF : F.FullyFaithful) (X : C) :
1284- F ⋙ uliftCoyoneda.obj. {v₁} (op (F.obj X)) ≅ uliftCoyoneda.obj. {v₂} (op X) :=
1284+ F ⋙ uliftCoyoneda.{v₁}.obj (op (F.obj X)) ≅ uliftCoyoneda.{v₂}.obj (op X) :=
12851285 NatIso.ofComponents
12861286 (fun Y => Equiv.toIso (Equiv.ulift.trans <| hF.homEquiv.symm.trans Equiv.ulift.symm))
12871287 (fun f => by ext; exact Equiv.ulift.injective (hF.map_injective (by simp)))
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