algebraic_geometry.morphisms.finite_typeMathlib.AlgebraicGeometry.Morphisms.FiniteType

This file has been ported!

Changes since the initial port

The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.

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Changes in mathlib3port

mathlib3
mathlib3port
Diff
@@ -3,8 +3,8 @@ Copyright (c) 2022 Andrew Yang. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Andrew Yang
 -/
-import Mathbin.AlgebraicGeometry.Morphisms.RingHomProperties
-import Mathbin.RingTheory.RingHom.FiniteType
+import AlgebraicGeometry.Morphisms.RingHomProperties
+import RingTheory.RingHom.FiniteType
 
 #align_import algebraic_geometry.morphisms.finite_type from "leanprover-community/mathlib"@"08b081ea92d80e3a41f899eea36ef6d56e0f1db0"
 
Diff
@@ -2,15 +2,12 @@
 Copyright (c) 2022 Andrew Yang. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Andrew Yang
-
-! This file was ported from Lean 3 source module algebraic_geometry.morphisms.finite_type
-! leanprover-community/mathlib commit 08b081ea92d80e3a41f899eea36ef6d56e0f1db0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.AlgebraicGeometry.Morphisms.RingHomProperties
 import Mathbin.RingTheory.RingHom.FiniteType
 
+#align_import algebraic_geometry.morphisms.finite_type from "leanprover-community/mathlib"@"08b081ea92d80e3a41f899eea36ef6d56e0f1db0"
+
 /-!
 # Morphisms of finite type
 
Diff
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Andrew Yang
 
 ! This file was ported from Lean 3 source module algebraic_geometry.morphisms.finite_type
-! leanprover-community/mathlib commit 70fd9563a21e7b963887c9360bd29b2393e6225a
+! leanprover-community/mathlib commit 08b081ea92d80e3a41f899eea36ef6d56e0f1db0
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.RingTheory.RingHom.FiniteType
 /-!
 # Morphisms of finite type
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 A morphism of schemes `f : X ⟶ Y` is locally of finite type if for each affine `U ⊆ Y` and
 `V ⊆ f ⁻¹' U`, The induced map `Γ(Y, U) ⟶ Γ(X, V)` is of finite type.
 
Diff
@@ -34,6 +34,7 @@ namespace AlgebraicGeometry
 
 variable {X Y : Scheme.{u}} (f : X ⟶ Y)
 
+#print AlgebraicGeometry.LocallyOfFiniteType /-
 /-- A morphism of schemes `f : X ⟶ Y` is locally of finite type if for each affine `U ⊆ Y` and
 `V ⊆ f ⁻¹' U`, The induced map `Γ(Y, U) ⟶ Γ(X, V)` is of finite type.
 -/
@@ -43,29 +44,39 @@ class LocallyOfFiniteType (f : X ⟶ Y) : Prop where
     ∀ (U : Y.affineOpens) (V : X.affineOpens) (e : V.1 ≤ (Opens.map f.1.base).obj U.1),
       (f.appLe e).FiniteType
 #align algebraic_geometry.locally_of_finite_type AlgebraicGeometry.LocallyOfFiniteType
+-/
 
+#print AlgebraicGeometry.locallyOfFiniteType_eq /-
 theorem locallyOfFiniteType_eq : @LocallyOfFiniteType = affineLocally @RingHom.FiniteType :=
   by
   ext X Y f
   rw [locally_of_finite_type_iff, affine_locally_iff_affine_opens_le]
   exact RingHom.finiteType_respectsIso
 #align algebraic_geometry.locally_of_finite_type_eq AlgebraicGeometry.locallyOfFiniteType_eq
+-/
 
+#print AlgebraicGeometry.locallyOfFiniteTypeOfIsOpenImmersion /-
 instance (priority := 900) locallyOfFiniteTypeOfIsOpenImmersion {X Y : Scheme} (f : X ⟶ Y)
     [IsOpenImmersionCat f] : LocallyOfFiniteType f :=
-  locallyOfFiniteType_eq.symm ▸ RingHom.finiteType_is_local.affineLocally_of_isOpenImmersionCat f
+  locallyOfFiniteType_eq.symm ▸ RingHom.finiteType_is_local.affineLocally_of_isOpenImmersion f
 #align algebraic_geometry.locally_of_finite_type_of_is_open_immersion AlgebraicGeometry.locallyOfFiniteTypeOfIsOpenImmersion
+-/
 
+#print AlgebraicGeometry.locallyOfFiniteType_stableUnderComposition /-
 theorem locallyOfFiniteType_stableUnderComposition :
     MorphismProperty.StableUnderComposition @LocallyOfFiniteType :=
   locallyOfFiniteType_eq.symm ▸ RingHom.finiteType_is_local.affineLocally_stableUnderComposition
 #align algebraic_geometry.locally_of_finite_type_stable_under_composition AlgebraicGeometry.locallyOfFiniteType_stableUnderComposition
+-/
 
+#print AlgebraicGeometry.locallyOfFiniteTypeComp /-
 instance locallyOfFiniteTypeComp {X Y Z : Scheme} (f : X ⟶ Y) (g : Y ⟶ Z)
     [hf : LocallyOfFiniteType f] [hg : LocallyOfFiniteType g] : LocallyOfFiniteType (f ≫ g) :=
   locallyOfFiniteType_stableUnderComposition f g hf hg
 #align algebraic_geometry.locally_of_finite_type_comp AlgebraicGeometry.locallyOfFiniteTypeComp
+-/
 
+#print AlgebraicGeometry.locallyOfFiniteTypeOfComp /-
 theorem locallyOfFiniteTypeOfComp {X Y Z : Scheme} (f : X ⟶ Y) (g : Y ⟶ Z)
     [hf : LocallyOfFiniteType (f ≫ g)] : LocallyOfFiniteType f :=
   by
@@ -75,29 +86,38 @@ theorem locallyOfFiniteTypeOfComp {X Y Z : Scheme} (f : X ⟶ Y) (g : Y ⟶ Z)
   introv H
   exact RingHom.FiniteType.of_comp_finiteType H
 #align algebraic_geometry.locally_of_finite_type_of_comp AlgebraicGeometry.locallyOfFiniteTypeOfComp
+-/
 
+#print AlgebraicGeometry.LocallyOfFiniteType.affine_openCover_iff /-
 theorem LocallyOfFiniteType.affine_openCover_iff {X Y : Scheme.{u}} (f : X ⟶ Y)
     (𝒰 : Scheme.OpenCover.{u} Y) [∀ i, IsAffine (𝒰.obj i)]
     (𝒰' : ∀ i, Scheme.OpenCover.{u} ((𝒰.pullbackCover f).obj i)) [∀ i j, IsAffine ((𝒰' i).obj j)] :
     LocallyOfFiniteType f ↔ ∀ i j, (Scheme.Γ.map ((𝒰' i).map j ≫ pullback.snd).op).FiniteType :=
   locallyOfFiniteType_eq.symm ▸ RingHom.finiteType_is_local.affine_openCover_iff f 𝒰 𝒰'
 #align algebraic_geometry.locally_of_finite_type.affine_open_cover_iff AlgebraicGeometry.LocallyOfFiniteType.affine_openCover_iff
+-/
 
+#print AlgebraicGeometry.LocallyOfFiniteType.source_openCover_iff /-
 theorem LocallyOfFiniteType.source_openCover_iff {X Y : Scheme.{u}} (f : X ⟶ Y)
     (𝒰 : Scheme.OpenCover.{u} X) : LocallyOfFiniteType f ↔ ∀ i, LocallyOfFiniteType (𝒰.map i ≫ f) :=
   locallyOfFiniteType_eq.symm ▸ RingHom.finiteType_is_local.source_openCover_iff f 𝒰
 #align algebraic_geometry.locally_of_finite_type.source_open_cover_iff AlgebraicGeometry.LocallyOfFiniteType.source_openCover_iff
+-/
 
+#print AlgebraicGeometry.LocallyOfFiniteType.openCover_iff /-
 theorem LocallyOfFiniteType.openCover_iff {X Y : Scheme.{u}} (f : X ⟶ Y)
     (𝒰 : Scheme.OpenCover.{u} Y) :
     LocallyOfFiniteType f ↔ ∀ i, LocallyOfFiniteType (pullback.snd : pullback f (𝒰.map i) ⟶ _) :=
   locallyOfFiniteType_eq.symm ▸ RingHom.finiteType_is_local.is_local_affineLocally.openCover_iff f 𝒰
 #align algebraic_geometry.locally_of_finite_type.open_cover_iff AlgebraicGeometry.LocallyOfFiniteType.openCover_iff
+-/
 
+#print AlgebraicGeometry.locallyOfFiniteType_respectsIso /-
 theorem locallyOfFiniteType_respectsIso : MorphismProperty.RespectsIso @LocallyOfFiniteType :=
   locallyOfFiniteType_eq.symm ▸
     targetAffineLocally_respectsIso (sourceAffineLocally_respectsIso RingHom.finiteType_respectsIso)
 #align algebraic_geometry.locally_of_finite_type_respects_iso AlgebraicGeometry.locallyOfFiniteType_respectsIso
+-/
 
 end AlgebraicGeometry
 
Diff
@@ -91,7 +91,7 @@ theorem LocallyOfFiniteType.source_openCover_iff {X Y : Scheme.{u}} (f : X ⟶ Y
 theorem LocallyOfFiniteType.openCover_iff {X Y : Scheme.{u}} (f : X ⟶ Y)
     (𝒰 : Scheme.OpenCover.{u} Y) :
     LocallyOfFiniteType f ↔ ∀ i, LocallyOfFiniteType (pullback.snd : pullback f (𝒰.map i) ⟶ _) :=
-  locallyOfFiniteType_eq.symm ▸ RingHom.finiteType_is_local.isLocalAffineLocally.openCover_iff f 𝒰
+  locallyOfFiniteType_eq.symm ▸ RingHom.finiteType_is_local.is_local_affineLocally.openCover_iff f 𝒰
 #align algebraic_geometry.locally_of_finite_type.open_cover_iff AlgebraicGeometry.LocallyOfFiniteType.openCover_iff
 
 theorem locallyOfFiniteType_respectsIso : MorphismProperty.RespectsIso @LocallyOfFiniteType :=
Diff
@@ -52,8 +52,8 @@ theorem locallyOfFiniteType_eq : @LocallyOfFiniteType = affineLocally @RingHom.F
 #align algebraic_geometry.locally_of_finite_type_eq AlgebraicGeometry.locallyOfFiniteType_eq
 
 instance (priority := 900) locallyOfFiniteTypeOfIsOpenImmersion {X Y : Scheme} (f : X ⟶ Y)
-    [IsOpenImmersion f] : LocallyOfFiniteType f :=
-  locallyOfFiniteType_eq.symm ▸ RingHom.finiteType_is_local.affineLocally_of_isOpenImmersion f
+    [IsOpenImmersionCat f] : LocallyOfFiniteType f :=
+  locallyOfFiniteType_eq.symm ▸ RingHom.finiteType_is_local.affineLocally_of_isOpenImmersionCat f
 #align algebraic_geometry.locally_of_finite_type_of_is_open_immersion AlgebraicGeometry.locallyOfFiniteTypeOfIsOpenImmersion
 
 theorem locallyOfFiniteType_stableUnderComposition :
Diff
@@ -46,7 +46,7 @@ class LocallyOfFiniteType (f : X ⟶ Y) : Prop where
 
 theorem locallyOfFiniteType_eq : @LocallyOfFiniteType = affineLocally @RingHom.FiniteType :=
   by
-  ext (X Y f)
+  ext X Y f
   rw [locally_of_finite_type_iff, affine_locally_iff_affine_opens_le]
   exact RingHom.finiteType_respectsIso
 #align algebraic_geometry.locally_of_finite_type_eq AlgebraicGeometry.locallyOfFiniteType_eq

Changes in mathlib4

mathlib3
mathlib4
feat(CategoryTheory): morphism properties that have the two-out-of-three property (#12460)

The type class MorphismProperty.HasTwoOutOfThreeProperty is introduced. The structure StableUnderComposition is also changed into a type class IsStableUnderComposition.

Co-authored-by: Joël Riou <37772949+joelriou@users.noreply.github.com>

Diff
@@ -52,14 +52,14 @@ instance (priority := 900) locallyOfFiniteTypeOfIsOpenImmersion {X Y : Scheme} (
   locallyOfFiniteType_eq.symm ▸ RingHom.finiteType_is_local.affineLocally_of_isOpenImmersion f
 #align algebraic_geometry.locally_of_finite_type_of_is_open_immersion AlgebraicGeometry.locallyOfFiniteTypeOfIsOpenImmersion
 
-theorem locallyOfFiniteType_stableUnderComposition :
-    MorphismProperty.StableUnderComposition @LocallyOfFiniteType :=
-  locallyOfFiniteType_eq.symm ▸ RingHom.finiteType_is_local.affineLocally_stableUnderComposition
-#align algebraic_geometry.locally_of_finite_type_stable_under_composition AlgebraicGeometry.locallyOfFiniteType_stableUnderComposition
+instance locallyOfFiniteType_isStableUnderComposition :
+    MorphismProperty.IsStableUnderComposition @LocallyOfFiniteType :=
+  locallyOfFiniteType_eq.symm ▸ RingHom.finiteType_is_local.affineLocally_isStableUnderComposition
+#align algebraic_geometry.locally_of_finite_type_stable_under_composition AlgebraicGeometry.locallyOfFiniteType_isStableUnderComposition
 
 instance locallyOfFiniteTypeComp {X Y Z : Scheme} (f : X ⟶ Y) (g : Y ⟶ Z)
     [hf : LocallyOfFiniteType f] [hg : LocallyOfFiniteType g] : LocallyOfFiniteType (f ≫ g) :=
-  locallyOfFiniteType_stableUnderComposition f g hf hg
+  MorphismProperty.comp_mem _ f g hf hg
 #align algebraic_geometry.locally_of_finite_type_comp AlgebraicGeometry.locallyOfFiniteTypeComp
 
 theorem locallyOfFiniteTypeOfComp {X Y Z : Scheme} (f : X ⟶ Y) (g : Y ⟶ Z)
@@ -95,4 +95,3 @@ theorem locallyOfFiniteType_respectsIso : MorphismProperty.RespectsIso @LocallyO
 #align algebraic_geometry.locally_of_finite_type_respects_iso AlgebraicGeometry.locallyOfFiniteType_respectsIso
 
 end AlgebraicGeometry
-
refactor: decapitalize names in @[mk_iff] (#9378)
  • @[mk_iff] class MyPred now generates myPred_iff, not MyPred_iff
  • add Lean.Name.decapitalize
  • fix indentation and a few typos in the docs/comments.

Partially addresses issue #9129

Diff
@@ -43,7 +43,7 @@ class LocallyOfFiniteType (f : X ⟶ Y) : Prop where
 
 theorem locallyOfFiniteType_eq : @LocallyOfFiniteType = affineLocally @RingHom.FiniteType := by
   ext X Y f
-  rw [LocallyOfFiniteType_iff, affineLocally_iff_affineOpens_le]
+  rw [locallyOfFiniteType_iff, affineLocally_iff_affineOpens_le]
   exact RingHom.finiteType_respectsIso
 #align algebraic_geometry.locally_of_finite_type_eq AlgebraicGeometry.locallyOfFiniteType_eq
 
chore: script to replace headers with #align_import statements (#5979)

Open in Gitpod

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

Diff
@@ -2,15 +2,12 @@
 Copyright (c) 2022 Andrew Yang. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Andrew Yang
-
-! This file was ported from Lean 3 source module algebraic_geometry.morphisms.finite_type
-! leanprover-community/mathlib commit 70fd9563a21e7b963887c9360bd29b2393e6225a
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties
 import Mathlib.RingTheory.RingHom.FiniteType
 
+#align_import algebraic_geometry.morphisms.finite_type from "leanprover-community/mathlib"@"70fd9563a21e7b963887c9360bd29b2393e6225a"
+
 /-!
 # Morphisms of finite type
 
feat: port AlgebraicGeometry.Morphisms.FiniteType (#5913)

Co-authored-by: Matthew Ballard <matt@mrb.email> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: Matthew Robert Ballard <100034030+mattrobball@users.noreply.github.com> Co-authored-by: Yury G. Kudryashov <urkud@urkud.name> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

Dependencies 11 + 940

941 files ported (98.8%)
389254 lines ported (98.6%)
Show graph

The unported dependencies are