category_theory.noetherian
⟷
Mathlib.CategoryTheory.Noetherian
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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mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -46,7 +46,7 @@ class NoetherianObject (X : C) : Prop where
-/
#print CategoryTheory.ArtinianObject /-
-/- ./././Mathport/Syntax/Translate/Command.lean:404:30: infer kinds are unsupported in Lean 4: #[`subobject_lt_wellFounded] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:400:30: infer kinds are unsupported in Lean 4: #[`subobject_lt_wellFounded] [] -/
/-- An artinian object is an object
which does not have infinite decreasing sequences of subobjects.
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -46,7 +46,7 @@ class NoetherianObject (X : C) : Prop where
-/
#print CategoryTheory.ArtinianObject /-
-/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`subobject_lt_wellFounded] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:404:30: infer kinds are unsupported in Lean 4: #[`subobject_lt_wellFounded] [] -/
/-- An artinian object is an object
which does not have infinite decreasing sequences of subobjects.
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,9 +3,9 @@ Copyright (c) 2022 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
-import Mathbin.CategoryTheory.Subobject.Lattice
-import Mathbin.CategoryTheory.EssentiallySmall
-import Mathbin.CategoryTheory.Simple
+import CategoryTheory.Subobject.Lattice
+import CategoryTheory.EssentiallySmall
+import CategoryTheory.Simple
#align_import category_theory.noetherian from "leanprover-community/mathlib"@"f2b757fc5c341d88741b9c4630b1e8ba973c5726"
@@ -46,7 +46,7 @@ class NoetherianObject (X : C) : Prop where
-/
#print CategoryTheory.ArtinianObject /-
-/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`subobject_lt_wellFounded] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`subobject_lt_wellFounded] [] -/
/-- An artinian object is an object
which does not have infinite decreasing sequences of subobjects.
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,16 +2,13 @@
Copyright (c) 2022 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-
-! This file was ported from Lean 3 source module category_theory.noetherian
-! leanprover-community/mathlib commit f2b757fc5c341d88741b9c4630b1e8ba973c5726
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.CategoryTheory.Subobject.Lattice
import Mathbin.CategoryTheory.EssentiallySmall
import Mathbin.CategoryTheory.Simple
+#align_import category_theory.noetherian from "leanprover-community/mathlib"@"f2b757fc5c341d88741b9c4630b1e8ba973c5726"
+
/-!
# Artinian and noetherian categories
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -49,7 +49,7 @@ class NoetherianObject (X : C) : Prop where
-/
#print CategoryTheory.ArtinianObject /-
-/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`subobject_lt_wellFounded] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`subobject_lt_wellFounded] [] -/
/-- An artinian object is an object
which does not have infinite decreasing sequences of subobjects.
@@ -86,6 +86,7 @@ open Subobject
variable [HasZeroMorphisms C] [HasZeroObject C]
+#print CategoryTheory.exists_simple_subobject /-
theorem exists_simple_subobject {X : C} [ArtinianObject X] (h : ¬IsZero X) :
∃ Y : Subobject X, Simple (Y : C) :=
by
@@ -95,6 +96,7 @@ theorem exists_simple_subobject {X : C} [ArtinianObject X] (h : ¬IsZero X) :
obtain ⟨Y, s⟩ := (IsAtomic.eq_bot_or_exists_atom_le (⊤ : subobject X)).resolve_left top_ne_bot
exact ⟨Y, (subobject_simple_iff_is_atom _).mpr s.1⟩
#align category_theory.exists_simple_subobject CategoryTheory.exists_simple_subobject
+-/
#print CategoryTheory.simpleSubobject /-
/-- Choose an arbitrary simple subobject of a non-zero artinian object. -/
mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297
@@ -49,7 +49,7 @@ class NoetherianObject (X : C) : Prop where
-/
#print CategoryTheory.ArtinianObject /-
-/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`subobject_lt_wellFounded] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`subobject_lt_wellFounded] [] -/
/-- An artinian object is an object
which does not have infinite decreasing sequences of subobjects.
mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb
@@ -107,7 +107,8 @@ noncomputable def simpleSubobject {X : C} [ArtinianObject X] (h : ¬IsZero X) :
/-- The monomorphism from the arbitrary simple subobject of a non-zero artinian object. -/
noncomputable def simpleSubobjectArrow {X : C} [ArtinianObject X] (h : ¬IsZero X) :
simpleSubobject h ⟶ X :=
- (exists_simple_subobject h).some.arrow deriving Mono
+ (exists_simple_subobject h).some.arrow
+deriving Mono
#align category_theory.simple_subobject_arrow CategoryTheory.simpleSubobjectArrow
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -86,12 +86,6 @@ open Subobject
variable [HasZeroMorphisms C] [HasZeroObject C]
-/- warning: category_theory.exists_simple_subobject -> CategoryTheory.exists_simple_subobject is a dubious translation:
-lean 3 declaration is
- forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Limits.HasZeroMorphisms.{u2, u1} C _inst_1] [_inst_3 : CategoryTheory.Limits.HasZeroObject.{u2, u1} C _inst_1] {X : C} [_inst_4 : CategoryTheory.ArtinianObject.{u1, u2} C _inst_1 X], (Not (CategoryTheory.Limits.IsZero.{u2, u1} C _inst_1 X)) -> (Exists.{succ (max u1 u2)} (CategoryTheory.Subobject.{u2, u1} C _inst_1 X) (fun (Y : CategoryTheory.Subobject.{u2, u1} C _inst_1 X) => CategoryTheory.Simple.{u2, u1} C _inst_1 _inst_2 ((fun (a : Type.{max u1 u2}) (b : Type.{u1}) [self : HasLiftT.{succ (max u1 u2), succ u1} a b] => self.0) (CategoryTheory.Subobject.{u2, u1} C _inst_1 X) C (HasLiftT.mk.{succ (max u1 u2), succ u1} (CategoryTheory.Subobject.{u2, u1} C _inst_1 X) C (CoeTCₓ.coe.{succ (max u1 u2), succ u1} (CategoryTheory.Subobject.{u2, u1} C _inst_1 X) C (coeBase.{succ (max u1 u2), succ u1} (CategoryTheory.Subobject.{u2, u1} C _inst_1 X) C (CategoryTheory.Subobject.hasCoe.{u2, u1} C _inst_1 X)))) Y)))
-but is expected to have type
- forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Limits.HasZeroMorphisms.{u1, u2} C _inst_1] [_inst_3 : CategoryTheory.Limits.HasZeroObject.{u1, u2} C _inst_1] {X : C} [_inst_4 : CategoryTheory.ArtinianObject.{u2, u1} C _inst_1 X], (Not (CategoryTheory.Limits.IsZero.{u1, u2} C _inst_1 X)) -> (Exists.{max (succ u2) (succ u1)} (CategoryTheory.Subobject.{u1, u2} C _inst_1 X) (fun (Y : CategoryTheory.Subobject.{u1, u2} C _inst_1 X) => CategoryTheory.Simple.{u1, u2} C _inst_1 _inst_2 (Prefunctor.obj.{max (succ u2) (succ u1), succ u1, max u2 u1, u2} (CategoryTheory.Subobject.{u1, u2} C _inst_1 X) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max u2 u1} (CategoryTheory.Subobject.{u1, u2} C _inst_1 X) (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max u2 u1} (CategoryTheory.Subobject.{u1, u2} C _inst_1 X) (Preorder.smallCategory.{max u2 u1} (CategoryTheory.Subobject.{u1, u2} C _inst_1 X) (PartialOrder.toPreorder.{max u2 u1} (CategoryTheory.Subobject.{u1, u2} C _inst_1 X) (CategoryTheory.instPartialOrderSubobject.{u1, u2} C _inst_1 X))))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{max u2 u1, u1, max u2 u1, u2} (CategoryTheory.Subobject.{u1, u2} C _inst_1 X) (Preorder.smallCategory.{max u2 u1} (CategoryTheory.Subobject.{u1, u2} C _inst_1 X) (PartialOrder.toPreorder.{max u2 u1} (CategoryTheory.Subobject.{u1, u2} C _inst_1 X) (CategoryTheory.instPartialOrderSubobject.{u1, u2} C _inst_1 X))) C _inst_1 (CategoryTheory.Subobject.underlying.{u1, u2} C _inst_1 X)) Y)))
-Case conversion may be inaccurate. Consider using '#align category_theory.exists_simple_subobject CategoryTheory.exists_simple_subobjectₓ'. -/
theorem exists_simple_subobject {X : C} [ArtinianObject X] (h : ¬IsZero X) :
∃ Y : Subobject X, Simple (Y : C) :=
by
mathlib commit https://github.com/leanprover-community/mathlib/commit/86d04064ca33ee3d3405fbfc497d494fd2dd4796
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
! This file was ported from Lean 3 source module category_theory.noetherian
-! leanprover-community/mathlib commit 7c4c90f422a4a4477e4d8bc4dc9f1e634e6b2349
+! leanprover-community/mathlib commit f2b757fc5c341d88741b9c4630b1e8ba973c5726
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -15,6 +15,9 @@ import Mathbin.CategoryTheory.Simple
/-!
# Artinian and noetherian categories
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
An artinian category is a category in which objects do not
have infinite decreasing sequences of subobjects.
mathlib commit https://github.com/leanprover-community/mathlib/commit/9b2b58d6b14b895b2f375108e765cb47de71aebd
@@ -34,6 +34,7 @@ open CategoryTheory.Limits
variable {C : Type _} [Category C]
+#print CategoryTheory.NoetherianObject /-
/-- A noetherian object is an object
which does not have infinite increasing sequences of subobjects.
@@ -42,7 +43,9 @@ See https://stacks.math.columbia.edu/tag/0FCG
class NoetherianObject (X : C) : Prop where
subobject_gt_wellFounded : WellFounded ((· > ·) : Subobject X → Subobject X → Prop)
#align category_theory.noetherian_object CategoryTheory.NoetherianObject
+-/
+#print CategoryTheory.ArtinianObject /-
/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`subobject_lt_wellFounded] [] -/
/-- An artinian object is an object
which does not have infinite decreasing sequences of subobjects.
@@ -52,20 +55,25 @@ See https://stacks.math.columbia.edu/tag/0FCF
class ArtinianObject (X : C) : Prop where
subobject_lt_wellFounded : WellFounded ((· < ·) : Subobject X → Subobject X → Prop)
#align category_theory.artinian_object CategoryTheory.ArtinianObject
+-/
variable (C)
+#print CategoryTheory.Noetherian /-
/-- A category is noetherian if it is essentially small and all objects are noetherian. -/
class Noetherian extends EssentiallySmall C where
NoetherianObject : ∀ X : C, NoetherianObject X
#align category_theory.noetherian CategoryTheory.Noetherian
+-/
attribute [instance] noetherian.noetherian_object
+#print CategoryTheory.Artinian /-
/-- A category is artinian if it is essentially small and all objects are artinian. -/
class Artinian extends EssentiallySmall C where
ArtinianObject : ∀ X : C, ArtinianObject X
#align category_theory.artinian CategoryTheory.Artinian
+-/
attribute [instance] artinian.artinian_object
@@ -75,6 +83,12 @@ open Subobject
variable [HasZeroMorphisms C] [HasZeroObject C]
+/- warning: category_theory.exists_simple_subobject -> CategoryTheory.exists_simple_subobject is a dubious translation:
+lean 3 declaration is
+ forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Limits.HasZeroMorphisms.{u2, u1} C _inst_1] [_inst_3 : CategoryTheory.Limits.HasZeroObject.{u2, u1} C _inst_1] {X : C} [_inst_4 : CategoryTheory.ArtinianObject.{u1, u2} C _inst_1 X], (Not (CategoryTheory.Limits.IsZero.{u2, u1} C _inst_1 X)) -> (Exists.{succ (max u1 u2)} (CategoryTheory.Subobject.{u2, u1} C _inst_1 X) (fun (Y : CategoryTheory.Subobject.{u2, u1} C _inst_1 X) => CategoryTheory.Simple.{u2, u1} C _inst_1 _inst_2 ((fun (a : Type.{max u1 u2}) (b : Type.{u1}) [self : HasLiftT.{succ (max u1 u2), succ u1} a b] => self.0) (CategoryTheory.Subobject.{u2, u1} C _inst_1 X) C (HasLiftT.mk.{succ (max u1 u2), succ u1} (CategoryTheory.Subobject.{u2, u1} C _inst_1 X) C (CoeTCₓ.coe.{succ (max u1 u2), succ u1} (CategoryTheory.Subobject.{u2, u1} C _inst_1 X) C (coeBase.{succ (max u1 u2), succ u1} (CategoryTheory.Subobject.{u2, u1} C _inst_1 X) C (CategoryTheory.Subobject.hasCoe.{u2, u1} C _inst_1 X)))) Y)))
+but is expected to have type
+ forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Limits.HasZeroMorphisms.{u1, u2} C _inst_1] [_inst_3 : CategoryTheory.Limits.HasZeroObject.{u1, u2} C _inst_1] {X : C} [_inst_4 : CategoryTheory.ArtinianObject.{u2, u1} C _inst_1 X], (Not (CategoryTheory.Limits.IsZero.{u1, u2} C _inst_1 X)) -> (Exists.{max (succ u2) (succ u1)} (CategoryTheory.Subobject.{u1, u2} C _inst_1 X) (fun (Y : CategoryTheory.Subobject.{u1, u2} C _inst_1 X) => CategoryTheory.Simple.{u1, u2} C _inst_1 _inst_2 (Prefunctor.obj.{max (succ u2) (succ u1), succ u1, max u2 u1, u2} (CategoryTheory.Subobject.{u1, u2} C _inst_1 X) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max u2 u1} (CategoryTheory.Subobject.{u1, u2} C _inst_1 X) (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max u2 u1} (CategoryTheory.Subobject.{u1, u2} C _inst_1 X) (Preorder.smallCategory.{max u2 u1} (CategoryTheory.Subobject.{u1, u2} C _inst_1 X) (PartialOrder.toPreorder.{max u2 u1} (CategoryTheory.Subobject.{u1, u2} C _inst_1 X) (CategoryTheory.instPartialOrderSubobject.{u1, u2} C _inst_1 X))))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{max u2 u1, u1, max u2 u1, u2} (CategoryTheory.Subobject.{u1, u2} C _inst_1 X) (Preorder.smallCategory.{max u2 u1} (CategoryTheory.Subobject.{u1, u2} C _inst_1 X) (PartialOrder.toPreorder.{max u2 u1} (CategoryTheory.Subobject.{u1, u2} C _inst_1 X) (CategoryTheory.instPartialOrderSubobject.{u1, u2} C _inst_1 X))) C _inst_1 (CategoryTheory.Subobject.underlying.{u1, u2} C _inst_1 X)) Y)))
+Case conversion may be inaccurate. Consider using '#align category_theory.exists_simple_subobject CategoryTheory.exists_simple_subobjectₓ'. -/
theorem exists_simple_subobject {X : C} [ArtinianObject X] (h : ¬IsZero X) :
∃ Y : Subobject X, Simple (Y : C) :=
by
@@ -85,16 +99,20 @@ theorem exists_simple_subobject {X : C} [ArtinianObject X] (h : ¬IsZero X) :
exact ⟨Y, (subobject_simple_iff_is_atom _).mpr s.1⟩
#align category_theory.exists_simple_subobject CategoryTheory.exists_simple_subobject
+#print CategoryTheory.simpleSubobject /-
/-- Choose an arbitrary simple subobject of a non-zero artinian object. -/
noncomputable def simpleSubobject {X : C} [ArtinianObject X] (h : ¬IsZero X) : C :=
(exists_simple_subobject h).some
#align category_theory.simple_subobject CategoryTheory.simpleSubobject
+-/
+#print CategoryTheory.simpleSubobjectArrow /-
/-- The monomorphism from the arbitrary simple subobject of a non-zero artinian object. -/
noncomputable def simpleSubobjectArrow {X : C} [ArtinianObject X] (h : ¬IsZero X) :
simpleSubobject h ⟶ X :=
(exists_simple_subobject h).some.arrow deriving Mono
#align category_theory.simple_subobject_arrow CategoryTheory.simpleSubobjectArrow
+-/
instance {X : C} [ArtinianObject X] (h : ¬IsZero X) : Simple (simpleSubobject h) :=
(exists_simple_subobject h).choose_spec
mathlib commit https://github.com/leanprover-community/mathlib/commit/09079525fd01b3dda35e96adaa08d2f943e1648c
@@ -43,7 +43,7 @@ class NoetherianObject (X : C) : Prop where
subobject_gt_wellFounded : WellFounded ((· > ·) : Subobject X → Subobject X → Prop)
#align category_theory.noetherian_object CategoryTheory.NoetherianObject
-/- ./././Mathport/Syntax/Translate/Command.lean:388:30: infer kinds are unsupported in Lean 4: #[`subobject_lt_wellFounded] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`subobject_lt_wellFounded] [] -/
/-- An artinian object is an object
which does not have infinite decreasing sequences of subobjects.
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -29,7 +29,7 @@ namespace CategoryTheory
open CategoryTheory.Limits
-variable {C : Type _} [Category C]
+variable {C : Type*} [Category C]
/-- A noetherian object is an object
which does not have infinite increasing sequences of subobjects.
@@ -60,14 +60,14 @@ lemma ArtinianObject.subobject_lt_wellFounded (X : C) [ArtinianObject X] :
variable (C)
/-- A category is noetherian if it is essentially small and all objects are noetherian. -/
-class Noetherian extends EssentiallySmall C where
+class Noetherian extends EssentiallySmall C : Prop where
noetherianObject : ∀ X : C, NoetherianObject X
#align category_theory.noetherian CategoryTheory.Noetherian
attribute [instance] Noetherian.noetherianObject
/-- A category is artinian if it is essentially small and all objects are artinian. -/
-class Artinian extends EssentiallySmall C where
+class Artinian extends EssentiallySmall C : Prop where
artinianObject : ∀ X : C, ArtinianObject X
#align category_theory.artinian CategoryTheory.Artinian
@@ -2,16 +2,13 @@
Copyright (c) 2022 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-
-! This file was ported from Lean 3 source module category_theory.noetherian
-! leanprover-community/mathlib commit 7c4c90f422a4a4477e4d8bc4dc9f1e634e6b2349
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.CategoryTheory.Subobject.Lattice
import Mathlib.CategoryTheory.EssentiallySmall
import Mathlib.CategoryTheory.Simple
+#align_import category_theory.noetherian from "leanprover-community/mathlib"@"7c4c90f422a4a4477e4d8bc4dc9f1e634e6b2349"
+
/-!
# Artinian and noetherian categories
The unported dependencies are