topology.sheaves.operations
⟷
Mathlib.Topology.Sheaves.Operations
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/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,10 +3,10 @@ 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.Algebra.Category.Ring.Instances
-import Mathbin.Algebra.Category.Ring.FilteredColimits
-import Mathbin.RingTheory.Localization.Basic
-import Mathbin.Topology.Sheaves.Stalks
+import Algebra.Category.Ring.Instances
+import Algebra.Category.Ring.FilteredColimits
+import RingTheory.Localization.Basic
+import Topology.Sheaves.Stalks
#align_import topology.sheaves.operations from "leanprover-community/mathlib"@"2a0ce625dbb0ffbc7d1316597de0b25c1ec75303"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,17 +2,14 @@
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 topology.sheaves.operations
-! leanprover-community/mathlib commit 2a0ce625dbb0ffbc7d1316597de0b25c1ec75303
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.Algebra.Category.Ring.Instances
import Mathbin.Algebra.Category.Ring.FilteredColimits
import Mathbin.RingTheory.Localization.Basic
import Mathbin.Topology.Sheaves.Stalks
+#align_import topology.sheaves.operations from "leanprover-community/mathlib"@"2a0ce625dbb0ffbc7d1316597de0b25c1ec75303"
+
/-!
# Operations on sheaves
mathlib commit https://github.com/leanprover-community/mathlib/commit/2a0ce625dbb0ffbc7d1316597de0b25c1ec75303
@@ -43,15 +43,18 @@ variable {X : TopCat.{w}} {C : Type u} [Category.{v} C] [ConcreteCategory C]
attribute [local instance] concrete_category.has_coe_to_sort
+#print TopCat.Presheaf.SubmonoidPresheaf /-
/-- A subpresheaf with a submonoid structure on each of the components. -/
structure SubmonoidPresheaf [∀ X : C, MulOneClass X] [∀ X Y : C, MonoidHomClass (X ⟶ Y) X Y]
(F : X.Presheaf C) where
obj : ∀ U, Submonoid (F.obj U)
map : ∀ {U V : (Opens X)ᵒᵖ} (i : U ⟶ V), obj U ≤ (obj V).comap (F.map i)
#align Top.presheaf.submonoid_presheaf TopCat.Presheaf.SubmonoidPresheaf
+-/
variable {F : X.Presheaf CommRingCat.{w}} (G : F.SubmonoidPresheaf)
+#print TopCat.Presheaf.SubmonoidPresheaf.localizationPresheaf /-
/-- The localization of a presheaf of `CommRing`s with respect to a `submonoid_presheaf`. -/
protected noncomputable def SubmonoidPresheaf.localizationPresheaf : X.Presheaf CommRingCat
where
@@ -68,19 +71,23 @@ protected noncomputable def SubmonoidPresheaf.localizationPresheaf : X.Presheaf
refine' Eq.trans _ (IsLocalization.map_comp_map _ _).symm
ext; dsimp; congr; rw [F.map_comp]; rfl
#align Top.presheaf.submonoid_presheaf.localization_presheaf TopCat.Presheaf.SubmonoidPresheaf.localizationPresheaf
+-/
+#print TopCat.Presheaf.SubmonoidPresheaf.toLocalizationPresheaf /-
/-- The map into the localization presheaf. -/
def SubmonoidPresheaf.toLocalizationPresheaf : F ⟶ G.localizationPresheaf
where
app U := CommRingCat.ofHom <| algebraMap (F.obj U) (Localization <| G.obj U)
naturality' U V i := (IsLocalization.map_comp (G.map i)).symm
#align Top.presheaf.submonoid_presheaf.to_localization_presheaf TopCat.Presheaf.SubmonoidPresheaf.toLocalizationPresheaf
+-/
instance : Epi G.toLocalizationPresheaf :=
@NatTrans.epi_of_epi_app _ _ G.toLocalizationPresheaf fun U => Localization.epi' (G.obj U)
variable (F)
+#print TopCat.Presheaf.submonoidPresheafOfStalk /-
/-- Given a submonoid at each of the stalks, we may define a submonoid presheaf consisting of
sections whose restriction onto each stalk falls in the given submonoid. -/
@[simps]
@@ -96,20 +103,25 @@ noncomputable def submonoidPresheafOfStalk (S : ∀ x : X, Submonoid (F.stalk x)
rw [F.germ_res]
exact hs _
#align Top.presheaf.submonoid_presheaf_of_stalk TopCat.Presheaf.submonoidPresheafOfStalk
+-/
noncomputable instance : Inhabited F.SubmonoidPresheaf :=
⟨F.submonoidPresheafOfStalk fun _ => ⊥⟩
+#print TopCat.Presheaf.totalQuotientPresheaf /-
/-- The localization of a presheaf of `CommRing`s at locally non-zero-divisor sections. -/
noncomputable def totalQuotientPresheaf : X.Presheaf CommRingCat.{w} :=
(F.submonoidPresheafOfStalk fun x => (F.stalk x)⁰).localizationPresheaf
#align Top.presheaf.total_quotient_presheaf TopCat.Presheaf.totalQuotientPresheaf
+-/
+#print TopCat.Presheaf.toTotalQuotientPresheaf /-
/-- The map into the presheaf of total quotient rings -/
noncomputable def toTotalQuotientPresheaf : F ⟶ F.totalQuotientPresheaf :=
SubmonoidPresheaf.toLocalizationPresheaf _
deriving Epi
#align Top.presheaf.to_total_quotient_presheaf TopCat.Presheaf.toTotalQuotientPresheaf
+-/
instance (F : X.Sheaf CommRingCat.{w}) : Mono F.Presheaf.toTotalQuotientPresheaf :=
by
mathlib commit https://github.com/leanprover-community/mathlib/commit/2a0ce625dbb0ffbc7d1316597de0b25c1ec75303
@@ -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 topology.sheaves.operations
-! leanprover-community/mathlib commit 70fd9563a21e7b963887c9360bd29b2393e6225a
+! leanprover-community/mathlib commit 2a0ce625dbb0ffbc7d1316597de0b25c1ec75303
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -17,6 +17,9 @@ import Mathbin.Topology.Sheaves.Stalks
# Operations on sheaves
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
## Main definition
- `submonoid_presheaf` : A subpresheaf with a submonoid structure on each of the components.
mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb
@@ -42,7 +42,7 @@ attribute [local instance] concrete_category.has_coe_to_sort
/-- A subpresheaf with a submonoid structure on each of the components. -/
structure SubmonoidPresheaf [∀ X : C, MulOneClass X] [∀ X Y : C, MonoidHomClass (X ⟶ Y) X Y]
- (F : X.Presheaf C) where
+ (F : X.Presheaf C) where
obj : ∀ U, Submonoid (F.obj U)
map : ∀ {U V : (Opens X)ᵒᵖ} (i : U ⟶ V), obj U ≤ (obj V).comap (F.map i)
#align Top.presheaf.submonoid_presheaf TopCat.Presheaf.SubmonoidPresheaf
@@ -63,7 +63,7 @@ protected noncomputable def SubmonoidPresheaf.localizationPresheaf : X.Presheaf
map_comp' U V W i j :=
by
refine' Eq.trans _ (IsLocalization.map_comp_map _ _).symm
- ext; dsimp; congr ; rw [F.map_comp]; rfl
+ ext; dsimp; congr; rw [F.map_comp]; rfl
#align Top.presheaf.submonoid_presheaf.localization_presheaf TopCat.Presheaf.SubmonoidPresheaf.localizationPresheaf
/-- The map into the localization presheaf. -/
@@ -87,7 +87,7 @@ noncomputable def submonoidPresheafOfStalk (S : ∀ x : X, Submonoid (F.stalk x)
obj U := ⨅ x : unop U, Submonoid.comap (F.germ x) (S x)
map U V i := by
intro s hs
- simp only [Submonoid.mem_comap, Submonoid.mem_iInf] at hs⊢
+ simp only [Submonoid.mem_comap, Submonoid.mem_iInf] at hs ⊢
intro x
change (F.map i.unop.op ≫ F.germ x) s ∈ _
rw [F.germ_res]
@@ -104,7 +104,8 @@ noncomputable def totalQuotientPresheaf : X.Presheaf CommRingCat.{w} :=
/-- The map into the presheaf of total quotient rings -/
noncomputable def toTotalQuotientPresheaf : F ⟶ F.totalQuotientPresheaf :=
- SubmonoidPresheaf.toLocalizationPresheaf _ deriving Epi
+ SubmonoidPresheaf.toLocalizationPresheaf _
+deriving Epi
#align Top.presheaf.to_total_quotient_presheaf TopCat.Presheaf.toTotalQuotientPresheaf
instance (F : X.Sheaf CommRingCat.{w}) : Mono F.Presheaf.toTotalQuotientPresheaf :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -26,7 +26,7 @@ import Mathbin.Topology.Sheaves.Stalks
-/
-open nonZeroDivisors
+open scoped nonZeroDivisors
open TopologicalSpace Opposite CategoryTheory
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -63,11 +63,7 @@ protected noncomputable def SubmonoidPresheaf.localizationPresheaf : X.Presheaf
map_comp' U V W i j :=
by
refine' Eq.trans _ (IsLocalization.map_comp_map _ _).symm
- ext
- dsimp
- congr
- rw [F.map_comp]
- rfl
+ ext; dsimp; congr ; rw [F.map_comp]; rfl
#align Top.presheaf.submonoid_presheaf.localization_presheaf TopCat.Presheaf.SubmonoidPresheaf.localizationPresheaf
/-- The map into the localization presheaf. -/
mathlib commit https://github.com/leanprover-community/mathlib/commit/e3fb84046afd187b710170887195d50bada934ee
@@ -91,7 +91,7 @@ noncomputable def submonoidPresheafOfStalk (S : ∀ x : X, Submonoid (F.stalk x)
obj U := ⨅ x : unop U, Submonoid.comap (F.germ x) (S x)
map U V i := by
intro s hs
- simp only [Submonoid.mem_comap, Submonoid.mem_infᵢ] at hs⊢
+ simp only [Submonoid.mem_comap, Submonoid.mem_iInf] at hs⊢
intro x
change (F.map i.unop.op ≫ F.germ x) s ∈ _
rw [F.germ_res]
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
In this pull request, I have systematically eliminated the leading whitespace preceding the colon (:
) within all unlabelled or unclassified porting notes. This adjustment facilitates a more efficient review process for the remaining notes by ensuring no entries are overlooked due to formatting inconsistencies.
@@ -55,7 +55,7 @@ protected noncomputable def SubmonoidPresheaf.localizationPresheaf : X.Presheaf
map_id U := by
simp_rw [F.map_id]
ext x
- -- Porting note : `M` and `S` needs to be specified manually
+ -- Porting note: `M` and `S` needs to be specified manually
exact IsLocalization.map_id (M := G.obj U) (S := Localization (G.obj U)) x
map_comp {U V W} i j := by
delta CommRingCat.ofHom CommRingCat.of Bundled.of
@@ -63,11 +63,11 @@ protected noncomputable def SubmonoidPresheaf.localizationPresheaf : X.Presheaf
rw [IsLocalization.map_comp_map]
#align Top.presheaf.submonoid_presheaf.localization_presheaf TopCat.Presheaf.SubmonoidPresheaf.localizationPresheaf
--- Porting note : this instance can't be synthesized
+-- Porting note: this instance can't be synthesized
instance (U) : Algebra ((forget CommRingCat).obj (F.obj U)) (G.localizationPresheaf.obj U) :=
show Algebra _ (Localization (G.obj U)) from inferInstance
--- Porting note : this instance can't be synthesized
+-- Porting note: this instance can't be synthesized
instance (U) : IsLocalization (G.obj U) (G.localizationPresheaf.obj U) :=
show IsLocalization (G.obj U) (Localization (G.obj U)) from inferInstance
@@ -111,30 +111,30 @@ noncomputable def toTotalQuotientPresheaf : F ⟶ F.totalQuotientPresheaf :=
SubmonoidPresheaf.toLocalizationPresheaf _
#align Top.presheaf.to_total_quotient_presheaf TopCat.Presheaf.toTotalQuotientPresheaf
--- Porting note : deriving `Epi` failed
+-- Porting note: deriving `Epi` failed
instance : Epi (toTotalQuotientPresheaf F) := epi_toLocalizationPresheaf _
instance (F : X.Sheaf CommRingCat.{w}) : Mono F.presheaf.toTotalQuotientPresheaf := by
- -- Porting note : was an `apply (config := { instances := false })`
+ -- Porting note: was an `apply (config := { instances := false })`
-- See https://github.com/leanprover/lean4/issues/2273
suffices ∀ (U : (Opens ↑X)ᵒᵖ), Mono (F.presheaf.toTotalQuotientPresheaf.app U) from
NatTrans.mono_of_mono_app _
intro U
apply ConcreteCategory.mono_of_injective
dsimp [toTotalQuotientPresheaf, CommRingCat.ofHom]
- -- Porting note : this is a hack to make the `refine` below works
+ -- Porting note: this is a hack to make the `refine` below works
set m := _
change Function.Injective (algebraMap _ (Localization m))
change Function.Injective (algebraMap (F.presheaf.obj U) _)
haveI : IsLocalization _ (Localization m) := Localization.isLocalization
- -- Porting note : `M` and `S` need to be specified manually, so used a hack to save some typing
+ -- Porting note: `M` and `S` need to be specified manually, so used a hack to save some typing
refine IsLocalization.injective (M := m) (S := Localization m) ?_
intro s hs t e
apply section_ext F (unop U)
intro x
rw [map_zero]
apply Submonoid.mem_iInf.mp hs x
- -- Porting note : added `dsimp` to make `rw [← map_mul]` work
+ -- Porting note: added `dsimp` to make `rw [← map_mul]` work
dsimp
rw [← map_mul, e, map_zero]
have
, replace
and suffices
(#10640)
No changes to tactic file, it's just boring fixes throughout the library.
This follows on from #6964.
Co-authored-by: sgouezel <sebastien.gouezel@univ-rennes1.fr> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
@@ -117,8 +117,8 @@ instance : Epi (toTotalQuotientPresheaf F) := epi_toLocalizationPresheaf _
instance (F : X.Sheaf CommRingCat.{w}) : Mono F.presheaf.toTotalQuotientPresheaf := by
-- Porting note : was an `apply (config := { instances := false })`
-- See https://github.com/leanprover/lean4/issues/2273
- suffices : ∀ (U : (Opens ↑X)ᵒᵖ), Mono (F.presheaf.toTotalQuotientPresheaf.app U)
- · apply NatTrans.mono_of_mono_app
+ suffices ∀ (U : (Opens ↑X)ᵒᵖ), Mono (F.presheaf.toTotalQuotientPresheaf.app U) from
+ NatTrans.mono_of_mono_app _
intro U
apply ConcreteCategory.mono_of_injective
dsimp [toTotalQuotientPresheaf, CommRingCat.ofHom]
@@ -134,9 +134,9 @@ instance (F : X.Sheaf CommRingCat.{w}) : Mono F.presheaf.toTotalQuotientPresheaf
intro x
rw [map_zero]
apply Submonoid.mem_iInf.mp hs x
- -- Porting note : added `dsimp` to make `rw ←map_mul` work
+ -- Porting note : added `dsimp` to make `rw [← map_mul]` work
dsimp
- rw [←map_mul, e, map_zero]
+ rw [← map_mul, e, map_zero]
end Presheaf
@@ -63,11 +63,11 @@ protected noncomputable def SubmonoidPresheaf.localizationPresheaf : X.Presheaf
rw [IsLocalization.map_comp_map]
#align Top.presheaf.submonoid_presheaf.localization_presheaf TopCat.Presheaf.SubmonoidPresheaf.localizationPresheaf
--- Porting note : this is instance can't be synthesized
+-- Porting note : this instance can't be synthesized
instance (U) : Algebra ((forget CommRingCat).obj (F.obj U)) (G.localizationPresheaf.obj U) :=
show Algebra _ (Localization (G.obj U)) from inferInstance
--- Porting note : this is instance can't be synthesized
+-- Porting note : this instance can't be synthesized
instance (U) : IsLocalization (G.obj U) (G.localizationPresheaf.obj U) :=
show IsLocalization (G.obj U) (Localization (G.obj U)) from inferInstance
@@ -2,17 +2,14 @@
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 topology.sheaves.operations
-! 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.Algebra.Category.Ring.Instances
import Mathlib.Algebra.Category.Ring.FilteredColimits
import Mathlib.RingTheory.Localization.Basic
import Mathlib.Topology.Sheaves.Stalks
+#align_import topology.sheaves.operations from "leanprover-community/mathlib"@"70fd9563a21e7b963887c9360bd29b2393e6225a"
+
/-!
# Operations on sheaves
This PR is the result of running
find . -type f -name "*.lean" -exec sed -i -E 's/^( +)\. /\1· /' {} \;
find . -type f -name "*.lean" -exec sed -i -E 'N;s/^( +·)\n +(.*)$/\1 \2/;P;D' {} \;
which firstly replaces .
focusing dots with ·
and secondly removes isolated instances of such dots, unifying them with the following line. A new rule is placed in the style linter to verify this.
@@ -121,7 +121,7 @@ instance (F : X.Sheaf CommRingCat.{w}) : Mono F.presheaf.toTotalQuotientPresheaf
-- Porting note : was an `apply (config := { instances := false })`
-- See https://github.com/leanprover/lean4/issues/2273
suffices : ∀ (U : (Opens ↑X)ᵒᵖ), Mono (F.presheaf.toTotalQuotientPresheaf.app U)
- . apply NatTrans.mono_of_mono_app
+ · apply NatTrans.mono_of_mono_app
intro U
apply ConcreteCategory.mono_of_injective
dsimp [toTotalQuotientPresheaf, CommRingCat.ofHom]
@@ -118,7 +118,8 @@ noncomputable def toTotalQuotientPresheaf : F ⟶ F.totalQuotientPresheaf :=
instance : Epi (toTotalQuotientPresheaf F) := epi_toLocalizationPresheaf _
instance (F : X.Sheaf CommRingCat.{w}) : Mono F.presheaf.toTotalQuotientPresheaf := by
- -- Porting note : was an `apply (config := { synthAssignedInstances := false })`
+ -- Porting note : was an `apply (config := { instances := false })`
+ -- See https://github.com/leanprover/lean4/issues/2273
suffices : ∀ (U : (Opens ↑X)ᵒᵖ), Mono (F.presheaf.toTotalQuotientPresheaf.app U)
. apply NatTrans.mono_of_mono_app
intro U
The unported dependencies are