algebraic_geometry.gluing ⟷ Mathlib.AlgebraicGeometry.Gluing

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -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 AlgebraicGeometry.PresheafedSpace.Gluing
-import AlgebraicGeometry.OpenImmersion.Scheme
+import Geometry.RingedSpace.PresheafedSpace.Gluing
+import AlgebraicGeometry.OpenImmersion
 
 #align_import algebraic_geometry.gluing from "leanprover-community/mathlib"@"d0b1936853671209a866fa35b9e54949c81116e2"
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -419,8 +419,8 @@ theorem fromGlued_injective : Function.Injective 𝒰.fromGlued.1.base :=
   intro x y h
   obtain ⟨i, x, rfl⟩ := 𝒰.glued_cover.ι_jointly_surjective x
   obtain ⟨j, y, rfl⟩ := 𝒰.glued_cover.ι_jointly_surjective y
-  simp_rw [← comp_apply, ← SheafedSpace.comp_base, ← LocallyRingedSpace.comp_val] at h 
-  erw [ι_from_glued, ι_from_glued] at h 
+  simp_rw [← comp_apply, ← SheafedSpace.comp_base, ← LocallyRingedSpace.comp_val] at h
+  erw [ι_from_glued, ι_from_glued] at h
   let e :=
     (TopCat.pullbackConeIsLimit _ _).conePointUniqueUpToIso
       (is_limit_of_has_pullback_of_preserves_limit Scheme.forget_to_Top (𝒰.map i) (𝒰.map j))
@@ -444,8 +444,8 @@ instance fromGlued_stalk_iso (x : 𝒰.gluedCover.glued.carrier) :
   have :=
     PresheafedSpace.stalk_map.congr_hom _ _
       (congr_arg LocallyRingedSpace.hom.val <| 𝒰.ι_from_glued i) x
-  erw [PresheafedSpace.stalk_map.comp] at this 
-  rw [← is_iso.eq_comp_inv] at this 
+  erw [PresheafedSpace.stalk_map.comp] at this
+  rw [← is_iso.eq_comp_inv] at this
   rw [this]
   infer_instance
 #align algebraic_geometry.Scheme.open_cover.from_glued_stalk_iso AlgebraicGeometry.Scheme.OpenCover.fromGlued_stalk_iso
@@ -457,7 +457,7 @@ theorem fromGlued_open_map : IsOpenMap 𝒰.fromGlued.1.base :=
   intro U hU
   rw [isOpen_iff_forall_mem_open]
   intro x hx
-  rw [𝒰.glued_cover.is_open_iff] at hU 
+  rw [𝒰.glued_cover.is_open_iff] at hU
   use 𝒰.from_glued.val.base '' U ∩ Set.range (𝒰.map (𝒰.f x)).1.base
   use Set.inter_subset_left _ _
   constructor
@@ -485,7 +485,7 @@ instance : Epi 𝒰.fromGlued.val.base :=
   obtain ⟨y, h⟩ := 𝒰.covers x
   use(𝒰.glued_cover.ι (𝒰.f x)).1.base y
   rw [← comp_apply]
-  rw [← 𝒰.ι_from_glued (𝒰.f x)] at h 
+  rw [← 𝒰.ι_from_glued (𝒰.f x)] at h
   exact h
 
 #print AlgebraicGeometry.Scheme.OpenCover.fromGlued_open_immersion /-

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451

@@ -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.PresheafedSpace.Gluing
-import Mathbin.AlgebraicGeometry.OpenImmersion.Scheme
+import AlgebraicGeometry.PresheafedSpace.Gluing
+import AlgebraicGeometry.OpenImmersion.Scheme
 
 #align_import algebraic_geometry.gluing from "leanprover-community/mathlib"@"d0b1936853671209a866fa35b9e54949c81116e2"
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/63721b2c3eba6c325ecf8ae8cca27155a4f6306f

@@ -483,7 +483,7 @@ instance : Epi 𝒰.fromGlued.val.base :=
   rw [TopCat.epi_iff_surjective]
   intro x
   obtain ⟨y, h⟩ := 𝒰.covers x
-  use (𝒰.glued_cover.ι (𝒰.f x)).1.base y
+  use(𝒰.glued_cover.ι (𝒰.f x)).1.base y
   rw [← comp_apply]
   rw [← 𝒰.ι_from_glued (𝒰.f x)] at h 
   exact h

mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345

@@ -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.gluing
-! leanprover-community/mathlib commit d0b1936853671209a866fa35b9e54949c81116e2
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.AlgebraicGeometry.PresheafedSpace.Gluing
 import Mathbin.AlgebraicGeometry.OpenImmersion.Scheme
 
+#align_import algebraic_geometry.gluing from "leanprover-community/mathlib"@"d0b1936853671209a866fa35b9e54949c81116e2"
+
 /-!
 # Gluing Schemes
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/728ef9dbb281241906f25cbeb30f90d83e0bb451

@@ -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.gluing
-! leanprover-community/mathlib commit 533f62f4dd62a5aad24a04326e6e787c8f7e98b1
+! leanprover-community/mathlib commit d0b1936853671209a866fa35b9e54949c81116e2
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.AlgebraicGeometry.OpenImmersion.Scheme
 /-!
 # Gluing Schemes
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 Given a family of gluing data of schemes, we may glue them together.
 
 ## Main definitions

mathlib commit https://github.com/leanprover-community/mathlib/commit/8b981918a93bc45a8600de608cde7944a80d92b9

@@ -66,6 +66,7 @@ namespace AlgebraicGeometry
 
 namespace Scheme
 
+#print AlgebraicGeometry.Scheme.GlueData /-
 /-- A family of gluing data consists of
 1. An index type `J`
 2. An scheme `U i` for each `i : J`.
@@ -88,6 +89,7 @@ that the `U i`'s are open subschemes of the glued space.
 structure GlueData extends CategoryTheory.GlueData Scheme where
   f_open : ∀ i j, IsOpenImmersionCat (f i j)
 #align algebraic_geometry.Scheme.glue_data AlgebraicGeometry.Scheme.GlueData
+-/
 
 attribute [instance] glue_data.f_open
 
@@ -97,12 +99,15 @@ variable (D : GlueData)
 
 local notation "𝖣" => D.toGlueData
 
+#print AlgebraicGeometry.Scheme.GlueData.toLocallyRingedSpaceGlueData /-
 /-- The glue data of locally ringed spaces spaces associated to a family of glue data of schemes. -/
 abbrev toLocallyRingedSpaceGlueData : LocallyRingedSpace.GlueData :=
   { f_open := D.f_open
     toGlueData := 𝖣.mapGlueData forgetToLocallyRingedSpace }
 #align algebraic_geometry.Scheme.glue_data.to_LocallyRingedSpace_glue_data AlgebraicGeometry.Scheme.GlueData.toLocallyRingedSpaceGlueData
+-/
 
+#print AlgebraicGeometry.Scheme.GlueData.gluedScheme /-
 /-- (Implementation). The glued scheme of a glue data.
 This should not be used outside this file. Use `Scheme.glue_data.glued` instead. -/
 def gluedScheme : Scheme :=
@@ -120,6 +125,7 @@ def gluedScheme : Scheme :=
     exact (D.U i).affineCover.Covers y
   · infer_instance
 #align algebraic_geometry.Scheme.glue_data.glued_Scheme AlgebraicGeometry.Scheme.GlueData.gluedScheme
+-/
 
 instance : CreatesColimit 𝖣.diagram.multispan forgetToLocallyRingedSpace :=
   createsColimitOfFullyFaithfulOfIso D.gluedScheme
@@ -133,47 +139,64 @@ instance : PreservesColimit 𝖣.diagram.multispan forgetToTop :=
 instance : HasMulticoequalizer 𝖣.diagram :=
   hasColimit_of_created _ forgetToLocallyRingedSpace
 
+#print AlgebraicGeometry.Scheme.GlueData.glued /-
 /-- The glued scheme of a glued space. -/
 abbrev glued : Scheme :=
   𝖣.glued
 #align algebraic_geometry.Scheme.glue_data.glued AlgebraicGeometry.Scheme.GlueData.glued
+-/
 
+#print AlgebraicGeometry.Scheme.GlueData.ι /-
 /-- The immersion from `D.U i` into the glued space. -/
 abbrev ι (i : D.J) : D.U i ⟶ D.glued :=
   𝖣.ι i
 #align algebraic_geometry.Scheme.glue_data.ι AlgebraicGeometry.Scheme.GlueData.ι
+-/
 
+#print AlgebraicGeometry.Scheme.GlueData.isoLocallyRingedSpace /-
 /-- The gluing as sheafed spaces is isomorphic to the gluing as presheafed spaces. -/
 abbrev isoLocallyRingedSpace :
     D.glued.toLocallyRingedSpace ≅ D.toLocallyRingedSpaceGlueData.toGlueData.glued :=
   𝖣.gluedIso forgetToLocallyRingedSpace
 #align algebraic_geometry.Scheme.glue_data.iso_LocallyRingedSpace AlgebraicGeometry.Scheme.GlueData.isoLocallyRingedSpace
+-/
 
+#print AlgebraicGeometry.Scheme.GlueData.ι_isoLocallyRingedSpace_inv /-
 theorem ι_isoLocallyRingedSpace_inv (i : D.J) :
     D.toLocallyRingedSpaceGlueData.toGlueData.ι i ≫ D.isoLocallyRingedSpace.inv = 𝖣.ι i :=
   𝖣.ι_gluedIso_inv forgetToLocallyRingedSpace i
 #align algebraic_geometry.Scheme.glue_data.ι_iso_LocallyRingedSpace_inv AlgebraicGeometry.Scheme.GlueData.ι_isoLocallyRingedSpace_inv
+-/
 
-instance ι_isOpenImmersionCat (i : D.J) : IsOpenImmersionCat (𝖣.ι i) := by
+#print AlgebraicGeometry.Scheme.GlueData.ι_isOpenImmersion /-
+instance ι_isOpenImmersion (i : D.J) : IsOpenImmersionCat (𝖣.ι i) := by
   rw [← D.ι_iso_LocallyRingedSpace_inv]; infer_instance
-#align algebraic_geometry.Scheme.glue_data.ι_is_open_immersion AlgebraicGeometry.Scheme.GlueData.ι_isOpenImmersionCat
+#align algebraic_geometry.Scheme.glue_data.ι_is_open_immersion AlgebraicGeometry.Scheme.GlueData.ι_isOpenImmersion
+-/
 
+#print AlgebraicGeometry.Scheme.GlueData.ι_jointly_surjective /-
 theorem ι_jointly_surjective (x : 𝖣.glued.carrier) :
     ∃ (i : D.J) (y : (D.U i).carrier), (D.ι i).1.base y = x :=
   𝖣.ι_jointly_surjective (forgetToTop ⋙ forget TopCat) x
 #align algebraic_geometry.Scheme.glue_data.ι_jointly_surjective AlgebraicGeometry.Scheme.GlueData.ι_jointly_surjective
+-/
 
+#print AlgebraicGeometry.Scheme.GlueData.glue_condition /-
 @[simp, reassoc]
 theorem glue_condition (i j : D.J) : D.t i j ≫ D.f j i ≫ D.ι j = D.f i j ≫ D.ι i :=
   𝖣.glue_condition i j
 #align algebraic_geometry.Scheme.glue_data.glue_condition AlgebraicGeometry.Scheme.GlueData.glue_condition
+-/
 
+#print AlgebraicGeometry.Scheme.GlueData.vPullbackCone /-
 /-- The pullback cone spanned by `V i j ⟶ U i` and `V i j ⟶ U j`.
 This is a pullback diagram (`V_pullback_cone_is_limit`). -/
 def vPullbackCone (i j : D.J) : PullbackCone (D.ι i) (D.ι j) :=
   PullbackCone.mk (D.f i j) (D.t i j ≫ D.f j i) (by simp)
 #align algebraic_geometry.Scheme.glue_data.V_pullback_cone AlgebraicGeometry.Scheme.GlueData.vPullbackCone
+-/
 
+#print AlgebraicGeometry.Scheme.GlueData.vPullbackConeIsLimit /-
 /-- The following diagram is a pullback, i.e. `Vᵢⱼ` is the intersection of `Uᵢ` and `Uⱼ` in `X`.
 
 Vᵢⱼ ⟶ Uᵢ
@@ -185,7 +208,9 @@ def vPullbackConeIsLimit (i j : D.J) : IsLimit (D.vPullbackCone i j) :=
   𝖣.vPullbackConeIsLimitOfMap forgetToLocallyRingedSpace i j
     (D.toLocallyRingedSpaceGlueData.vPullbackConeIsLimit _ _)
 #align algebraic_geometry.Scheme.glue_data.V_pullback_cone_is_limit AlgebraicGeometry.Scheme.GlueData.vPullbackConeIsLimit
+-/
 
+#print AlgebraicGeometry.Scheme.GlueData.isoCarrier /-
 /-- The underlying topological space of the glued scheme is isomorphic to the gluing of the
 underlying spacess -/
 def isoCarrier :
@@ -200,7 +225,9 @@ def isoCarrier :
       LocallyRingedSpace.glue_data.iso_SheafedSpace _
   exact Scheme.glue_data.iso_LocallyRingedSpace _
 #align algebraic_geometry.Scheme.glue_data.iso_carrier AlgebraicGeometry.Scheme.GlueData.isoCarrier
+-/
 
+#print AlgebraicGeometry.Scheme.GlueData.ι_isoCarrier_inv /-
 @[simp]
 theorem ι_isoCarrier_inv (i : D.J) :
     D.toLocallyRingedSpaceGlueData.toSheafedSpaceGlueData.toPresheafedSpaceGlueData.toTopGlueData.toGlueData.ι
@@ -218,14 +245,18 @@ theorem ι_isoCarrier_inv (i : D.J) :
   change (_ ≫ D.iso_LocallyRingedSpace.inv).1.base = _
   rw [D.ι_iso_LocallyRingedSpace_inv i]
 #align algebraic_geometry.Scheme.glue_data.ι_iso_carrier_inv AlgebraicGeometry.Scheme.GlueData.ι_isoCarrier_inv
+-/
 
+#print AlgebraicGeometry.Scheme.GlueData.Rel /-
 /-- An equivalence relation on `Σ i, D.U i` that holds iff `𝖣 .ι i x = 𝖣 .ι j y`.
 See `Scheme.gluing_data.ι_eq_iff`. -/
 def Rel (a b : Σ i, ((D.U i).carrier : Type _)) : Prop :=
   a = b ∨
     ∃ x : (D.V (a.1, b.1)).carrier, (D.f _ _).1.base x = a.2 ∧ (D.t _ _ ≫ D.f _ _).1.base x = b.2
 #align algebraic_geometry.Scheme.glue_data.rel AlgebraicGeometry.Scheme.GlueData.Rel
+-/
 
+#print AlgebraicGeometry.Scheme.GlueData.ι_eq_iff /-
 theorem ι_eq_iff (i j : D.J) (x : (D.U i).carrier) (y : (D.U j).carrier) :
     (𝖣.ι i).1.base x = (𝖣.ι j).1.base y ↔ D.Rel ⟨i, x⟩ ⟨j, y⟩ :=
   by
@@ -236,7 +267,9 @@ theorem ι_eq_iff (i j : D.J) (x : (D.U i).carrier) (y : (D.U j).carrier) :
   rw [← ((TopCat.mono_iff_injective D.iso_carrier.inv).mp inferInstance).eq_iff]
   simp_rw [← comp_apply, D.ι_iso_carrier_inv]
 #align algebraic_geometry.Scheme.glue_data.ι_eq_iff AlgebraicGeometry.Scheme.GlueData.ι_eq_iff
+-/
 
+#print AlgebraicGeometry.Scheme.GlueData.isOpen_iff /-
 theorem isOpen_iff (U : Set D.glued.carrier) : IsOpen U ↔ ∀ i, IsOpen ((D.ι i).1.base ⁻¹' U) :=
   by
   rw [← (TopCat.homeoOfIso D.iso_carrier.symm).isOpen_preimage]
@@ -245,7 +278,9 @@ theorem isOpen_iff (U : Set D.glued.carrier) : IsOpen U ↔ ∀ i, IsOpen ((D.ι
   intro i
   erw [← Set.preimage_comp, ← coe_comp, ι_iso_carrier_inv]
 #align algebraic_geometry.Scheme.glue_data.is_open_iff AlgebraicGeometry.Scheme.GlueData.isOpen_iff
+-/
 
+#print AlgebraicGeometry.Scheme.GlueData.openCover /-
 /-- The open cover of the glued space given by the glue data. -/
 def openCover (D : Scheme.GlueData) : OpenCover D.glued
     where
@@ -255,6 +290,7 @@ def openCover (D : Scheme.GlueData) : OpenCover D.glued
   f x := (D.ι_jointly_surjective x).some
   Covers x := ⟨_, (D.ι_jointly_surjective x).choose_spec.choose_spec⟩
 #align algebraic_geometry.Scheme.glue_data.open_cover AlgebraicGeometry.Scheme.GlueData.openCover
+-/
 
 end GlueData
 
@@ -262,6 +298,7 @@ namespace OpenCover
 
 variable {X : Scheme.{u}} (𝒰 : OpenCover.{u} X)
 
+#print AlgebraicGeometry.Scheme.OpenCover.gluedCoverT' /-
 /-- (Implementation) the transition maps in the glue data associated with an open cover. -/
 def gluedCoverT' (x y z : 𝒰.J) :
     pullback (pullback.fst : pullback (𝒰.map x) (𝒰.map y) ⟶ _)
@@ -276,43 +313,57 @@ def gluedCoverT' (x y z : 𝒰.J) :
   · simp [pullback.condition]
   · simp
 #align algebraic_geometry.Scheme.open_cover.glued_cover_t' AlgebraicGeometry.Scheme.OpenCover.gluedCoverT'
+-/
 
+#print AlgebraicGeometry.Scheme.OpenCover.gluedCoverT'_fst_fst /-
 @[simp, reassoc]
 theorem gluedCoverT'_fst_fst (x y z : 𝒰.J) :
     𝒰.gluedCoverT' x y z ≫ pullback.fst ≫ pullback.fst = pullback.fst ≫ pullback.snd := by
   delta glued_cover_t'; simp
 #align algebraic_geometry.Scheme.open_cover.glued_cover_t'_fst_fst AlgebraicGeometry.Scheme.OpenCover.gluedCoverT'_fst_fst
+-/
 
+#print AlgebraicGeometry.Scheme.OpenCover.gluedCoverT'_fst_snd /-
 @[simp, reassoc]
 theorem gluedCoverT'_fst_snd (x y z : 𝒰.J) :
     gluedCoverT' 𝒰 x y z ≫ pullback.fst ≫ pullback.snd = pullback.snd ≫ pullback.snd := by
   delta glued_cover_t'; simp
 #align algebraic_geometry.Scheme.open_cover.glued_cover_t'_fst_snd AlgebraicGeometry.Scheme.OpenCover.gluedCoverT'_fst_snd
+-/
 
+#print AlgebraicGeometry.Scheme.OpenCover.gluedCoverT'_snd_fst /-
 @[simp, reassoc]
 theorem gluedCoverT'_snd_fst (x y z : 𝒰.J) :
     gluedCoverT' 𝒰 x y z ≫ pullback.snd ≫ pullback.fst = pullback.fst ≫ pullback.snd := by
   delta glued_cover_t'; simp
 #align algebraic_geometry.Scheme.open_cover.glued_cover_t'_snd_fst AlgebraicGeometry.Scheme.OpenCover.gluedCoverT'_snd_fst
+-/
 
+#print AlgebraicGeometry.Scheme.OpenCover.gluedCoverT'_snd_snd /-
 @[simp, reassoc]
 theorem gluedCoverT'_snd_snd (x y z : 𝒰.J) :
     gluedCoverT' 𝒰 x y z ≫ pullback.snd ≫ pullback.snd = pullback.fst ≫ pullback.fst := by
   delta glued_cover_t'; simp
 #align algebraic_geometry.Scheme.open_cover.glued_cover_t'_snd_snd AlgebraicGeometry.Scheme.OpenCover.gluedCoverT'_snd_snd
+-/
 
+#print AlgebraicGeometry.Scheme.OpenCover.glued_cover_cocycle_fst /-
 theorem glued_cover_cocycle_fst (x y z : 𝒰.J) :
     gluedCoverT' 𝒰 x y z ≫ gluedCoverT' 𝒰 y z x ≫ gluedCoverT' 𝒰 z x y ≫ pullback.fst =
       pullback.fst :=
   by apply pullback.hom_ext <;> simp
 #align algebraic_geometry.Scheme.open_cover.glued_cover_cocycle_fst AlgebraicGeometry.Scheme.OpenCover.glued_cover_cocycle_fst
+-/
 
+#print AlgebraicGeometry.Scheme.OpenCover.glued_cover_cocycle_snd /-
 theorem glued_cover_cocycle_snd (x y z : 𝒰.J) :
     gluedCoverT' 𝒰 x y z ≫ gluedCoverT' 𝒰 y z x ≫ gluedCoverT' 𝒰 z x y ≫ pullback.snd =
       pullback.snd :=
   by apply pullback.hom_ext <;> simp [pullback.condition]
 #align algebraic_geometry.Scheme.open_cover.glued_cover_cocycle_snd AlgebraicGeometry.Scheme.OpenCover.glued_cover_cocycle_snd
+-/
 
+#print AlgebraicGeometry.Scheme.OpenCover.glued_cover_cocycle /-
 theorem glued_cover_cocycle (x y z : 𝒰.J) :
     gluedCoverT' 𝒰 x y z ≫ gluedCoverT' 𝒰 y z x ≫ gluedCoverT' 𝒰 z x y = 𝟙 _ :=
   by
@@ -320,7 +371,9 @@ theorem glued_cover_cocycle (x y z : 𝒰.J) :
   apply glued_cover_cocycle_fst
   apply glued_cover_cocycle_snd
 #align algebraic_geometry.Scheme.open_cover.glued_cover_cocycle AlgebraicGeometry.Scheme.OpenCover.glued_cover_cocycle
+-/
 
+#print AlgebraicGeometry.Scheme.OpenCover.gluedCover /-
 /-- The glue data associated with an open cover.
 The canonical isomorphism `𝒰.glued_cover.glued ⟶ X` is provided by `𝒰.from_glued`. -/
 @[simps]
@@ -338,7 +391,9 @@ def gluedCover : Scheme.GlueData.{u} where
   cocycle x y z := glued_cover_cocycle 𝒰 x y z
   f_open x := inferInstance
 #align algebraic_geometry.Scheme.open_cover.glued_cover AlgebraicGeometry.Scheme.OpenCover.gluedCover
+-/
 
+#print AlgebraicGeometry.Scheme.OpenCover.fromGlued /-
 /-- The canonical morphism from the gluing of an open cover of `X` into `X`.
 This is an isomorphism, as witnessed by an `is_iso` instance. -/
 def fromGlued : 𝒰.gluedCover.glued ⟶ X :=
@@ -349,12 +404,16 @@ def fromGlued : 𝒰.gluedCover.glued ⟶ X :=
   change pullback.fst ≫ _ = ((pullback_symmetry _ _).Hom ≫ pullback.fst) ≫ _
   simpa using pullback.condition
 #align algebraic_geometry.Scheme.open_cover.from_glued AlgebraicGeometry.Scheme.OpenCover.fromGlued
+-/
 
+#print AlgebraicGeometry.Scheme.OpenCover.ι_fromGlued /-
 @[simp, reassoc]
 theorem ι_fromGlued (x : 𝒰.J) : 𝒰.gluedCover.ι x ≫ 𝒰.fromGlued = 𝒰.map x :=
   Multicoequalizer.π_desc _ _ _ _ _
 #align algebraic_geometry.Scheme.open_cover.ι_from_glued AlgebraicGeometry.Scheme.OpenCover.ι_fromGlued
+-/
 
+#print AlgebraicGeometry.Scheme.OpenCover.fromGlued_injective /-
 theorem fromGlued_injective : Function.Injective 𝒰.fromGlued.1.base :=
   by
   intro x y h
@@ -375,7 +434,9 @@ theorem fromGlued_injective : Function.Injective 𝒰.fromGlued.1.base :=
       is_limit.cone_point_unique_up_to_iso_hom_comp _ _ walking_cospan.right]
     rfl
 #align algebraic_geometry.Scheme.open_cover.from_glued_injective AlgebraicGeometry.Scheme.OpenCover.fromGlued_injective
+-/
 
+#print AlgebraicGeometry.Scheme.OpenCover.fromGlued_stalk_iso /-
 instance fromGlued_stalk_iso (x : 𝒰.gluedCover.glued.carrier) :
     IsIso (PresheafedSpace.stalkMap 𝒰.fromGlued.val x) :=
   by
@@ -388,7 +449,9 @@ instance fromGlued_stalk_iso (x : 𝒰.gluedCover.glued.carrier) :
   rw [this]
   infer_instance
 #align algebraic_geometry.Scheme.open_cover.from_glued_stalk_iso AlgebraicGeometry.Scheme.OpenCover.fromGlued_stalk_iso
+-/
 
+#print AlgebraicGeometry.Scheme.OpenCover.fromGlued_open_map /-
 theorem fromGlued_open_map : IsOpenMap 𝒰.fromGlued.1.base :=
   by
   intro U hU
@@ -406,11 +469,14 @@ theorem fromGlued_open_map : IsOpenMap 𝒰.fromGlued.1.base :=
     refine' Set.preimage_image_eq _ 𝒰.from_glued_injective
   · exact ⟨hx, 𝒰.covers x⟩
 #align algebraic_geometry.Scheme.open_cover.from_glued_open_map AlgebraicGeometry.Scheme.OpenCover.fromGlued_open_map
+-/
 
+#print AlgebraicGeometry.Scheme.OpenCover.fromGlued_openEmbedding /-
 theorem fromGlued_openEmbedding : OpenEmbedding 𝒰.fromGlued.1.base :=
   openEmbedding_of_continuous_injective_open (by continuity) 𝒰.fromGlued_injective
     𝒰.fromGlued_open_map
 #align algebraic_geometry.Scheme.open_cover.from_glued_open_embedding AlgebraicGeometry.Scheme.OpenCover.fromGlued_openEmbedding
+-/
 
 instance : Epi 𝒰.fromGlued.val.base :=
   by
@@ -422,9 +488,11 @@ instance : Epi 𝒰.fromGlued.val.base :=
   rw [← 𝒰.ι_from_glued (𝒰.f x)] at h 
   exact h
 
+#print AlgebraicGeometry.Scheme.OpenCover.fromGlued_open_immersion /-
 instance fromGlued_open_immersion : IsOpenImmersionCat 𝒰.fromGlued :=
   SheafedSpace.IsOpenImmersion.of_stalk_iso _ 𝒰.fromGlued_openEmbedding
 #align algebraic_geometry.Scheme.open_cover.from_glued_open_immersion AlgebraicGeometry.Scheme.OpenCover.fromGlued_open_immersion
+-/
 
 instance : IsIso 𝒰.fromGlued :=
   by
@@ -435,6 +503,7 @@ instance : IsIso 𝒰.fromGlued :=
   change @is_iso (PresheafedSpace _) _ _ _ 𝒰.from_glued.val
   apply PresheafedSpace.is_open_immersion.to_iso
 
+#print AlgebraicGeometry.Scheme.OpenCover.glueMorphisms /-
 /-- Given an open cover of `X`, and a morphism `𝒰.obj x ⟶ Y` for each open subscheme in the cover,
 such that these morphisms are compatible in the intersection (pullback), we may glue the morphisms
 together into a morphism `X ⟶ Y`.
@@ -453,7 +522,9 @@ def glueMorphisms {Y : Scheme} (f : ∀ x, 𝒰.obj x ⟶ Y)
   erw [pullback_symmetry_hom_comp_fst]
   exact hf i j
 #align algebraic_geometry.Scheme.open_cover.glue_morphisms AlgebraicGeometry.Scheme.OpenCover.glueMorphisms
+-/
 
+#print AlgebraicGeometry.Scheme.OpenCover.ι_glueMorphisms /-
 @[simp, reassoc]
 theorem ι_glueMorphisms {Y : Scheme} (f : ∀ x, 𝒰.obj x ⟶ Y)
     (hf : ∀ x y, (pullback.fst : pullback (𝒰.map x) (𝒰.map y) ⟶ _) ≫ f x = pullback.snd ≫ f y)
@@ -462,7 +533,9 @@ theorem ι_glueMorphisms {Y : Scheme} (f : ∀ x, 𝒰.obj x ⟶ Y)
   rw [← ι_from_glued, category.assoc]
   erw [is_iso.hom_inv_id_assoc, multicoequalizer.π_desc]
 #align algebraic_geometry.Scheme.open_cover.ι_glue_morphisms AlgebraicGeometry.Scheme.OpenCover.ι_glueMorphisms
+-/
 
+#print AlgebraicGeometry.Scheme.OpenCover.hom_ext /-
 theorem hom_ext {Y : Scheme} (f₁ f₂ : X ⟶ Y) (h : ∀ x, 𝒰.map x ≫ f₁ = 𝒰.map x ≫ f₂) : f₁ = f₂ :=
   by
   rw [← cancel_epi 𝒰.from_glued]
@@ -472,6 +545,7 @@ theorem hom_ext {Y : Scheme} (f₁ f₂ : X ⟶ Y) (h : ∀ x, 𝒰.map x ≫ f
   erw [multicoequalizer.π_desc_assoc]
   exact h x
 #align algebraic_geometry.Scheme.open_cover.hom_ext AlgebraicGeometry.Scheme.OpenCover.hom_ext
+-/
 
 end OpenCover
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/6285167a053ad0990fc88e56c48ccd9fae6550eb

@@ -86,7 +86,7 @@ that the `U i`'s are open subschemes of the glued space.
 -/
 @[nolint has_nonempty_instance]
 structure GlueData extends CategoryTheory.GlueData Scheme where
-  f_open : ∀ i j, IsOpenImmersion (f i j)
+  f_open : ∀ i j, IsOpenImmersionCat (f i j)
 #align algebraic_geometry.Scheme.glue_data AlgebraicGeometry.Scheme.GlueData
 
 attribute [instance] glue_data.f_open
@@ -154,9 +154,9 @@ theorem ι_isoLocallyRingedSpace_inv (i : D.J) :
   𝖣.ι_gluedIso_inv forgetToLocallyRingedSpace i
 #align algebraic_geometry.Scheme.glue_data.ι_iso_LocallyRingedSpace_inv AlgebraicGeometry.Scheme.GlueData.ι_isoLocallyRingedSpace_inv
 
-instance ι_isOpenImmersion (i : D.J) : IsOpenImmersion (𝖣.ι i) := by
+instance ι_isOpenImmersionCat (i : D.J) : IsOpenImmersionCat (𝖣.ι i) := by
   rw [← D.ι_iso_LocallyRingedSpace_inv]; infer_instance
-#align algebraic_geometry.Scheme.glue_data.ι_is_open_immersion AlgebraicGeometry.Scheme.GlueData.ι_isOpenImmersion
+#align algebraic_geometry.Scheme.glue_data.ι_is_open_immersion AlgebraicGeometry.Scheme.GlueData.ι_isOpenImmersionCat
 
 theorem ι_jointly_surjective (x : 𝖣.glued.carrier) :
     ∃ (i : D.J) (y : (D.U i).carrier), (D.ι i).1.base y = x :=
@@ -422,7 +422,7 @@ instance : Epi 𝒰.fromGlued.val.base :=
   rw [← 𝒰.ι_from_glued (𝒰.f x)] at h 
   exact h
 
-instance fromGlued_open_immersion : IsOpenImmersion 𝒰.fromGlued :=
+instance fromGlued_open_immersion : IsOpenImmersionCat 𝒰.fromGlued :=
   SheafedSpace.IsOpenImmersion.of_stalk_iso _ 𝒰.fromGlued_openEmbedding
 #align algebraic_geometry.Scheme.open_cover.from_glued_open_immersion AlgebraicGeometry.Scheme.OpenCover.fromGlued_open_immersion
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/2a0ce625dbb0ffbc7d1316597de0b25c1ec75303

@@ -423,7 +423,7 @@ instance : Epi 𝒰.fromGlued.val.base :=
   exact h
 
 instance fromGlued_open_immersion : IsOpenImmersion 𝒰.fromGlued :=
-  SheafedSpace.IsOpenImmersion.ofStalkIso _ 𝒰.fromGlued_openEmbedding
+  SheafedSpace.IsOpenImmersion.of_stalk_iso _ 𝒰.fromGlued_openEmbedding
 #align algebraic_geometry.Scheme.open_cover.from_glued_open_immersion AlgebraicGeometry.Scheme.OpenCover.fromGlued_open_immersion
 
 instance : IsIso 𝒰.fromGlued :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/2a0ce625dbb0ffbc7d1316597de0b25c1ec75303

@@ -423,7 +423,7 @@ instance : Epi 𝒰.fromGlued.val.base :=
   exact h
 
 instance fromGlued_open_immersion : IsOpenImmersion 𝒰.fromGlued :=
-  SheafedSpace.IsOpenImmersion.of_stalk_iso _ 𝒰.fromGlued_openEmbedding
+  SheafedSpace.IsOpenImmersion.ofStalkIso _ 𝒰.fromGlued_openEmbedding
 #align algebraic_geometry.Scheme.open_cover.from_glued_open_immersion AlgebraicGeometry.Scheme.OpenCover.fromGlued_open_immersion
 
 instance : IsIso 𝒰.fromGlued :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423

@@ -95,9 +95,6 @@ namespace GlueData
 
 variable (D : GlueData)
 
-include D
-
--- mathport name: «expr𝖣»
 local notation "𝖣" => D.toGlueData
 
 /-- The glue data of locally ringed spaces spaces associated to a family of glue data of schemes. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/a3209ddf94136d36e5e5c624b10b2a347cc9d090

@@ -4,11 +4,12 @@ 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.gluing
-! leanprover-community/mathlib commit a9402e0a11843994283cd0a918e61fa51360e26a
+! leanprover-community/mathlib commit 533f62f4dd62a5aad24a04326e6e787c8f7e98b1
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.AlgebraicGeometry.PresheafedSpace.Gluing
+import Mathbin.AlgebraicGeometry.OpenImmersion.Scheme
 
 /-!
 # Gluing Schemes

mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb

@@ -161,7 +161,7 @@ instance ι_isOpenImmersion (i : D.J) : IsOpenImmersion (𝖣.ι i) := by
 #align algebraic_geometry.Scheme.glue_data.ι_is_open_immersion AlgebraicGeometry.Scheme.GlueData.ι_isOpenImmersion
 
 theorem ι_jointly_surjective (x : 𝖣.glued.carrier) :
-    ∃ (i : D.J)(y : (D.U i).carrier), (D.ι i).1.base y = x :=
+    ∃ (i : D.J) (y : (D.U i).carrier), (D.ι i).1.base y = x :=
   𝖣.ι_jointly_surjective (forgetToTop ⋙ forget TopCat) x
 #align algebraic_geometry.Scheme.glue_data.ι_jointly_surjective AlgebraicGeometry.Scheme.GlueData.ι_jointly_surjective
 
@@ -223,7 +223,7 @@ theorem ι_isoCarrier_inv (i : D.J) :
 
 /-- An equivalence relation on `Σ i, D.U i` that holds iff `𝖣 .ι i x = 𝖣 .ι j y`.
 See `Scheme.gluing_data.ι_eq_iff`. -/
-def Rel (a b : Σi, ((D.U i).carrier : Type _)) : Prop :=
+def Rel (a b : Σ i, ((D.U i).carrier : Type _)) : Prop :=
   a = b ∨
     ∃ x : (D.V (a.1, b.1)).carrier, (D.f _ _).1.base x = a.2 ∧ (D.t _ _ ≫ D.f _ _).1.base x = b.2
 #align algebraic_geometry.Scheme.glue_data.rel AlgebraicGeometry.Scheme.GlueData.Rel
@@ -362,8 +362,8 @@ theorem fromGlued_injective : Function.Injective 𝒰.fromGlued.1.base :=
   intro x y h
   obtain ⟨i, x, rfl⟩ := 𝒰.glued_cover.ι_jointly_surjective x
   obtain ⟨j, y, rfl⟩ := 𝒰.glued_cover.ι_jointly_surjective y
-  simp_rw [← comp_apply, ← SheafedSpace.comp_base, ← LocallyRingedSpace.comp_val] at h
-  erw [ι_from_glued, ι_from_glued] at h
+  simp_rw [← comp_apply, ← SheafedSpace.comp_base, ← LocallyRingedSpace.comp_val] at h 
+  erw [ι_from_glued, ι_from_glued] at h 
   let e :=
     (TopCat.pullbackConeIsLimit _ _).conePointUniqueUpToIso
       (is_limit_of_has_pullback_of_preserves_limit Scheme.forget_to_Top (𝒰.map i) (𝒰.map j))
@@ -385,8 +385,8 @@ instance fromGlued_stalk_iso (x : 𝒰.gluedCover.glued.carrier) :
   have :=
     PresheafedSpace.stalk_map.congr_hom _ _
       (congr_arg LocallyRingedSpace.hom.val <| 𝒰.ι_from_glued i) x
-  erw [PresheafedSpace.stalk_map.comp] at this
-  rw [← is_iso.eq_comp_inv] at this
+  erw [PresheafedSpace.stalk_map.comp] at this 
+  rw [← is_iso.eq_comp_inv] at this 
   rw [this]
   infer_instance
 #align algebraic_geometry.Scheme.open_cover.from_glued_stalk_iso AlgebraicGeometry.Scheme.OpenCover.fromGlued_stalk_iso
@@ -396,7 +396,7 @@ theorem fromGlued_open_map : IsOpenMap 𝒰.fromGlued.1.base :=
   intro U hU
   rw [isOpen_iff_forall_mem_open]
   intro x hx
-  rw [𝒰.glued_cover.is_open_iff] at hU
+  rw [𝒰.glued_cover.is_open_iff] at hU 
   use 𝒰.from_glued.val.base '' U ∩ Set.range (𝒰.map (𝒰.f x)).1.base
   use Set.inter_subset_left _ _
   constructor
@@ -421,7 +421,7 @@ instance : Epi 𝒰.fromGlued.val.base :=
   obtain ⟨y, h⟩ := 𝒰.covers x
   use (𝒰.glued_cover.ι (𝒰.f x)).1.base y
   rw [← comp_apply]
-  rw [← 𝒰.ι_from_glued (𝒰.f x)] at h
+  rw [← 𝒰.ι_from_glued (𝒰.f x)] at h 
   exact h
 
 instance fromGlued_open_immersion : IsOpenImmersion 𝒰.fromGlued :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

@@ -156,10 +156,8 @@ theorem ι_isoLocallyRingedSpace_inv (i : D.J) :
   𝖣.ι_gluedIso_inv forgetToLocallyRingedSpace i
 #align algebraic_geometry.Scheme.glue_data.ι_iso_LocallyRingedSpace_inv AlgebraicGeometry.Scheme.GlueData.ι_isoLocallyRingedSpace_inv
 
-instance ι_isOpenImmersion (i : D.J) : IsOpenImmersion (𝖣.ι i) :=
-  by
-  rw [← D.ι_iso_LocallyRingedSpace_inv]
-  infer_instance
+instance ι_isOpenImmersion (i : D.J) : IsOpenImmersion (𝖣.ι i) := by
+  rw [← D.ι_iso_LocallyRingedSpace_inv]; infer_instance
 #align algebraic_geometry.Scheme.glue_data.ι_is_open_immersion AlgebraicGeometry.Scheme.GlueData.ι_isOpenImmersion
 
 theorem ι_jointly_surjective (x : 𝖣.glued.carrier) :
@@ -283,34 +281,26 @@ def gluedCoverT' (x y z : 𝒰.J) :
 
 @[simp, reassoc]
 theorem gluedCoverT'_fst_fst (x y z : 𝒰.J) :
-    𝒰.gluedCoverT' x y z ≫ pullback.fst ≫ pullback.fst = pullback.fst ≫ pullback.snd :=
-  by
-  delta glued_cover_t'
-  simp
+    𝒰.gluedCoverT' x y z ≫ pullback.fst ≫ pullback.fst = pullback.fst ≫ pullback.snd := by
+  delta glued_cover_t'; simp
 #align algebraic_geometry.Scheme.open_cover.glued_cover_t'_fst_fst AlgebraicGeometry.Scheme.OpenCover.gluedCoverT'_fst_fst
 
 @[simp, reassoc]
 theorem gluedCoverT'_fst_snd (x y z : 𝒰.J) :
-    gluedCoverT' 𝒰 x y z ≫ pullback.fst ≫ pullback.snd = pullback.snd ≫ pullback.snd :=
-  by
-  delta glued_cover_t'
-  simp
+    gluedCoverT' 𝒰 x y z ≫ pullback.fst ≫ pullback.snd = pullback.snd ≫ pullback.snd := by
+  delta glued_cover_t'; simp
 #align algebraic_geometry.Scheme.open_cover.glued_cover_t'_fst_snd AlgebraicGeometry.Scheme.OpenCover.gluedCoverT'_fst_snd
 
 @[simp, reassoc]
 theorem gluedCoverT'_snd_fst (x y z : 𝒰.J) :
-    gluedCoverT' 𝒰 x y z ≫ pullback.snd ≫ pullback.fst = pullback.fst ≫ pullback.snd :=
-  by
-  delta glued_cover_t'
-  simp
+    gluedCoverT' 𝒰 x y z ≫ pullback.snd ≫ pullback.fst = pullback.fst ≫ pullback.snd := by
+  delta glued_cover_t'; simp
 #align algebraic_geometry.Scheme.open_cover.glued_cover_t'_snd_fst AlgebraicGeometry.Scheme.OpenCover.gluedCoverT'_snd_fst
 
 @[simp, reassoc]
 theorem gluedCoverT'_snd_snd (x y z : 𝒰.J) :
-    gluedCoverT' 𝒰 x y z ≫ pullback.snd ≫ pullback.snd = pullback.fst ≫ pullback.fst :=
-  by
-  delta glued_cover_t'
-  simp
+    gluedCoverT' 𝒰 x y z ≫ pullback.snd ≫ pullback.snd = pullback.fst ≫ pullback.fst := by
+  delta glued_cover_t'; simp
 #align algebraic_geometry.Scheme.open_cover.glued_cover_t'_snd_snd AlgebraicGeometry.Scheme.OpenCover.gluedCoverT'_snd_snd
 
 theorem glued_cover_cocycle_fst (x y z : 𝒰.J) :
@@ -382,8 +372,7 @@ theorem fromGlued_injective : Function.Injective 𝒰.fromGlued.1.base :=
   use e.hom ⟨⟨x, y⟩, h⟩
   simp_rw [← comp_apply]
   constructor
-  · erw [is_limit.cone_point_unique_up_to_iso_hom_comp _ _ walking_cospan.left]
-    rfl
+  · erw [is_limit.cone_point_unique_up_to_iso_hom_comp _ _ walking_cospan.left]; rfl
   · erw [pullback_symmetry_hom_comp_fst,
       is_limit.cone_point_unique_up_to_iso_hom_comp _ _ walking_cospan.right]
     rfl
@@ -414,9 +403,7 @@ theorem fromGlued_open_map : IsOpenMap 𝒰.fromGlued.1.base :=
   · rw [← Set.image_preimage_eq_inter_range]
     apply show is_open_immersion (𝒰.map (𝒰.f x)) by infer_instance.base_open.IsOpenMap
     convert hU (𝒰.f x) using 1
-    rw [← ι_from_glued]
-    erw [coe_comp]
-    rw [Set.preimage_comp]
+    rw [← ι_from_glued]; erw [coe_comp]; rw [Set.preimage_comp]
     congr 1
     refine' Set.preimage_image_eq _ 𝒰.from_glued_injective
   · exact ⟨hx, 𝒰.covers x⟩

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

@@ -438,7 +438,7 @@ instance : Epi 𝒰.fromGlued.val.base :=
   exact h
 
 instance fromGlued_open_immersion : IsOpenImmersion 𝒰.fromGlued :=
-  SheafedSpace.IsOpenImmersion.ofStalkIso _ 𝒰.fromGlued_openEmbedding
+  SheafedSpace.IsOpenImmersion.of_stalk_iso _ 𝒰.fromGlued_openEmbedding
 #align algebraic_geometry.Scheme.open_cover.from_glued_open_immersion AlgebraicGeometry.Scheme.OpenCover.fromGlued_open_immersion
 
 instance : IsIso 𝒰.fromGlued :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/75e7fca56381d056096ce5d05e938f63a6567828

@@ -167,7 +167,7 @@ theorem ι_jointly_surjective (x : 𝖣.glued.carrier) :
   𝖣.ι_jointly_surjective (forgetToTop ⋙ forget TopCat) x
 #align algebraic_geometry.Scheme.glue_data.ι_jointly_surjective AlgebraicGeometry.Scheme.GlueData.ι_jointly_surjective
 
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem glue_condition (i j : D.J) : D.t i j ≫ D.f j i ≫ D.ι j = D.f i j ≫ D.ι i :=
   𝖣.glue_condition i j
 #align algebraic_geometry.Scheme.glue_data.glue_condition AlgebraicGeometry.Scheme.GlueData.glue_condition
@@ -281,7 +281,7 @@ def gluedCoverT' (x y z : 𝒰.J) :
   · simp
 #align algebraic_geometry.Scheme.open_cover.glued_cover_t' AlgebraicGeometry.Scheme.OpenCover.gluedCoverT'
 
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem gluedCoverT'_fst_fst (x y z : 𝒰.J) :
     𝒰.gluedCoverT' x y z ≫ pullback.fst ≫ pullback.fst = pullback.fst ≫ pullback.snd :=
   by
@@ -289,7 +289,7 @@ theorem gluedCoverT'_fst_fst (x y z : 𝒰.J) :
   simp
 #align algebraic_geometry.Scheme.open_cover.glued_cover_t'_fst_fst AlgebraicGeometry.Scheme.OpenCover.gluedCoverT'_fst_fst
 
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem gluedCoverT'_fst_snd (x y z : 𝒰.J) :
     gluedCoverT' 𝒰 x y z ≫ pullback.fst ≫ pullback.snd = pullback.snd ≫ pullback.snd :=
   by
@@ -297,7 +297,7 @@ theorem gluedCoverT'_fst_snd (x y z : 𝒰.J) :
   simp
 #align algebraic_geometry.Scheme.open_cover.glued_cover_t'_fst_snd AlgebraicGeometry.Scheme.OpenCover.gluedCoverT'_fst_snd
 
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem gluedCoverT'_snd_fst (x y z : 𝒰.J) :
     gluedCoverT' 𝒰 x y z ≫ pullback.snd ≫ pullback.fst = pullback.fst ≫ pullback.snd :=
   by
@@ -305,7 +305,7 @@ theorem gluedCoverT'_snd_fst (x y z : 𝒰.J) :
   simp
 #align algebraic_geometry.Scheme.open_cover.glued_cover_t'_snd_fst AlgebraicGeometry.Scheme.OpenCover.gluedCoverT'_snd_fst
 
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem gluedCoverT'_snd_snd (x y z : 𝒰.J) :
     gluedCoverT' 𝒰 x y z ≫ pullback.snd ≫ pullback.snd = pullback.fst ≫ pullback.fst :=
   by
@@ -362,7 +362,7 @@ def fromGlued : 𝒰.gluedCover.glued ⟶ X :=
   simpa using pullback.condition
 #align algebraic_geometry.Scheme.open_cover.from_glued AlgebraicGeometry.Scheme.OpenCover.fromGlued
 
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem ι_fromGlued (x : 𝒰.J) : 𝒰.gluedCover.ι x ≫ 𝒰.fromGlued = 𝒰.map x :=
   Multicoequalizer.π_desc _ _ _ _ _
 #align algebraic_geometry.Scheme.open_cover.ι_from_glued AlgebraicGeometry.Scheme.OpenCover.ι_fromGlued
@@ -469,7 +469,7 @@ def glueMorphisms {Y : Scheme} (f : ∀ x, 𝒰.obj x ⟶ Y)
   exact hf i j
 #align algebraic_geometry.Scheme.open_cover.glue_morphisms AlgebraicGeometry.Scheme.OpenCover.glueMorphisms
 
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem ι_glueMorphisms {Y : Scheme} (f : ∀ x, 𝒰.obj x ⟶ Y)
     (hf : ∀ x y, (pullback.fst : pullback (𝒰.map x) (𝒰.map y) ⟶ _) ≫ f x = pullback.snd ≫ f y)
     (x : 𝒰.J) : 𝒰.map x ≫ 𝒰.glueMorphisms f hf = f x :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/33c67ae661dd8988516ff7f247b0be3018cdd952

@@ -438,7 +438,7 @@ instance : Epi 𝒰.fromGlued.val.base :=
   exact h
 
 instance fromGlued_open_immersion : IsOpenImmersion 𝒰.fromGlued :=
-  SheafedSpace.IsOpenImmersion.of_stalk_iso _ 𝒰.fromGlued_openEmbedding
+  SheafedSpace.IsOpenImmersion.ofStalkIso _ 𝒰.fromGlued_openEmbedding
 #align algebraic_geometry.Scheme.open_cover.from_glued_open_immersion AlgebraicGeometry.Scheme.OpenCover.fromGlued_open_immersion
 
 instance : IsIso 𝒰.fromGlued :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/57e09a1296bfb4330ddf6624f1028ba186117d82

@@ -364,7 +364,7 @@ def fromGlued : 𝒰.gluedCover.glued ⟶ X :=
 
 @[simp, reassoc.1]
 theorem ι_fromGlued (x : 𝒰.J) : 𝒰.gluedCover.ι x ≫ 𝒰.fromGlued = 𝒰.map x :=
-  multicoequalizer.π_desc _ _ _ _ _
+  Multicoequalizer.π_desc _ _ _ _ _
 #align algebraic_geometry.Scheme.open_cover.ι_from_glued AlgebraicGeometry.Scheme.OpenCover.ι_fromGlued
 
 theorem fromGlued_injective : Function.Injective 𝒰.fromGlued.1.base :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/eb0cb4511aaef0da2462207b67358a0e1fe1e2ee

@@ -133,7 +133,7 @@ instance : PreservesColimit 𝖣.diagram.multispan forgetToTop :=
   infer_instance
 
 instance : HasMulticoequalizer 𝖣.diagram :=
-  hasColimitOfCreated _ forgetToLocallyRingedSpace
+  hasColimit_of_created _ forgetToLocallyRingedSpace
 
 /-- The glued scheme of a glued space. -/
 abbrev glued : Scheme :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc

A PR accompanying #12339.

Zulip discussion

@@ -129,7 +129,8 @@ def gluedScheme : Scheme := by
   intro x
   obtain ⟨i, y, rfl⟩ := D.toLocallyRingedSpaceGlueData.ι_jointly_surjective x
   refine' ⟨_, _ ≫ D.toLocallyRingedSpaceGlueData.toGlueData.ι i, _⟩
-  swap; exact (D.U i).affineCover.map y
+  swap
+  · exact (D.U i).affineCover.map y
   constructor
   · dsimp [-Set.mem_range]
     rw [coe_comp, Set.range_comp]
@@ -329,8 +330,8 @@ theorem glued_cover_cocycle_snd (x y z : 𝒰.J) :
 theorem glued_cover_cocycle (x y z : 𝒰.J) :
     gluedCoverT' 𝒰 x y z ≫ gluedCoverT' 𝒰 y z x ≫ gluedCoverT' 𝒰 z x y = 𝟙 _ := by
   apply pullback.hom_ext <;> simp_rw [Category.id_comp, Category.assoc]
-  apply glued_cover_cocycle_fst
-  apply glued_cover_cocycle_snd
+  · apply glued_cover_cocycle_fst
+  · apply glued_cover_cocycle_snd
 #align algebraic_geometry.Scheme.open_cover.glued_cover_cocycle AlgebraicGeometry.Scheme.OpenCover.glued_cover_cocycle
 
 /-- The glue data associated with an open cover.
@@ -355,7 +356,7 @@ def gluedCover : Scheme.GlueData.{u} where
 This is an isomorphism, as witnessed by an `IsIso` instance. -/
 def fromGlued : 𝒰.gluedCover.glued ⟶ X := by
   fapply Multicoequalizer.desc
-  exact fun x => 𝒰.map x
+  · exact fun x => 𝒰.map x
   rintro ⟨x, y⟩
   change pullback.fst ≫ _ = ((pullbackSymmetry _ _).hom ≫ pullback.fst) ≫ _
   simpa using pullback.condition
@@ -453,7 +454,7 @@ def glueMorphisms {Y : Scheme} (f : ∀ x, 𝒰.obj x ⟶ Y)
     X ⟶ Y := by
   refine' inv 𝒰.fromGlued ≫ _
   fapply Multicoequalizer.desc
-  exact f
+  · exact f
   rintro ⟨i, j⟩
   change pullback.fst ≫ f i = (_ ≫ _) ≫ f j
   erw [pullbackSymmetry_hom_comp_fst]

Reference the newly created issues #12094 and #12096, as well as the pre-existing #5171. Change all references to #10927 to #5171. Some of these changes were not labelled as "porting note"; change this for good measure.

@@ -82,7 +82,7 @@ such that
 We can then glue the schemes `U i` together by identifying `V i j` with `V j i`, such
 that the `U i`'s are open subschemes of the glued space.
 -/
--- Porting note: @[nolint has_nonempty_instance]
+-- Porting note(#5171): @[nolint has_nonempty_instance]; linter not ported yet
 structure GlueData extends CategoryTheory.GlueData Scheme where
   f_open : ∀ i j, IsOpenImmersion (f i j)
 #align algebraic_geometry.Scheme.glue_data AlgebraicGeometry.Scheme.GlueData

This proof had two changes added during porting, and these produce a massive timeout after the changes in https://github.com/leanprover/lean4/pull/3807.

This PR replace the change with the appropriate erw, and is now fast before and after the change.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -379,12 +379,8 @@ theorem fromGlued_injective : Function.Injective 𝒰.fromGlued.1.base := by
   right
   use e.hom ⟨⟨x, y⟩, h⟩
   constructor
-  -- Porting note: in the two subproofs below, added the `change` lines
-  · change (e.hom ≫ _) ⟨(x, y), h⟩ = x
-    erw [IsLimit.conePointUniqueUpToIso_hom_comp _ _ WalkingCospan.left]; rfl
-  · change (e.hom ≫ ((gluedCover 𝒰).toGlueData.t i j ≫
-      (gluedCover 𝒰).toGlueData.f j i).val.base) ⟨(x, y), h⟩ = y
-    erw [pullbackSymmetry_hom_comp_fst,
+  · erw [← comp_apply e.hom, IsLimit.conePointUniqueUpToIso_hom_comp _ _ WalkingCospan.left]; rfl
+  · erw [← comp_apply e.hom, pullbackSymmetry_hom_comp_fst,
       IsLimit.conePointUniqueUpToIso_hom_comp _ _ WalkingCospan.right]
     rfl
 #align algebraic_geometry.Scheme.open_cover.from_glued_injective AlgebraicGeometry.Scheme.OpenCover.fromGlued_injective

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.

@@ -180,7 +180,7 @@ theorem ι_jointly_surjective (x : 𝖣.glued.carrier) :
   𝖣.ι_jointly_surjective (forgetToTop ⋙ forget TopCat) x
 #align algebraic_geometry.Scheme.glue_data.ι_jointly_surjective AlgebraicGeometry.Scheme.GlueData.ι_jointly_surjective
 
--- Porting note : promote to higher priority to short circuit simplifier
+-- Porting note: promote to higher priority to short circuit simplifier
 @[simp (high), reassoc]
 theorem glue_condition (i j : D.J) : D.t i j ≫ D.f j i ≫ D.ι j = D.f i j ≫ D.ι i :=
   𝖣.glue_condition i j

I replaced a few "terminal" refine/refine's with exact.

The strategy was very simple-minded: essentially any refine whose following line had smaller indentation got replaced by exact and then I cleaned up the mess.

This PR certainly leaves some further terminal refines, but maybe the current change is beneficial.

@@ -414,7 +414,7 @@ theorem fromGlued_open_map : IsOpenMap 𝒰.fromGlued.1.base := by
     convert hU (𝒰.f x) using 1
     rw [← ι_fromGlued]; erw [coe_comp]; rw [Set.preimage_comp]
     congr! 1
-    refine' Set.preimage_image_eq _ 𝒰.fromGlued_injective
+    exact Set.preimage_image_eq _ 𝒰.fromGlued_injective
   · exact ⟨hx, 𝒰.Covers x⟩
 #align algebraic_geometry.Scheme.open_cover.from_glued_open_map AlgebraicGeometry.Scheme.OpenCover.fromGlued_open_map
 

Create new folder Geometry.RingedSpace for (locally) ringed spaces and move about half of the contents of AlgebraicGeometry there. Files renamed:

AlgebraicGeometry.OpenImmersion.Scheme → AlgebraicGeometry.OpenImmersion
AlgebraicGeometry.RingedSpace → Geometry.RingedSpace.Basic
AlgebraicGeometry.LocallyRingedSpace → Geometry.RingedSpace.LocallyRingedSpace
AlgebraicGeometry.LocallyRingedSpace.HasColimits → Geometry.RingedSpace.LocallyRingedSpace.HasColimits
AlgebraicGeometry.OpenImmersion.Basic → Geometry.RingedSpace.OpenImmersion
AlgebraicGeometry.PresheafedSpace → Geometry.RingedSpace.PresheafedSpace
AlgebraicGeometry.PresheafedSpace.Gluing → Geometry.RingedSpace.PresheafedSpace.Gluing
AlgebraicGeometry.PresheafedSpace.HasColimits → Geometry.RingedSpace.PresheafedSpace.HasColimits
AlgebraicGeometry.SheafedSpace → Geometry.RingedSpace.SheafedSpace
AlgebraicGeometry.Stalks → Geometry.RingedSpace.Stalks

See Zulip.

@@ -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 Mathlib.AlgebraicGeometry.PresheafedSpace.Gluing
-import Mathlib.AlgebraicGeometry.OpenImmersion.Scheme
+import Mathlib.Geometry.RingedSpace.PresheafedSpace.Gluing
+import Mathlib.AlgebraicGeometry.OpenImmersion
 
 #align_import algebraic_geometry.gluing from "leanprover-community/mathlib"@"533f62f4dd62a5aad24a04326e6e787c8f7e98b1"
 

Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -378,7 +378,6 @@ theorem fromGlued_injective : Function.Injective 𝒰.fromGlued.1.base := by
   rw [𝒰.gluedCover.ι_eq_iff]
   right
   use e.hom ⟨⟨x, y⟩, h⟩
-  simp_rw [← comp_apply]
   constructor
   -- Porting note: in the two subproofs below, added the `change` lines
   · change (e.hom ≫ _) ⟨(x, y), h⟩ = x

• depends on: #5966

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

@@ -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.gluing
-! leanprover-community/mathlib commit 533f62f4dd62a5aad24a04326e6e787c8f7e98b1
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.AlgebraicGeometry.PresheafedSpace.Gluing
 import Mathlib.AlgebraicGeometry.OpenImmersion.Scheme
 
+#align_import algebraic_geometry.gluing from "leanprover-community/mathlib"@"533f62f4dd62a5aad24a04326e6e787c8f7e98b1"
+
 /-!
 # Gluing Schemes
 

@@ -41,7 +41,7 @@ Given a family of gluing data of schemes, we may glue them together.
   (intersection) of `U i` and `U j` over the glued space.
 * `AlgebraicGeometry.Scheme.GlueData.ι_eq_iff` : `ι i x = ι j y` if and only if they coincide
   when restricted to `V i i`.
-* `AlgebraicGeometry.Scheme.GlueData.isOpen_iff` : An subset of the glued scheme is open iff
+* `AlgebraicGeometry.Scheme.GlueData.isOpen_iff` : A subset of the glued scheme is open iff
   all its preimages in `U i` are open.
 
 ## Implementation details
@@ -69,8 +69,8 @@ namespace Scheme
 
 /-- A family of gluing data consists of
 1. An index type `J`
-2. An scheme `U i` for each `i : J`.
-3. An scheme `V i j` for each `i j : J`.
+2. A scheme `U i` for each `i : J`.
+3. A scheme `V i j` for each `i j : J`.
   (Note that this is `J × J → Scheme` rather than `J → J → Scheme` to connect to the
   limits library easier.)
 4. An open immersion `f i j : V i j ⟶ U i` for each `i j : ι`.

@@ -25,8 +25,8 @@ Given a family of gluing data of schemes, we may glue them together.
 * `AlgebraicGeometry.Scheme.GlueData.ι`: The immersion `ι i : U i ⟶ glued` for each `i : J`.
 * `AlgebraicGeometry.Scheme.GlueData.isoCarrier`: The isomorphism between the underlying space
   of the glued scheme and the gluing of the underlying topological spaces.
-* `algebraic_geometry.Scheme.OpenCover.gluedCover`: The glue data associated with an open cover.
-* `algebraic_geometry.Scheme.OpenCover.fromGlued`: The canonical morphism
+* `AlgebraicGeometry.Scheme.OpenCover.gluedCover`: The glue data associated with an open cover.
+* `AlgebraicGeometry.Scheme.OpenCover.fromGlued`: The canonical morphism
   `𝒰.gluedCover.glued ⟶ X`. This has an `is_iso` instance.
 * `AlgebraicGeometry.Scheme.OpenCover.glueMorphisms`: We may glue a family of compatible
   morphisms defined on an open cover of a scheme.
@@ -39,7 +39,7 @@ Given a family of gluing data of schemes, we may glue them together.
   `ι i : U i ⟶ glued` are jointly surjective.
 * `AlgebraicGeometry.Scheme.GlueData.vPullbackConeIsLimit` : `V i j` is the pullback
   (intersection) of `U i` and `U j` over the glued space.
-* `algebraic_geometry.Scheme.glue_data.ι_eq_iff_rel` : `ι i x = ι j y` if and only if they coincide
+* `AlgebraicGeometry.Scheme.GlueData.ι_eq_iff` : `ι i x = ι j y` if and only if they coincide
   when restricted to `V i i`.
 * `AlgebraicGeometry.Scheme.GlueData.isOpen_iff` : An subset of the glued scheme is open iff
   all its preimages in `U i` are open.
@@ -125,7 +125,7 @@ instance (i : 𝖣.J) :
   apply LocallyRingedSpace.GlueData.ι_isOpenImmersion
 
 /-- (Implementation). The glued scheme of a glue data.
-This should not be used outside this file. Use `Scheme.glue_data.glued` instead. -/
+This should not be used outside this file. Use `AlgebraicGeometry.Scheme.GlueData.glued` instead. -/
 def gluedScheme : Scheme := by
   apply LocallyRingedSpace.IsOpenImmersion.scheme
     D.toLocallyRingedSpaceGlueData.toGlueData.glued
@@ -190,7 +190,7 @@ theorem glue_condition (i j : D.J) : D.t i j ≫ D.f j i ≫ D.ι j = D.f i j 
 #align algebraic_geometry.Scheme.glue_data.glue_condition AlgebraicGeometry.Scheme.GlueData.glue_condition
 
 /-- The pullback cone spanned by `V i j ⟶ U i` and `V i j ⟶ U j`.
-This is a pullback diagram (`V_pullback_cone_is_limit`). -/
+This is a pullback diagram (`vPullbackConeIsLimit`). -/
 def vPullbackCone (i j : D.J) : PullbackCone (D.ι i) (D.ι j) :=
   PullbackCone.mk (D.f i j) (D.t i j ≫ D.f j i) (by simp)
 #align algebraic_geometry.Scheme.glue_data.V_pullback_cone AlgebraicGeometry.Scheme.GlueData.vPullbackCone
@@ -238,7 +238,7 @@ theorem ι_isoCarrier_inv (i : D.J) :
 #align algebraic_geometry.Scheme.glue_data.ι_iso_carrier_inv AlgebraicGeometry.Scheme.GlueData.ι_isoCarrier_inv
 
 /-- An equivalence relation on `Σ i, D.U i` that holds iff `𝖣 .ι i x = 𝖣 .ι j y`.
-See `Scheme.gluing_data.ι_eq_iff`. -/
+See `AlgebraicGeometry.Scheme.GlueData.ι_eq_iff`. -/
 def Rel (a b : Σ i, ((D.U i).carrier : Type _)) : Prop :=
   a = b ∨
     ∃ x : (D.V (a.1, b.1)).carrier, (D.f _ _).1.base x = a.2 ∧ (D.t _ _ ≫ D.f _ _).1.base x = b.2
@@ -337,7 +337,7 @@ theorem glued_cover_cocycle (x y z : 𝒰.J) :
 #align algebraic_geometry.Scheme.open_cover.glued_cover_cocycle AlgebraicGeometry.Scheme.OpenCover.glued_cover_cocycle
 
 /-- The glue data associated with an open cover.
-The canonical isomorphism `𝒰.glued_cover.glued ⟶ X` is provided by `𝒰.from_glued`. -/
+The canonical isomorphism `𝒰.gluedCover.glued ⟶ X` is provided by `𝒰.fromGlued`. -/
 @[simps]
 def gluedCover : Scheme.GlueData.{u} where
   J := 𝒰.J
@@ -355,7 +355,7 @@ def gluedCover : Scheme.GlueData.{u} where
 #align algebraic_geometry.Scheme.open_cover.glued_cover AlgebraicGeometry.Scheme.OpenCover.gluedCover
 
 /-- The canonical morphism from the gluing of an open cover of `X` into `X`.
-This is an isomorphism, as witnessed by an `is_iso` instance. -/
+This is an isomorphism, as witnessed by an `IsIso` instance. -/
 def fromGlued : 𝒰.gluedCover.glued ⟶ X := by
   fapply Multicoequalizer.desc
   exact fun x => 𝒰.map x

Co-authored-by: Johan Commelin <johan@commelin.net> Co-authored-by: Jujian Zhang <jujian.zhang1998@outlook.com>