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Mathlib/AlgebraicGeometry/IdealSheaf/Subscheme.lean

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@@ -612,10 +612,7 @@ noncomputable section image
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open Limits
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variable {X Y : Scheme.{u}} (f : X.Hom Y)
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section
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variable (U : Y.affineOpens)
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variable {X Y : Scheme.{u}} (f : X.Hom Y) (U : Y.affineOpens)
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/-- The scheme theoretic image of a morphism. -/
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abbrev Hom.image : Scheme.{u} := f.ker.subscheme
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exact (RingHom.lift_injective_of_ker_le_ideal _ _ (by simp)).comp
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(f.ker.subschemeObjIso U).commRingCatIsoToRingEquiv.injective
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end
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lemma Hom.stalkFunctor_toImage_injective [QuasiCompact f] (x) :
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Function.Injective ((TopCat.Presheaf.stalkFunctor _ x).map f.toImage.c) := by
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apply TopCat.Presheaf.stalkFunctor_map_injective_of_isBasis

Mathlib/CategoryTheory/Functor/Functorial.lean

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@@ -50,8 +50,6 @@ instance (F : C ⥤ D) : Functorial.{v₁, v₂} F.obj :=
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theorem map_functorial_obj (F : C ⥤ D) {X Y : C} (f : X ⟶ Y) : map F.obj f = F.map f :=
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rfl
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attribute [grind] id
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instance functorial_id : Functorial.{v₁, v₁} (id : C → C) where map f := f
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section

Mathlib/CategoryTheory/Iso.lean

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@@ -208,7 +208,7 @@ theorem hom_eq_inv (α : X ≅ Y) (β : Y ≅ X) : α.hom = β.inv ↔ β.hom =
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rw [← symm_inv, inv_eq_inv α.symm β, eq_comm]
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rfl
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attribute [grind] Function.LeftInverse Function.RightInverse
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attribute [local grind] Function.LeftInverse Function.RightInverse
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/-- The bijection `(Z ⟶ X) ≃ (Z ⟶ Y)` induced by `α : X ≅ Y`. -/
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@[simps]

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