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8 changes: 6 additions & 2 deletions Mathlib/AlgebraicGeometry/Sites/AffineEtale.lean
Original file line number Diff line number Diff line change
Expand Up @@ -52,13 +52,17 @@ namespace AffineEtale
protected def mk {R : CommRingCat.{u}} (f : Spec R ⟶ S) [Etale f] : AffineEtale S :=
MorphismProperty.CostructuredArrow.mk ⊤ f ‹_›

set_option trace.Elab.Deriving true
/-- The `Spec` functor from the small affine étale site of `S` to the small étale site of `S`. -/
@[simps! obj_left obj_hom map_left]
protected def Spec (S : Scheme.{u}) : S.AffineEtale ⥤ S.Etale :=
MorphismProperty.CostructuredArrow.toOver _ _ _
deriving Functor.Full, Functor.Faithful

instance : (AffineEtale.Spec S).Faithful :=
inferInstanceAs <| (MorphismProperty.CostructuredArrow.toOver _ _ _).Faithful
#check instFaithfulCostructuredArrowOppositeCommRingCatEtaleTopMorphismPropertySpecOverSpec
set_option trace.Meta.synthInstance true in
instance : (AffineEtale.Spec S).Faithful := inferInstance
-- inferInstanceAs <| (MorphismProperty.CostructuredArrow.toOver _ _ _).Faithful

instance : (AffineEtale.Spec S).Full :=
inferInstanceAs <| (MorphismProperty.CostructuredArrow.toOver _ _ _).Full
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