algebraic_geometry.presheafed_space.gluing ⟷ Mathlib.Geometry.RingedSpace.PresheafedSpace.Gluing

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

@@ -4,8 +4,8 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Andrew Yang
 -/
 import Topology.Gluing
-import AlgebraicGeometry.OpenImmersion.Basic
-import AlgebraicGeometry.LocallyRingedSpace.HasColimits
+import Geometry.RingedSpace.OpenImmersion
+import Geometry.RingedSpace.LocallyRingedSpace.HasColimits
 
 #align_import algebraic_geometry.presheafed_space.gluing from "leanprover-community/mathlib"@"fdc286cc6967a012f41b87f76dcd2797b53152af"
 

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

@@ -167,7 +167,7 @@ theorem f_invApp_f_app (i j k : D.J) (U : Opens (D.V (i, j)).carrier) :
                 apply pullback_base)) :=
   by
   have := PresheafedSpace.congr_app (@pullback.condition _ _ _ _ _ (D.f i j) (D.f i k) _)
-  dsimp only [comp_c_app] at this 
+  dsimp only [comp_c_app] at this
   rw [← cancel_epi (inv ((D.f_open i j).invApp U)), is_iso.inv_hom_id_assoc,
     is_open_immersion.inv_inv_app]
   simp_rw [category.assoc]
@@ -202,8 +202,8 @@ theorem snd_invApp_t_app' (i j k : D.J) (U : Opens (pullback (D.f i j) (D.f i k)
     eq_to_hom_trans]
   rintro x ⟨y, hy, eq⟩
   replace eq := concrete_category.congr_arg (𝖣.t i k).base Eq
-  change ((π₂ i, j, k) ≫ D.t i k).base y = (D.t k i ≫ D.t i k).base x at eq 
-  rw [𝖣.t_inv, id_base, TopCat.id_app] at eq 
+  change ((π₂ i, j, k) ≫ D.t i k).base y = (D.t k i ≫ D.t i k).base x at eq
+  rw [𝖣.t_inv, id_base, TopCat.id_app] at eq
   subst Eq
   use(inv (D.t' k i j)).base y
   change (inv (D.t' k i j) ≫ π₁ k, i, j).base y = _
@@ -534,7 +534,7 @@ def vPullbackConeIsLimit (i j : D.J) : IsLimit (𝖣.vPullbackCone i j) :=
         rw [← 𝖣.ι_gluedIso_hom (PresheafedSpace.forget _) _, ←
           𝖣.ι_gluedIso_hom (PresheafedSpace.forget _) _]
         have := congr_arg PresheafedSpace.hom.base s.condition
-        rw [comp_base, comp_base] at this 
+        rw [comp_base, comp_base] at this
         reassoc! this
         exact this _
       rw [← Set.image_subset_iff, ← Set.image_univ, ← Set.image_comp, Set.image_univ, ← coe_comp,

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

@@ -3,9 +3,9 @@ Copyright (c) 2021 Andrew Yang. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Andrew Yang
 -/
-import Mathbin.Topology.Gluing
-import Mathbin.AlgebraicGeometry.OpenImmersion.Basic
-import Mathbin.AlgebraicGeometry.LocallyRingedSpace.HasColimits
+import Topology.Gluing
+import AlgebraicGeometry.OpenImmersion.Basic
+import AlgebraicGeometry.LocallyRingedSpace.HasColimits
 
 #align_import algebraic_geometry.presheafed_space.gluing from "leanprover-community/mathlib"@"fdc286cc6967a012f41b87f76dcd2797b53152af"
 

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

@@ -205,7 +205,7 @@ theorem snd_invApp_t_app' (i j k : D.J) (U : Opens (pullback (D.f i j) (D.f i k)
   change ((π₂ i, j, k) ≫ D.t i k).base y = (D.t k i ≫ D.t i k).base x at eq 
   rw [𝖣.t_inv, id_base, TopCat.id_app] at eq 
   subst Eq
-  use (inv (D.t' k i j)).base y
+  use(inv (D.t' k i j)).base y
   change (inv (D.t' k i j) ≫ π₁ k, i, j).base y = _
   congr 2
   rw [is_iso.inv_comp_eq, 𝖣.t_fac_assoc, 𝖣.t_inv, category.comp_id]

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

@@ -2,16 +2,13 @@
 Copyright (c) 2021 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.presheafed_space.gluing
-! leanprover-community/mathlib commit fdc286cc6967a012f41b87f76dcd2797b53152af
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Topology.Gluing
 import Mathbin.AlgebraicGeometry.OpenImmersion.Basic
 import Mathbin.AlgebraicGeometry.LocallyRingedSpace.HasColimits
 
+#align_import algebraic_geometry.presheafed_space.gluing from "leanprover-community/mathlib"@"fdc286cc6967a012f41b87f76dcd2797b53152af"
+
 /-!
 # Gluing Structured spaces
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/fdc286cc6967a012f41b87f76dcd2797b53152af

@@ -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.presheafed_space.gluing
-! leanprover-community/mathlib commit 533f62f4dd62a5aad24a04326e6e787c8f7e98b1
+! leanprover-community/mathlib commit fdc286cc6967a012f41b87f76dcd2797b53152af
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.AlgebraicGeometry.LocallyRingedSpace.HasColimits
 /-!
 # Gluing Structured spaces
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 Given a family of gluing data of structured spaces (presheafed spaces, sheafed spaces, or locally
 ringed spaces), we may glue them together.
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/d30d31261cdb4d2f5e612eabc3c4bf45556350d5

@@ -75,6 +75,7 @@ variable (C : Type u) [Category.{v} C]
 
 namespace PresheafedSpace
 
+#print AlgebraicGeometry.PresheafedSpace.GlueData /-
 /-- A family of gluing data consists of
 1. An index type `J`
 2. A presheafed space `U i` for each `i : J`.
@@ -97,6 +98,7 @@ that the `U i`'s are open subspaces of the glued space.
 structure GlueData extends GlueData (PresheafedSpace.{v} C) where
   f_open : ∀ i j, IsOpenImmersion (f i j)
 #align algebraic_geometry.PresheafedSpace.glue_data AlgebraicGeometry.PresheafedSpace.GlueData
+-/
 
 attribute [instance] glue_data.f_open
 
@@ -116,12 +118,15 @@ local notation "π₁⁻¹ " i ", " j ", " k =>
 local notation "π₂⁻¹ " i ", " j ", " k =>
   (PresheafedSpace.IsOpenImmersion.pullbackSndOfLeft (D.f i j) (D.f i k)).invApp
 
+#print AlgebraicGeometry.PresheafedSpace.GlueData.toTopGlueData /-
 /-- The glue data of topological spaces associated to a family of glue data of PresheafedSpaces. -/
 abbrev toTopGlueData : TopCat.GlueData :=
   { f_open := fun i j => (D.f_open i j).base_open
     toGlueData := 𝖣.mapGlueData (forget C) }
 #align algebraic_geometry.PresheafedSpace.glue_data.to_Top_glue_data AlgebraicGeometry.PresheafedSpace.GlueData.toTopGlueData
+-/
 
+#print AlgebraicGeometry.PresheafedSpace.GlueData.ι_openEmbedding /-
 theorem ι_openEmbedding [HasLimits C] (i : D.J) : OpenEmbedding (𝖣.ι i).base :=
   by
   rw [← show _ = (𝖣.ι i).base from 𝖣.ι_gluedIso_inv (PresheafedSpace.forget _) _]
@@ -130,7 +135,9 @@ theorem ι_openEmbedding [HasLimits C] (i : D.J) : OpenEmbedding (𝖣.ι i).bas
       (TopCat.homeoOfIso (𝖣.gluedIso (PresheafedSpace.forget _)).symm).OpenEmbedding
       (D.to_Top_glue_data.ι_open_embedding i)
 #align algebraic_geometry.PresheafedSpace.glue_data.ι_open_embedding AlgebraicGeometry.PresheafedSpace.GlueData.ι_openEmbedding
+-/
 
+#print AlgebraicGeometry.PresheafedSpace.GlueData.pullback_base /-
 theorem pullback_base (i j k : D.J) (S : Set (D.V (i, j)).carrier) :
     (π₂ i, j, k) '' ((π₁ i, j, k) ⁻¹' S) = D.f i k ⁻¹' (D.f i j '' S) :=
   by
@@ -142,7 +149,9 @@ theorem pullback_base (i j k : D.J) (S : Set (D.V (i, j)).carrier) :
   rw [← TopCat.epi_iff_surjective]
   infer_instance
 #align algebraic_geometry.PresheafedSpace.glue_data.pullback_base AlgebraicGeometry.PresheafedSpace.GlueData.pullback_base
+-/
 
+#print AlgebraicGeometry.PresheafedSpace.GlueData.f_invApp_f_app /-
 /-- The red and the blue arrows in ![this diagram](https://i.imgur.com/0GiBUh6.png) commute. -/
 @[simp, reassoc]
 theorem f_invApp_f_app (i j k : D.J) (U : Opens (D.V (i, j)).carrier) :
@@ -169,7 +178,9 @@ theorem f_invApp_f_app (i j k : D.J) (U : Opens (D.V (i, j)).carrier) :
   erw [(D.V (i, k)).Presheaf.map_id]
   rfl
 #align algebraic_geometry.PresheafedSpace.glue_data.f_inv_app_f_app AlgebraicGeometry.PresheafedSpace.GlueData.f_invApp_f_app
+-/
 
+#print AlgebraicGeometry.PresheafedSpace.GlueData.snd_invApp_t_app' /-
 /-- We can prove the `eq` along with the lemma. Thus this is bundled together here, and the
 lemma itself is separated below.
 -/
@@ -199,7 +210,9 @@ theorem snd_invApp_t_app' (i j k : D.J) (U : Opens (pullback (D.f i j) (D.f i k)
   congr 2
   rw [is_iso.inv_comp_eq, 𝖣.t_fac_assoc, 𝖣.t_inv, category.comp_id]
 #align algebraic_geometry.PresheafedSpace.glue_data.snd_inv_app_t_app' AlgebraicGeometry.PresheafedSpace.GlueData.snd_invApp_t_app'
+-/
 
+#print AlgebraicGeometry.PresheafedSpace.GlueData.snd_invApp_t_app /-
 /-- The red and the blue arrows in ![this diagram](https://i.imgur.com/q6X1GJ9.png) commute. -/
 @[simp, reassoc]
 theorem snd_invApp_t_app (i j k : D.J) (U : Opens (pullback (D.f i j) (D.f i k)).carrier) :
@@ -213,9 +226,11 @@ theorem snd_invApp_t_app (i j k : D.J) (U : Opens (pullback (D.f i j) (D.f i k))
   rw [← e]
   simp [eq_to_hom_map]
 #align algebraic_geometry.PresheafedSpace.glue_data.snd_inv_app_t_app AlgebraicGeometry.PresheafedSpace.GlueData.snd_invApp_t_app
+-/
 
 variable [HasLimits C]
 
+#print AlgebraicGeometry.PresheafedSpace.GlueData.ι_image_preimage_eq /-
 theorem ι_image_preimage_eq (i j : D.J) (U : Opens (D.U i).carrier) :
     (Opens.map (𝖣.ι j).base).obj ((D.ι_openEmbedding i).IsOpenMap.Functor.obj U) =
       (D.f_open j i).openFunctor.obj
@@ -240,7 +255,9 @@ theorem ι_image_preimage_eq (i j : D.J) (U : Opens (D.U i).carrier) :
   · rw [← TopCat.mono_iff_injective]
     infer_instance
 #align algebraic_geometry.PresheafedSpace.glue_data.ι_image_preimage_eq AlgebraicGeometry.PresheafedSpace.GlueData.ι_image_preimage_eq
+-/
 
+#print AlgebraicGeometry.PresheafedSpace.GlueData.opensImagePreimageMap /-
 /-- (Implementation). The map `Γ(𝒪_{U_i}, U) ⟶ Γ(𝒪_{U_j}, 𝖣.ι j ⁻¹' (𝖣.ι i '' U))` -/
 def opensImagePreimageMap (i j : D.J) (U : Opens (D.U i).carrier) :
     (D.U i).Presheaf.obj (op U) ⟶ (D.U j).Presheaf.obj _ :=
@@ -249,7 +266,9 @@ def opensImagePreimageMap (i j : D.J) (U : Opens (D.U i).carrier) :
       (D.f_open j i).invApp (unop _) ≫
         (𝖣.U j).Presheaf.map (eqToHom (D.ι_image_preimage_eq i j U)).op
 #align algebraic_geometry.PresheafedSpace.glue_data.opens_image_preimage_map AlgebraicGeometry.PresheafedSpace.GlueData.opensImagePreimageMap
+-/
 
+#print AlgebraicGeometry.PresheafedSpace.GlueData.opensImagePreimageMap_app' /-
 theorem opensImagePreimageMap_app' (i j k : D.J) (U : Opens (D.U i).carrier) :
     ∃ eq,
       D.opensImagePreimageMap i j U ≫ (D.f j k).c.app _ =
@@ -268,7 +287,9 @@ theorem opensImagePreimageMap_app' (i j k : D.J) (U : Opens (D.U i).carrier) :
   rw [eq_to_hom_map (opens.map _), eq_to_hom_op, eq_to_hom_trans]
   congr
 #align algebraic_geometry.PresheafedSpace.glue_data.opens_image_preimage_map_app' AlgebraicGeometry.PresheafedSpace.GlueData.opensImagePreimageMap_app'
+-/
 
+#print AlgebraicGeometry.PresheafedSpace.GlueData.opensImagePreimageMap_app /-
 /-- The red and the blue arrows in ![this diagram](https://i.imgur.com/mBzV1Rx.png) commute. -/
 theorem opensImagePreimageMap_app (i j k : D.J) (U : Opens (D.U i).carrier) :
     D.opensImagePreimageMap i j U ≫ (D.f j k).c.app _ =
@@ -277,7 +298,9 @@ theorem opensImagePreimageMap_app (i j k : D.J) (U : Opens (D.U i).carrier) :
           (D.V (j, k)).Presheaf.map (eqToHom (opensImagePreimageMap_app' D i j k U).some) :=
   (opensImagePreimageMap_app' D i j k U).choose_spec
 #align algebraic_geometry.PresheafedSpace.glue_data.opens_image_preimage_map_app AlgebraicGeometry.PresheafedSpace.GlueData.opensImagePreimageMap_app
+-/
 
+#print AlgebraicGeometry.PresheafedSpace.GlueData.opensImagePreimageMap_app_assoc /-
 -- This is proved separately since `reassoc` somehow timeouts.
 theorem opensImagePreimageMap_app_assoc (i j k : D.J) (U : Opens (D.U i).carrier) {X' : C}
     (f' : _ ⟶ X') :
@@ -289,19 +312,25 @@ theorem opensImagePreimageMap_app_assoc (i j k : D.J) (U : Opens (D.U i).carrier
   simpa only [category.assoc] using
     congr_arg (fun g => g ≫ f') (opens_image_preimage_map_app D i j k U)
 #align algebraic_geometry.PresheafedSpace.glue_data.opens_image_preimage_map_app_assoc AlgebraicGeometry.PresheafedSpace.GlueData.opensImagePreimageMap_app_assoc
+-/
 
+#print AlgebraicGeometry.PresheafedSpace.GlueData.diagramOverOpen /-
 /-- (Implementation) Given an open subset of one of the spaces `U ⊆ Uᵢ`, the sheaf component of
 the image `ι '' U` in the glued space is the limit of this diagram. -/
 abbrev diagramOverOpen {i : D.J} (U : Opens (D.U i).carrier) : (WalkingMultispan _ _)ᵒᵖ ⥤ C :=
   componentwiseDiagram 𝖣.diagram.multispan ((D.ι_openEmbedding i).IsOpenMap.Functor.obj U)
 #align algebraic_geometry.PresheafedSpace.glue_data.diagram_over_open AlgebraicGeometry.PresheafedSpace.GlueData.diagramOverOpen
+-/
 
+#print AlgebraicGeometry.PresheafedSpace.GlueData.diagramOverOpenπ /-
 /-- (Implementation)
 The projection from the limit of `diagram_over_open` to a component of `D.U j`. -/
 abbrev diagramOverOpenπ {i : D.J} (U : Opens (D.U i).carrier) (j : D.J) :=
   limit.π (D.diagramOverOpen U) (op (WalkingMultispan.right j))
 #align algebraic_geometry.PresheafedSpace.glue_data.diagram_over_open_π AlgebraicGeometry.PresheafedSpace.GlueData.diagramOverOpenπ
+-/
 
+#print AlgebraicGeometry.PresheafedSpace.GlueData.ιInvAppπApp /-
 /-- (Implementation) We construct the map `Γ(𝒪_{U_i}, U) ⟶ Γ(𝒪_V, U_V)` for each `V` in the gluing
 diagram. We will lift these maps into `ι_inv_app`. -/
 def ιInvAppπApp {i : D.J} (U : Opens (D.U i).carrier) (j) :
@@ -319,7 +348,9 @@ def ιInvAppπApp {i : D.J} (U : Opens (D.U i).carrier) (j) :
     exact colimit.w 𝖣.diagram.multispan (walking_multispan.hom.fst (j, k))
   · exact D.opens_image_preimage_map i j U
 #align algebraic_geometry.PresheafedSpace.glue_data.ι_inv_app_π_app AlgebraicGeometry.PresheafedSpace.GlueData.ιInvAppπApp
+-/
 
+#print AlgebraicGeometry.PresheafedSpace.GlueData.ιInvApp /-
 /-- (Implementation) The natural map `Γ(𝒪_{U_i}, U) ⟶ Γ(𝒪_X, 𝖣.ι i '' U)`.
 This forms the inverse of `(𝖣.ι i).c.app (op U)`. -/
 def ιInvApp {i : D.J} (U : Opens (D.U i).carrier) :
@@ -373,7 +404,9 @@ def ιInvApp {i : D.J} (U : Opens (D.U i).carrier) :
             repeat' erw [← (D.V (j, k)).Presheaf.map_comp]
             congr } }
 #align algebraic_geometry.PresheafedSpace.glue_data.ι_inv_app AlgebraicGeometry.PresheafedSpace.GlueData.ιInvApp
+-/
 
+#print AlgebraicGeometry.PresheafedSpace.GlueData.ιInvApp_π /-
 /-- `ι_inv_app` is the left inverse of `D.ι i` on `U`. -/
 theorem ιInvApp_π {i : D.J} (U : Opens (D.U i).carrier) :
     ∃ eq, D.ιInvApp U ≫ D.diagramOverOpenπ U i = (D.U i).Presheaf.map (eqToHom Eq) :=
@@ -391,12 +424,16 @@ theorem ιInvApp_π {i : D.J} (U : Opens (D.U i).carrier) :
   · rw [← TopCat.epi_iff_surjective]
     infer_instance
 #align algebraic_geometry.PresheafedSpace.glue_data.ι_inv_app_π AlgebraicGeometry.PresheafedSpace.GlueData.ιInvApp_π
+-/
 
+#print AlgebraicGeometry.PresheafedSpace.GlueData.ιInvAppπEqMap /-
 /-- The `eq_to_hom` given by `ι_inv_app_π`. -/
 abbrev ιInvAppπEqMap {i : D.J} (U : Opens (D.U i).carrier) :=
   (D.U i).Presheaf.map (eqToIso (D.ιInvApp_π U).some).inv
 #align algebraic_geometry.PresheafedSpace.glue_data.ι_inv_app_π_eq_map AlgebraicGeometry.PresheafedSpace.GlueData.ιInvAppπEqMap
+-/
 
+#print AlgebraicGeometry.PresheafedSpace.GlueData.π_ιInvApp_π /-
 /-- `ι_inv_app` is the right inverse of `D.ι i` on `U`. -/
 theorem π_ιInvApp_π (i j : D.J) (U : Opens (D.U i).carrier) :
     D.diagramOverOpenπ U i ≫ D.ιInvAppπEqMap U ≫ D.ιInvApp U ≫ D.diagramOverOpenπ U j =
@@ -430,7 +467,9 @@ theorem π_ιInvApp_π (i j : D.J) (U : Opens (D.U i).carrier) :
     erw [D.ι_image_preimage_eq i j U]
     all_goals infer_instance
 #align algebraic_geometry.PresheafedSpace.glue_data.π_ι_inv_app_π AlgebraicGeometry.PresheafedSpace.GlueData.π_ιInvApp_π
+-/
 
+#print AlgebraicGeometry.PresheafedSpace.GlueData.π_ιInvApp_eq_id /-
 /-- `ι_inv_app` is the inverse of `D.ι i` on `U`. -/
 theorem π_ιInvApp_eq_id (i : D.J) (U : Opens (D.U i).carrier) :
     D.diagramOverOpenπ U i ≫ D.ιInvAppπEqMap U ≫ D.ιInvApp U = 𝟙 _ :=
@@ -449,7 +488,11 @@ theorem π_ιInvApp_eq_id (i : D.J) (U : Opens (D.U i).carrier) :
     rw [category.id_comp]
     apply π_ι_inv_app_π
 #align algebraic_geometry.PresheafedSpace.glue_data.π_ι_inv_app_eq_id AlgebraicGeometry.PresheafedSpace.GlueData.π_ιInvApp_eq_id
+-/
 
+/- warning: algebraic_geometry.PresheafedSpace.glue_data.componentwise_diagram_π_is_iso clashes with algebraic_geometry.PresheafedSpace.glue_data.componentwise_diagram_π_IsIso -> AlgebraicGeometry.PresheafedSpace.GlueData.componentwise_diagram_π_isIso
+Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.glue_data.componentwise_diagram_π_is_iso AlgebraicGeometry.PresheafedSpace.GlueData.componentwise_diagram_π_isIsoₓ'. -/
+#print AlgebraicGeometry.PresheafedSpace.GlueData.componentwise_diagram_π_isIso /-
 instance componentwise_diagram_π_isIso (i : D.J) (U : Opens (D.U i).carrier) :
     IsIso (D.diagramOverOpenπ U i) :=
   by
@@ -459,13 +502,19 @@ instance componentwise_diagram_π_isIso (i : D.J) (U : Opens (D.U i).carrier) :
   · rw [category.assoc, (D.ι_inv_app_π _).choose_spec]
     exact iso.inv_hom_id ((D.to_glue_data.U i).Presheaf.mapIso (eq_to_iso _))
 #align algebraic_geometry.PresheafedSpace.glue_data.componentwise_diagram_π_is_iso AlgebraicGeometry.PresheafedSpace.GlueData.componentwise_diagram_π_isIso
+-/
 
+/- warning: algebraic_geometry.PresheafedSpace.glue_data.ι_is_open_immersion clashes with algebraic_geometry.PresheafedSpace.glue_data.ι_IsOpenImmersion -> AlgebraicGeometry.PresheafedSpace.GlueData.ιIsOpenImmersion
+Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.glue_data.ι_is_open_immersion AlgebraicGeometry.PresheafedSpace.GlueData.ιIsOpenImmersionₓ'. -/
+#print AlgebraicGeometry.PresheafedSpace.GlueData.ιIsOpenImmersion /-
 instance ιIsOpenImmersion (i : D.J) : IsOpenImmersion (𝖣.ι i)
     where
   base_open := D.ι_openEmbedding i
   c_iso U := by erw [← colimit_presheaf_obj_iso_componentwise_limit_hom_π]; infer_instance
 #align algebraic_geometry.PresheafedSpace.glue_data.ι_is_open_immersion AlgebraicGeometry.PresheafedSpace.GlueData.ιIsOpenImmersion
+-/
 
+#print AlgebraicGeometry.PresheafedSpace.GlueData.vPullbackConeIsLimit /-
 /-- The following diagram is a pullback, i.e. `Vᵢⱼ` is the intersection of `Uᵢ` and `Uⱼ` in `X`.
 
 Vᵢⱼ ⟶ Uᵢ
@@ -497,10 +546,13 @@ def vPullbackConeIsLimit (i j : D.J) : IsLimit (𝖣.vPullbackCone i j) :=
       erw [is_open_immersion.lift_fac_assoc]
     · intro m e₁ e₂; rw [← cancel_mono (D.f i j)]; erw [e₁]; rw [is_open_immersion.lift_fac]
 #align algebraic_geometry.PresheafedSpace.glue_data.V_pullback_cone_is_limit AlgebraicGeometry.PresheafedSpace.GlueData.vPullbackConeIsLimit
+-/
 
+#print AlgebraicGeometry.PresheafedSpace.GlueData.ι_jointly_surjective /-
 theorem ι_jointly_surjective (x : 𝖣.glued) : ∃ (i : D.J) (y : D.U i), (𝖣.ι i).base y = x :=
   𝖣.ι_jointly_surjective (PresheafedSpace.forget _ ⋙ CategoryTheory.forget TopCat) x
 #align algebraic_geometry.PresheafedSpace.glue_data.ι_jointly_surjective AlgebraicGeometry.PresheafedSpace.GlueData.ι_jointly_surjective
+-/
 
 end GlueData
 
@@ -560,9 +612,13 @@ theorem ι_isoPresheafedSpace_inv (i : D.J) :
   𝖣.ι_gluedIso_inv _ _
 #align algebraic_geometry.SheafedSpace.glue_data.ι_iso_PresheafedSpace_inv AlgebraicGeometry.SheafedSpaceₓ.GlueData.ι_isoPresheafedSpace_inv
 
+/- warning: algebraic_geometry.SheafedSpace.glue_data.ι_is_open_immersion clashes with algebraic_geometry.SheafedSpace.glue_data.ι_IsOpenImmersion -> AlgebraicGeometry.SheafedSpaceₓ.GlueData.ιIsOpenImmersion
+Case conversion may be inaccurate. Consider using '#align algebraic_geometry.SheafedSpace.glue_data.ι_is_open_immersion AlgebraicGeometry.SheafedSpaceₓ.GlueData.ιIsOpenImmersionₓ'. -/
+#print AlgebraicGeometry.SheafedSpaceₓ.GlueData.ιIsOpenImmersion /-
 instance ιIsOpenImmersion (i : D.J) : IsOpenImmersion (𝖣.ι i) := by
   rw [← D.ι_iso_PresheafedSpace_inv]; infer_instance
 #align algebraic_geometry.SheafedSpace.glue_data.ι_is_open_immersion AlgebraicGeometry.SheafedSpaceₓ.GlueData.ιIsOpenImmersion
+-/
 
 theorem ι_jointly_surjective (x : 𝖣.glued) : ∃ (i : D.J) (y : D.U i), (𝖣.ι i).base y = x :=
   𝖣.ι_jointly_surjective (SheafedSpace.forget _ ⋙ CategoryTheory.forget TopCat) x
@@ -586,6 +642,7 @@ end SheafedSpace
 
 namespace LocallyRingedSpace
 
+#print AlgebraicGeometry.LocallyRingedSpace.GlueData /-
 /-- A family of gluing data consists of
 1. An index type `J`
 2. A locally ringed space `U i` for each `i : J`.
@@ -608,6 +665,7 @@ that the `U i`'s are open subspaces of the glued space.
 structure GlueData extends GlueData LocallyRingedSpace where
   f_open : ∀ i j, LocallyRingedSpace.IsOpenImmersion (f i j)
 #align algebraic_geometry.LocallyRingedSpace.glue_data AlgebraicGeometry.LocallyRingedSpace.GlueData
+-/
 
 attribute [instance] glue_data.f_open
 
@@ -617,36 +675,49 @@ variable (D : GlueData)
 
 local notation "𝖣" => D.toGlueData
 
+#print AlgebraicGeometry.LocallyRingedSpace.GlueData.toSheafedSpaceGlueData /-
 /-- The glue data of ringed spaces associated to a family of glue data of locally ringed spaces. -/
 abbrev toSheafedSpaceGlueData : SheafedSpace.GlueData CommRingCat :=
   { f_open := D.f_open
     toGlueData := 𝖣.mapGlueData forgetToSheafedSpace }
 #align algebraic_geometry.LocallyRingedSpace.glue_data.to_SheafedSpace_glue_data AlgebraicGeometry.LocallyRingedSpace.GlueData.toSheafedSpaceGlueData
+-/
 
+#print AlgebraicGeometry.LocallyRingedSpace.GlueData.isoSheafedSpace /-
 /-- The gluing as locally ringed spaces is isomorphic to the gluing as ringed spaces. -/
 abbrev isoSheafedSpace : 𝖣.glued.toSheafedSpace ≅ D.toSheafedSpaceGlueData.toGlueData.glued :=
   𝖣.gluedIso forgetToSheafedSpace
 #align algebraic_geometry.LocallyRingedSpace.glue_data.iso_SheafedSpace AlgebraicGeometry.LocallyRingedSpace.GlueData.isoSheafedSpace
+-/
 
+#print AlgebraicGeometry.LocallyRingedSpace.GlueData.ι_isoSheafedSpace_inv /-
 theorem ι_isoSheafedSpace_inv (i : D.J) :
     D.toSheafedSpaceGlueData.toGlueData.ι i ≫ D.isoSheafedSpace.inv = (𝖣.ι i).1 :=
   𝖣.ι_gluedIso_inv forgetToSheafedSpace i
 #align algebraic_geometry.LocallyRingedSpace.glue_data.ι_iso_SheafedSpace_inv AlgebraicGeometry.LocallyRingedSpace.GlueData.ι_isoSheafedSpace_inv
+-/
 
+/- warning: algebraic_geometry.LocallyRingedSpace.glue_data.ι_is_open_immersion clashes with algebraic_geometry.LocallyRingedSpace.glue_data.ι_IsOpenImmersion -> AlgebraicGeometry.LocallyRingedSpace.GlueData.ι_isOpenImmersion
+Case conversion may be inaccurate. Consider using '#align algebraic_geometry.LocallyRingedSpace.glue_data.ι_is_open_immersion AlgebraicGeometry.LocallyRingedSpace.GlueData.ι_isOpenImmersionₓ'. -/
+#print AlgebraicGeometry.LocallyRingedSpace.GlueData.ι_isOpenImmersion /-
 instance ι_isOpenImmersion (i : D.J) : IsOpenImmersion (𝖣.ι i) :=
   by
   delta is_open_immersion; rw [← D.ι_iso_SheafedSpace_inv]
   apply PresheafedSpace.is_open_immersion.comp
 #align algebraic_geometry.LocallyRingedSpace.glue_data.ι_is_open_immersion AlgebraicGeometry.LocallyRingedSpace.GlueData.ι_isOpenImmersion
+-/
 
 instance (i j k : D.J) : PreservesLimit (cospan (𝖣.f i j) (𝖣.f i k)) forgetToSheafedSpace :=
   inferInstance
 
+#print AlgebraicGeometry.LocallyRingedSpace.GlueData.ι_jointly_surjective /-
 theorem ι_jointly_surjective (x : 𝖣.glued) : ∃ (i : D.J) (y : D.U i), (𝖣.ι i).1.base y = x :=
   𝖣.ι_jointly_surjective
     ((LocallyRingedSpace.forgetToSheafedSpace ⋙ SheafedSpace.forget _) ⋙ forget TopCat) x
 #align algebraic_geometry.LocallyRingedSpace.glue_data.ι_jointly_surjective AlgebraicGeometry.LocallyRingedSpace.GlueData.ι_jointly_surjective
+-/
 
+#print AlgebraicGeometry.LocallyRingedSpace.GlueData.vPullbackConeIsLimit /-
 /-- The following diagram is a pullback, i.e. `Vᵢⱼ` is the intersection of `Uᵢ` and `Uⱼ` in `X`.
 
 Vᵢⱼ ⟶ Uᵢ
@@ -658,6 +729,7 @@ def vPullbackConeIsLimit (i j : D.J) : IsLimit (𝖣.vPullbackCone i j) :=
   𝖣.vPullbackConeIsLimitOfMap forgetToSheafedSpace i j
     (D.toSheafedSpaceGlueData.vPullbackConeIsLimit _ _)
 #align algebraic_geometry.LocallyRingedSpace.glue_data.V_pullback_cone_is_limit AlgebraicGeometry.LocallyRingedSpace.GlueData.vPullbackConeIsLimit
+-/
 
 end GlueData
 

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

@@ -531,7 +531,7 @@ that the `U i`'s are open subspaces of the glued space.
 @[nolint has_nonempty_instance]
 structure GlueData extends GlueData (SheafedSpace.{v} C) where
   f_open : ∀ i j, SheafedSpace.IsOpenImmersion (f i j)
-#align algebraic_geometry.SheafedSpace.glue_data AlgebraicGeometry.SheafedSpace.GlueData
+#align algebraic_geometry.SheafedSpace.glue_data AlgebraicGeometry.SheafedSpaceₓ.GlueData
 
 attribute [instance] glue_data.f_open
 
@@ -545,7 +545,7 @@ local notation "𝖣" => D.toGlueData
 abbrev toPresheafedSpaceGlueData : PresheafedSpace.GlueData C :=
   { f_open := D.f_open
     toGlueData := 𝖣.mapGlueData forgetToPresheafedSpace }
-#align algebraic_geometry.SheafedSpace.glue_data.to_PresheafedSpace_glue_data AlgebraicGeometry.SheafedSpace.GlueData.toPresheafedSpaceGlueData
+#align algebraic_geometry.SheafedSpace.glue_data.to_PresheafedSpace_glue_data AlgebraicGeometry.SheafedSpaceₓ.GlueData.toPresheafedSpaceGlueData
 
 variable [HasLimits C]
 
@@ -553,20 +553,20 @@ variable [HasLimits C]
 abbrev isoPresheafedSpace :
     𝖣.glued.toPresheafedSpace ≅ D.toPresheafedSpaceGlueData.toGlueData.glued :=
   𝖣.gluedIso forgetToPresheafedSpace
-#align algebraic_geometry.SheafedSpace.glue_data.iso_PresheafedSpace AlgebraicGeometry.SheafedSpace.GlueData.isoPresheafedSpace
+#align algebraic_geometry.SheafedSpace.glue_data.iso_PresheafedSpace AlgebraicGeometry.SheafedSpaceₓ.GlueData.isoPresheafedSpace
 
 theorem ι_isoPresheafedSpace_inv (i : D.J) :
     D.toPresheafedSpaceGlueData.toGlueData.ι i ≫ D.isoPresheafedSpace.inv = 𝖣.ι i :=
   𝖣.ι_gluedIso_inv _ _
-#align algebraic_geometry.SheafedSpace.glue_data.ι_iso_PresheafedSpace_inv AlgebraicGeometry.SheafedSpace.GlueData.ι_isoPresheafedSpace_inv
+#align algebraic_geometry.SheafedSpace.glue_data.ι_iso_PresheafedSpace_inv AlgebraicGeometry.SheafedSpaceₓ.GlueData.ι_isoPresheafedSpace_inv
 
-instance ι_isOpenImmersion (i : D.J) : IsOpenImmersion (𝖣.ι i) := by
+instance ιIsOpenImmersion (i : D.J) : IsOpenImmersion (𝖣.ι i) := by
   rw [← D.ι_iso_PresheafedSpace_inv]; infer_instance
-#align algebraic_geometry.SheafedSpace.glue_data.ι_is_open_immersion AlgebraicGeometry.SheafedSpace.GlueData.ι_isOpenImmersion
+#align algebraic_geometry.SheafedSpace.glue_data.ι_is_open_immersion AlgebraicGeometry.SheafedSpaceₓ.GlueData.ιIsOpenImmersion
 
 theorem ι_jointly_surjective (x : 𝖣.glued) : ∃ (i : D.J) (y : D.U i), (𝖣.ι i).base y = x :=
   𝖣.ι_jointly_surjective (SheafedSpace.forget _ ⋙ CategoryTheory.forget TopCat) x
-#align algebraic_geometry.SheafedSpace.glue_data.ι_jointly_surjective AlgebraicGeometry.SheafedSpace.GlueData.ι_jointly_surjective
+#align algebraic_geometry.SheafedSpace.glue_data.ι_jointly_surjective AlgebraicGeometry.SheafedSpaceₓ.GlueData.ι_jointly_surjective
 
 /-- The following diagram is a pullback, i.e. `Vᵢⱼ` is the intersection of `Uᵢ` and `Uⱼ` in `X`.
 
@@ -578,7 +578,7 @@ Vᵢⱼ ⟶ Uᵢ
 def vPullbackConeIsLimit (i j : D.J) : IsLimit (𝖣.vPullbackCone i j) :=
   𝖣.vPullbackConeIsLimitOfMap forgetToPresheafedSpace i j
     (D.toPresheafedSpaceGlueData.vPullbackConeIsLimit _ _)
-#align algebraic_geometry.SheafedSpace.glue_data.V_pullback_cone_is_limit AlgebraicGeometry.SheafedSpace.GlueData.vPullbackConeIsLimit
+#align algebraic_geometry.SheafedSpace.glue_data.V_pullback_cone_is_limit AlgebraicGeometry.SheafedSpaceₓ.GlueData.vPullbackConeIsLimit
 
 end GlueData
 

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

@@ -104,20 +104,15 @@ namespace GlueData
 
 variable {C} (D : GlueData C)
 
--- mathport name: «expr𝖣»
 local notation "𝖣" => D.toGlueData
 
--- mathport name: «exprπ₁ , , »
 local notation "π₁ " i ", " j ", " k => @pullback.fst _ _ _ _ _ (D.f i j) (D.f i k) _
 
--- mathport name: «exprπ₂ , , »
 local notation "π₂ " i ", " j ", " k => @pullback.snd _ _ _ _ _ (D.f i j) (D.f i k) _
 
--- mathport name: «exprπ₁⁻¹ , , »
 local notation "π₁⁻¹ " i ", " j ", " k =>
   (PresheafedSpace.IsOpenImmersion.pullbackFstOfRight (D.f i j) (D.f i k)).invApp
 
--- mathport name: «exprπ₂⁻¹ , , »
 local notation "π₂⁻¹ " i ", " j ", " k =>
   (PresheafedSpace.IsOpenImmersion.pullbackSndOfLeft (D.f i j) (D.f i k)).invApp
 
@@ -544,7 +539,6 @@ namespace GlueData
 
 variable {C} (D : GlueData C)
 
--- mathport name: «expr𝖣»
 local notation "𝖣" => D.toGlueData
 
 /-- The glue data of presheafed spaces associated to a family of glue data of sheafed spaces. -/
@@ -621,7 +615,6 @@ namespace GlueData
 
 variable (D : GlueData)
 
--- mathport name: «expr𝖣»
 local notation "𝖣" => D.toGlueData
 
 /-- The glue data of ringed spaces associated to a family of glue data of locally ringed spaces. -/

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

@@ -4,12 +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.presheafed_space.gluing
-! leanprover-community/mathlib commit d39590fc8728fbf6743249802486f8c91ffe07bc
+! 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.Topology.Gluing
-import Mathbin.AlgebraicGeometry.OpenImmersion
+import Mathbin.AlgebraicGeometry.OpenImmersion.Basic
 import Mathbin.AlgebraicGeometry.LocallyRingedSpace.HasColimits
 
 /-!

mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297

@@ -170,7 +170,7 @@ theorem f_invApp_f_app (i j k : D.J) (U : Opens (D.V (i, j)).carrier) :
   erw [(π₁ i, j, k).c.naturality_assoc, reassoc_of this, ← functor.map_comp_assoc,
     is_open_immersion.inv_naturality_assoc, is_open_immersion.app_inv_app_assoc, ←
     (D.V (i, k)).Presheaf.map_comp, ← (D.V (i, k)).Presheaf.map_comp]
-  convert(category.comp_id _).symm
+  convert (category.comp_id _).symm
   erw [(D.V (i, k)).Presheaf.map_id]
   rfl
 #align algebraic_geometry.PresheafedSpace.glue_data.f_inv_app_f_app AlgebraicGeometry.PresheafedSpace.GlueData.f_invApp_f_app
@@ -424,7 +424,8 @@ theorem π_ιInvApp_π (i j : D.J) (U : Opens (D.U i).carrier) :
   iterate 3 rw [← functor.map_comp_assoc]
   rw [nat_trans.naturality_assoc]
   erw [← (D.V (i, j)).Presheaf.map_comp]
-  convert limit.w (componentwise_diagram 𝖣.diagram.multispan _)
+  convert
+    limit.w (componentwise_diagram 𝖣.diagram.multispan _)
       (Quiver.Hom.op (walking_multispan.hom.fst (i, j)))
   · rw [category.comp_id]
     apply (config := { instances := false }) mono_comp

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

@@ -163,7 +163,7 @@ theorem f_invApp_f_app (i j k : D.J) (U : Opens (D.V (i, j)).carrier) :
                 apply pullback_base)) :=
   by
   have := PresheafedSpace.congr_app (@pullback.condition _ _ _ _ _ (D.f i j) (D.f i k) _)
-  dsimp only [comp_c_app] at this
+  dsimp only [comp_c_app] at this 
   rw [← cancel_epi (inv ((D.f_open i j).invApp U)), is_iso.inv_hom_id_assoc,
     is_open_immersion.inv_inv_app]
   simp_rw [category.assoc]
@@ -196,8 +196,8 @@ theorem snd_invApp_t_app' (i j k : D.J) (U : Opens (pullback (D.f i j) (D.f i k)
     eq_to_hom_trans]
   rintro x ⟨y, hy, eq⟩
   replace eq := concrete_category.congr_arg (𝖣.t i k).base Eq
-  change ((π₂ i, j, k) ≫ D.t i k).base y = (D.t k i ≫ D.t i k).base x at eq
-  rw [𝖣.t_inv, id_base, TopCat.id_app] at eq
+  change ((π₂ i, j, k) ≫ D.t i k).base y = (D.t k i ≫ D.t i k).base x at eq 
+  rw [𝖣.t_inv, id_base, TopCat.id_app] at eq 
   subst Eq
   use (inv (D.t' k i j)).base y
   change (inv (D.t' k i j) ≫ π₁ k, i, j).base y = _
@@ -489,7 +489,7 @@ def vPullbackConeIsLimit (i j : D.J) : IsLimit (𝖣.vPullbackCone i j) :=
         rw [← 𝖣.ι_gluedIso_hom (PresheafedSpace.forget _) _, ←
           𝖣.ι_gluedIso_hom (PresheafedSpace.forget _) _]
         have := congr_arg PresheafedSpace.hom.base s.condition
-        rw [comp_base, comp_base] at this
+        rw [comp_base, comp_base] at this 
         reassoc! this
         exact this _
       rw [← Set.image_subset_iff, ← Set.image_univ, ← Set.image_comp, Set.image_univ, ← coe_comp,
@@ -502,7 +502,7 @@ def vPullbackConeIsLimit (i j : D.J) : IsLimit (𝖣.vPullbackCone i j) :=
     · intro m e₁ e₂; rw [← cancel_mono (D.f i j)]; erw [e₁]; rw [is_open_immersion.lift_fac]
 #align algebraic_geometry.PresheafedSpace.glue_data.V_pullback_cone_is_limit AlgebraicGeometry.PresheafedSpace.GlueData.vPullbackConeIsLimit
 
-theorem ι_jointly_surjective (x : 𝖣.glued) : ∃ (i : D.J)(y : D.U i), (𝖣.ι i).base y = x :=
+theorem ι_jointly_surjective (x : 𝖣.glued) : ∃ (i : D.J) (y : D.U i), (𝖣.ι i).base y = x :=
   𝖣.ι_jointly_surjective (PresheafedSpace.forget _ ⋙ CategoryTheory.forget TopCat) x
 #align algebraic_geometry.PresheafedSpace.glue_data.ι_jointly_surjective AlgebraicGeometry.PresheafedSpace.GlueData.ι_jointly_surjective
 
@@ -569,7 +569,7 @@ instance ι_isOpenImmersion (i : D.J) : IsOpenImmersion (𝖣.ι i) := by
   rw [← D.ι_iso_PresheafedSpace_inv]; infer_instance
 #align algebraic_geometry.SheafedSpace.glue_data.ι_is_open_immersion AlgebraicGeometry.SheafedSpace.GlueData.ι_isOpenImmersion
 
-theorem ι_jointly_surjective (x : 𝖣.glued) : ∃ (i : D.J)(y : D.U i), (𝖣.ι i).base y = x :=
+theorem ι_jointly_surjective (x : 𝖣.glued) : ∃ (i : D.J) (y : D.U i), (𝖣.ι i).base y = x :=
   𝖣.ι_jointly_surjective (SheafedSpace.forget _ ⋙ CategoryTheory.forget TopCat) x
 #align algebraic_geometry.SheafedSpace.glue_data.ι_jointly_surjective AlgebraicGeometry.SheafedSpace.GlueData.ι_jointly_surjective
 
@@ -648,7 +648,7 @@ instance ι_isOpenImmersion (i : D.J) : IsOpenImmersion (𝖣.ι i) :=
 instance (i j k : D.J) : PreservesLimit (cospan (𝖣.f i j) (𝖣.f i k)) forgetToSheafedSpace :=
   inferInstance
 
-theorem ι_jointly_surjective (x : 𝖣.glued) : ∃ (i : D.J)(y : D.U i), (𝖣.ι i).1.base y = x :=
+theorem ι_jointly_surjective (x : 𝖣.glued) : ∃ (i : D.J) (y : D.U i), (𝖣.ι i).1.base y = x :=
   𝖣.ι_jointly_surjective
     ((LocallyRingedSpace.forgetToSheafedSpace ⋙ SheafedSpace.forget _) ⋙ forget TopCat) x
 #align algebraic_geometry.LocallyRingedSpace.glue_data.ι_jointly_surjective AlgebraicGeometry.LocallyRingedSpace.GlueData.ι_jointly_surjective

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

@@ -316,8 +316,7 @@ def ιInvAppπApp {i : D.J} (U : Opens (D.U i).carrier) (j) :
   · refine'
       D.opens_image_preimage_map i j U ≫ (D.f j k).c.app _ ≫ (D.V (j, k)).Presheaf.map (eq_to_hom _)
     rw [functor.op_obj]
-    congr 1
-    ext1
+    congr 1; ext1
     dsimp only [functor.op_obj, opens.map_coe, unop_op, IsOpenMap.functor_obj_coe]
     rw [Set.preimage_preimage]
     change (D.f j k ≫ 𝖣.ι j).base ⁻¹' _ = _
@@ -337,15 +336,11 @@ def ιInvApp {i : D.J} (U : Opens (D.U i).carrier) :
           naturality' := fun X Y f' => by
             induction X using Opposite.rec'
             induction Y using Opposite.rec'
-            let f : Y ⟶ X := f'.unop
-            have : f' = f.op := rfl
-            clear_value f
-            subst this
+            let f : Y ⟶ X := f'.unop; have : f' = f.op := rfl; clear_value f; subst this
             rcases f with (_ | ⟨j, k⟩ | ⟨j, k⟩)
             · erw [category.id_comp, CategoryTheory.Functor.map_id]
               rw [category.comp_id]
-            · erw [category.id_comp]
-              congr 1
+            · erw [category.id_comp]; congr 1
             erw [category.id_comp]
             -- It remains to show that the blue is equal to red + green in the original diagram.
             -- The proof strategy is illustrated in ![this diagram](https://i.imgur.com/mBzV1Rx.png)
@@ -472,9 +467,7 @@ instance componentwise_diagram_π_isIso (i : D.J) (U : Opens (D.U i).carrier) :
 instance ιIsOpenImmersion (i : D.J) : IsOpenImmersion (𝖣.ι i)
     where
   base_open := D.ι_openEmbedding i
-  c_iso U := by
-    erw [← colimit_presheaf_obj_iso_componentwise_limit_hom_π]
-    infer_instance
+  c_iso U := by erw [← colimit_presheaf_obj_iso_componentwise_limit_hom_π]; infer_instance
 #align algebraic_geometry.PresheafedSpace.glue_data.ι_is_open_immersion AlgebraicGeometry.PresheafedSpace.GlueData.ιIsOpenImmersion
 
 /-- The following diagram is a pullback, i.e. `Vᵢⱼ` is the intersection of `Uᵢ` and `Uⱼ` in `X`.
@@ -506,10 +499,7 @@ def vPullbackConeIsLimit (i j : D.J) : IsLimit (𝖣.vPullbackCone i j) :=
     · rw [← cancel_mono (𝖣.ι j), category.assoc, ← (𝖣.vPullbackCone i j).condition]
       conv_rhs => rw [← s.condition]
       erw [is_open_immersion.lift_fac_assoc]
-    · intro m e₁ e₂
-      rw [← cancel_mono (D.f i j)]
-      erw [e₁]
-      rw [is_open_immersion.lift_fac]
+    · intro m e₁ e₂; rw [← cancel_mono (D.f i j)]; erw [e₁]; rw [is_open_immersion.lift_fac]
 #align algebraic_geometry.PresheafedSpace.glue_data.V_pullback_cone_is_limit AlgebraicGeometry.PresheafedSpace.GlueData.vPullbackConeIsLimit
 
 theorem ι_jointly_surjective (x : 𝖣.glued) : ∃ (i : D.J)(y : D.U i), (𝖣.ι i).base y = x :=
@@ -575,10 +565,8 @@ theorem ι_isoPresheafedSpace_inv (i : D.J) :
   𝖣.ι_gluedIso_inv _ _
 #align algebraic_geometry.SheafedSpace.glue_data.ι_iso_PresheafedSpace_inv AlgebraicGeometry.SheafedSpace.GlueData.ι_isoPresheafedSpace_inv
 
-instance ι_isOpenImmersion (i : D.J) : IsOpenImmersion (𝖣.ι i) :=
-  by
-  rw [← D.ι_iso_PresheafedSpace_inv]
-  infer_instance
+instance ι_isOpenImmersion (i : D.J) : IsOpenImmersion (𝖣.ι i) := by
+  rw [← D.ι_iso_PresheafedSpace_inv]; infer_instance
 #align algebraic_geometry.SheafedSpace.glue_data.ι_is_open_immersion AlgebraicGeometry.SheafedSpace.GlueData.ι_isOpenImmersion
 
 theorem ι_jointly_surjective (x : 𝖣.glued) : ∃ (i : D.J)(y : D.U i), (𝖣.ι i).base y = x :=
@@ -653,8 +641,7 @@ theorem ι_isoSheafedSpace_inv (i : D.J) :
 
 instance ι_isOpenImmersion (i : D.J) : IsOpenImmersion (𝖣.ι i) :=
   by
-  delta is_open_immersion
-  rw [← D.ι_iso_SheafedSpace_inv]
+  delta is_open_immersion; rw [← D.ι_iso_SheafedSpace_inv]
   apply PresheafedSpace.is_open_immersion.comp
 #align algebraic_geometry.LocallyRingedSpace.glue_data.ι_is_open_immersion AlgebraicGeometry.LocallyRingedSpace.GlueData.ι_isOpenImmersion
 

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

@@ -575,11 +575,11 @@ theorem ι_isoPresheafedSpace_inv (i : D.J) :
   𝖣.ι_gluedIso_inv _ _
 #align algebraic_geometry.SheafedSpace.glue_data.ι_iso_PresheafedSpace_inv AlgebraicGeometry.SheafedSpace.GlueData.ι_isoPresheafedSpace_inv
 
-instance ιIsOpenImmersion (i : D.J) : IsOpenImmersion (𝖣.ι i) :=
+instance ι_isOpenImmersion (i : D.J) : IsOpenImmersion (𝖣.ι i) :=
   by
   rw [← D.ι_iso_PresheafedSpace_inv]
   infer_instance
-#align algebraic_geometry.SheafedSpace.glue_data.ι_is_open_immersion AlgebraicGeometry.SheafedSpace.GlueData.ιIsOpenImmersion
+#align algebraic_geometry.SheafedSpace.glue_data.ι_is_open_immersion AlgebraicGeometry.SheafedSpace.GlueData.ι_isOpenImmersion
 
 theorem ι_jointly_surjective (x : 𝖣.glued) : ∃ (i : D.J)(y : D.U i), (𝖣.ι i).base y = x :=
   𝖣.ι_jointly_surjective (SheafedSpace.forget _ ⋙ CategoryTheory.forget TopCat) x

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

@@ -149,7 +149,7 @@ theorem pullback_base (i j k : D.J) (S : Set (D.V (i, j)).carrier) :
 #align algebraic_geometry.PresheafedSpace.glue_data.pullback_base AlgebraicGeometry.PresheafedSpace.GlueData.pullback_base
 
 /-- The red and the blue arrows in ![this diagram](https://i.imgur.com/0GiBUh6.png) commute. -/
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem f_invApp_f_app (i j k : D.J) (U : Opens (D.V (i, j)).carrier) :
     (D.f_open i j).invApp U ≫ (D.f i k).c.app _ =
       (π₁ i, j, k).c.app (op U) ≫
@@ -206,7 +206,7 @@ theorem snd_invApp_t_app' (i j k : D.J) (U : Opens (pullback (D.f i j) (D.f i k)
 #align algebraic_geometry.PresheafedSpace.glue_data.snd_inv_app_t_app' AlgebraicGeometry.PresheafedSpace.GlueData.snd_invApp_t_app'
 
 /-- The red and the blue arrows in ![this diagram](https://i.imgur.com/q6X1GJ9.png) commute. -/
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem snd_invApp_t_app (i j k : D.J) (U : Opens (pullback (D.f i j) (D.f i k)).carrier) :
     (π₂⁻¹ i, j, k) U ≫ (D.t k i).c.app _ =
       (D.t' k i j).c.app _ ≫

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

@@ -575,11 +575,11 @@ theorem ι_isoPresheafedSpace_inv (i : D.J) :
   𝖣.ι_gluedIso_inv _ _
 #align algebraic_geometry.SheafedSpace.glue_data.ι_iso_PresheafedSpace_inv AlgebraicGeometry.SheafedSpace.GlueData.ι_isoPresheafedSpace_inv
 
-instance ι_isOpenImmersion (i : D.J) : IsOpenImmersion (𝖣.ι i) :=
+instance ιIsOpenImmersion (i : D.J) : IsOpenImmersion (𝖣.ι i) :=
   by
   rw [← D.ι_iso_PresheafedSpace_inv]
   infer_instance
-#align algebraic_geometry.SheafedSpace.glue_data.ι_is_open_immersion AlgebraicGeometry.SheafedSpace.GlueData.ι_isOpenImmersion
+#align algebraic_geometry.SheafedSpace.glue_data.ι_is_open_immersion AlgebraicGeometry.SheafedSpace.GlueData.ιIsOpenImmersion
 
 theorem ι_jointly_surjective (x : 𝖣.glued) : ∃ (i : D.J)(y : D.U i), (𝖣.ι i).base y = x :=
   𝖣.ι_jointly_surjective (SheafedSpace.forget _ ⋙ CategoryTheory.forget TopCat) x

mathlib commit https://github.com/leanprover-community/mathlib/commit/49b7f94aab3a3bdca1f9f34c5d818afb253b3993

@@ -335,8 +335,8 @@ def ιInvApp {i : D.J} (U : Opens (D.U i).carrier) :
       π :=
         { app := fun j => D.ιInvAppπApp U (unop j)
           naturality' := fun X Y f' => by
-            induction X using Opposite.rec
-            induction Y using Opposite.rec
+            induction X using Opposite.rec'
+            induction Y using Opposite.rec'
             let f : Y ⟶ X := f'.unop
             have : f' = f.op := rfl
             clear_value f
@@ -445,7 +445,7 @@ theorem π_ιInvApp_eq_id (i : D.J) (U : Opens (D.U i).carrier) :
     D.diagramOverOpenπ U i ≫ D.ιInvAppπEqMap U ≫ D.ιInvApp U = 𝟙 _ :=
   by
   ext j
-  induction j using Opposite.rec
+  induction j using Opposite.rec'
   rcases j with (⟨j, k⟩ | ⟨j⟩)
   · rw [←
       limit.w (componentwise_diagram 𝖣.diagram.multispan _)

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce7e9d53d4bbc38065db3b595cd5bd73c323bc1d

@@ -170,7 +170,7 @@ theorem f_invApp_f_app (i j k : D.J) (U : Opens (D.V (i, j)).carrier) :
   erw [(π₁ i, j, k).c.naturality_assoc, reassoc_of this, ← functor.map_comp_assoc,
     is_open_immersion.inv_naturality_assoc, is_open_immersion.app_inv_app_assoc, ←
     (D.V (i, k)).Presheaf.map_comp, ← (D.V (i, k)).Presheaf.map_comp]
-  convert (category.comp_id _).symm
+  convert(category.comp_id _).symm
   erw [(D.V (i, k)).Presheaf.map_id]
   rfl
 #align algebraic_geometry.PresheafedSpace.glue_data.f_inv_app_f_app AlgebraicGeometry.PresheafedSpace.GlueData.f_invApp_f_app
@@ -429,8 +429,7 @@ theorem π_ιInvApp_π (i j : D.J) (U : Opens (D.U i).carrier) :
   iterate 3 rw [← functor.map_comp_assoc]
   rw [nat_trans.naturality_assoc]
   erw [← (D.V (i, j)).Presheaf.map_comp]
-  convert
-    limit.w (componentwise_diagram 𝖣.diagram.multispan _)
+  convert limit.w (componentwise_diagram 𝖣.diagram.multispan _)
       (Quiver.Hom.op (walking_multispan.hom.fst (i, j)))
   · rw [category.comp_id]
     apply (config := { instances := false }) mono_comp

mathlib commit https://github.com/leanprover-community/mathlib/commit/9da1b3534b65d9661eb8f42443598a92bbb49211

@@ -331,7 +331,7 @@ This forms the inverse of `(𝖣.ι i).c.app (op U)`. -/
 def ιInvApp {i : D.J} (U : Opens (D.U i).carrier) :
     (D.U i).Presheaf.obj (op U) ⟶ limit (D.diagramOverOpen U) :=
   limit.lift (D.diagramOverOpen U)
-    { x := (D.U i).Presheaf.obj (op U)
+    { pt := (D.U i).Presheaf.obj (op U)
       π :=
         { app := fun j => D.ιInvAppπApp U (unop j)
           naturality' := fun X Y f' => by

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

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.

@@ -91,7 +91,7 @@ such that
 We can then glue the spaces `U i` together by identifying `V i j` with `V j i`, such
 that the `U i`'s are open subspaces of the glued space.
 -/
--- Porting note: removed
+-- Porting note(#5171): this linter isn't ported yet.
 -- @[nolint has_nonempty_instance]
 structure GlueData extends GlueData (PresheafedSpace.{u, v, v} C) where
   f_open : ∀ i j, IsOpenImmersion (f i j)
@@ -579,7 +579,7 @@ such that
 We can then glue the spaces `U i` together by identifying `V i j` with `V j i`, such
 that the `U i`'s are open subspaces of the glued space.
 -/
--- Porting note: removed
+-- Porting note(#5171): this linter isn't ported yet.
 -- @[nolint has_nonempty_instance]
 structure GlueData extends CategoryTheory.GlueData (SheafedSpace.{u, v, v} C) where
   f_open : ∀ i j, SheafedSpace.IsOpenImmersion (f i j)
@@ -660,7 +660,7 @@ such that
 We can then glue the spaces `U i` together by identifying `V i j` with `V j i`, such
 that the `U i`'s are open subspaces of the glued space.
 -/
--- Porting note: removed
+-- Porting note(#5171): this linter isn't ported yet.
 -- @[nolint has_nonempty_instance]
 structure GlueData extends CategoryTheory.GlueData LocallyRingedSpace where
   f_open : ∀ i j, LocallyRingedSpace.IsOpenImmersion (f i j)

Classifies by adding issue number #11224 to porting notes claiming:

change rw to erw

@@ -253,7 +253,7 @@ theorem ι_image_preimage_eq (i j : D.J) (U : Opens (D.U i).carrier) :
   dsimp only [Opens.map_coe, IsOpenMap.functor_obj_coe]
   rw [← show _ = (𝖣.ι i).base from 𝖣.ι_gluedIso_inv (PresheafedSpace.forget _) i, ←
     show _ = (𝖣.ι j).base from 𝖣.ι_gluedIso_inv (PresheafedSpace.forget _) j]
-  -- Porting note: change `rw` to `erw` on `coe_comp`
+  -- Porting note (#11224): change `rw` to `erw` on `coe_comp`
   erw [coe_comp, coe_comp, coe_comp]
   rw [Set.image_comp, Set.preimage_comp]
   erw [Set.preimage_image_eq]
@@ -474,7 +474,7 @@ theorem π_ιInvApp_π (i j : D.J) (U : Opens (D.U i).carrier) :
   rw [congr_app (D.t_id _), id_c_app]
   simp_rw [Category.assoc]
   rw [← Functor.map_comp_assoc]
-  -- Porting note: change `rw` to `erw`
+  -- Porting note (#11224): change `rw` to `erw`
   erw [IsOpenImmersion.inv_naturality_assoc]
   erw [IsOpenImmersion.app_invApp_assoc]
   iterate 3 rw [← Functor.map_comp_assoc]
@@ -538,7 +538,7 @@ def vPullbackConeIsLimit (i j : D.J) : IsLimit (𝖣.vPullbackCone i j) :=
         replace this := reassoc_of% this
         exact this _
       rw [← Set.image_subset_iff, ← Set.image_univ, ← Set.image_comp, Set.image_univ]
-      -- Porting note: change `rw` to `erw`
+      -- Porting note (#11224): change `rw` to `erw`
       erw [← coe_comp]
       rw [this, coe_comp, ← Set.image_univ, Set.image_comp]
       exact Set.image_subset_range _ _

@@ -323,7 +323,7 @@ theorem opensImagePreimageMap_app_assoc (i j k : D.J) (U : Opens (D.U i).carrier
 /-- (Implementation) Given an open subset of one of the spaces `U ⊆ Uᵢ`, the sheaf component of
 the image `ι '' U` in the glued space is the limit of this diagram. -/
 abbrev diagramOverOpen {i : D.J} (U : Opens (D.U i).carrier) :
-    -- Portinge note : ↓ these need to be explicit
+    -- Porting note : ↓ these need to be explicit
     (WalkingMultispan D.diagram.fstFrom D.diagram.sndFrom)ᵒᵖ ⥤ C :=
   componentwiseDiagram 𝖣.diagram.multispan ((D.ι_openEmbedding i).isOpenMap.functor.obj U)
 #align algebraic_geometry.PresheafedSpace.glue_data.diagram_over_open AlgebraicGeometry.PresheafedSpace.GlueData.diagramOverOpen

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.

@@ -91,7 +91,7 @@ such that
 We can then glue the spaces `U i` together by identifying `V i j` with `V j i`, such
 that the `U i`'s are open subspaces of the glued space.
 -/
--- Porting note : removed
+-- Porting note: removed
 -- @[nolint has_nonempty_instance]
 structure GlueData extends GlueData (PresheafedSpace.{u, v, v} C) where
   f_open : ∀ i j, IsOpenImmersion (f i j)
@@ -126,7 +126,7 @@ abbrev toTopGlueData : TopCat.GlueData :=
 
 theorem ι_openEmbedding [HasLimits C] (i : D.J) : OpenEmbedding (𝖣.ι i).base := by
   rw [← show _ = (𝖣.ι i).base from 𝖣.ι_gluedIso_inv (PresheafedSpace.forget _) _]
-  -- Porting note : added this erewrite
+  -- Porting note: added this erewrite
   erw [coe_comp]
   refine
     OpenEmbedding.comp
@@ -139,10 +139,10 @@ theorem pullback_base (i j k : D.J) (S : Set (D.V (i, j)).carrier) :
   have eq₁ : _ = (π₁ i, j, k).base := PreservesPullback.iso_hom_fst (forget C) _ _
   have eq₂ : _ = (π₂ i, j, k).base := PreservesPullback.iso_hom_snd (forget C) _ _
   rw [← eq₁, ← eq₂]
-  -- Porting note : `rw` to `erw` on `coe_comp`
+  -- Porting note: `rw` to `erw` on `coe_comp`
   erw [coe_comp]
   rw [Set.image_comp]
-  -- Porting note : `rw` to `erw` on `coe_comp`
+  -- Porting note: `rw` to `erw` on `coe_comp`
   erw [coe_comp]
   rw [Set.preimage_comp, Set.image_preimage_eq, TopCat.pullback_snd_image_fst_preimage]
   rfl
@@ -171,7 +171,7 @@ theorem f_invApp_f_app (i j k : D.J) (U : Opens (D.V (i, j)).carrier) :
   erw [(π₁ i, j, k).c.naturality_assoc, reassoc_of% this, ← Functor.map_comp_assoc,
     IsOpenImmersion.inv_naturality_assoc, IsOpenImmersion.app_invApp_assoc, ←
     (D.V (i, k)).presheaf.map_comp, ← (D.V (i, k)).presheaf.map_comp]
-  -- Porting note : need to provide an explicit argument, otherwise Lean does not know which
+  -- Porting note: need to provide an explicit argument, otherwise Lean does not know which
   -- category we are talking about
   convert (Category.comp_id ((f D.toGlueData i k).c.app _)).symm
   erw [(D.V (i, k)).presheaf.map_id]
@@ -253,7 +253,7 @@ theorem ι_image_preimage_eq (i j : D.J) (U : Opens (D.U i).carrier) :
   dsimp only [Opens.map_coe, IsOpenMap.functor_obj_coe]
   rw [← show _ = (𝖣.ι i).base from 𝖣.ι_gluedIso_inv (PresheafedSpace.forget _) i, ←
     show _ = (𝖣.ι j).base from 𝖣.ι_gluedIso_inv (PresheafedSpace.forget _) j]
-  -- Porting note : change `rw` to `erw` on `coe_comp`
+  -- Porting note: change `rw` to `erw` on `coe_comp`
   erw [coe_comp, coe_comp, coe_comp]
   rw [Set.image_comp, Set.preimage_comp]
   erw [Set.preimage_image_eq]
@@ -346,7 +346,7 @@ def ιInvAppπApp {i : D.J} (U : Opens (D.U i).carrier) (j) :
     dsimp only [Functor.op_obj, Opens.map_coe, unop_op, IsOpenMap.functor_obj_coe]
     rw [Set.preimage_preimage]
     change (D.f j k ≫ 𝖣.ι j).base ⁻¹' _ = _
-    -- Porting note : used to be `congr 3`
+    -- Porting note: used to be `congr 3`
     refine congr_arg (· ⁻¹' _) ?_
     convert congr_arg (ContinuousMap.toFun (α := D.V ⟨j, k⟩) (β := D.glued) ·) ?_
     refine congr_arg (PresheafedSpace.Hom.base (C := C) ·) ?_
@@ -354,7 +354,7 @@ def ιInvAppπApp {i : D.J} (U : Opens (D.U i).carrier) (j) :
   · exact D.opensImagePreimageMap i j U
 #align algebraic_geometry.PresheafedSpace.glue_data.ι_inv_app_π_app AlgebraicGeometry.PresheafedSpace.GlueData.ιInvAppπApp
 
--- Porting note : time out started in `erw [... congr_app (pullbackSymmetry_hom_comp_snd _ _)]` and
+-- Porting note: time out started in `erw [... congr_app (pullbackSymmetry_hom_comp_snd _ _)]` and
 -- the last congr has a very difficult `rfl : eqToHom _ ≫ eqToHom _ ≫ ... = eqToHom ... `
 set_option maxHeartbeats 600000 in
 /-- (Implementation) The natural map `Γ(𝒪_{U_i}, U) ⟶ Γ(𝒪_X, 𝖣.ι i '' U)`.
@@ -407,7 +407,7 @@ def ιInvApp {i : D.J} (U : Opens (D.U i).carrier) :
             erw [IsOpenImmersion.inv_naturality_assoc, IsOpenImmersion.inv_naturality_assoc,
               IsOpenImmersion.inv_naturality_assoc, IsOpenImmersion.app_invApp_assoc]
             repeat' erw [← (D.V (j, k)).presheaf.map_comp]
-            -- Porting note : was just `congr`
+            -- Porting note: was just `congr`
             exact congr_arg ((D.V (j, k)).presheaf.map ·) rfl } }
 #align algebraic_geometry.PresheafedSpace.glue_data.ι_inv_app AlgebraicGeometry.PresheafedSpace.GlueData.ιInvApp
 
@@ -453,7 +453,7 @@ abbrev ιInvAppπEqMap {i : D.J} (U : Opens (D.U i).carrier) :=
 theorem π_ιInvApp_π (i j : D.J) (U : Opens (D.U i).carrier) :
     D.diagramOverOpenπ U i ≫ D.ιInvAppπEqMap U ≫ D.ιInvApp U ≫ D.diagramOverOpenπ U j =
       D.diagramOverOpenπ U j := by
-  -- Porting note : originally, the proof of monotonicity was left a blank and proved in the end
+  -- Porting note: originally, the proof of monotonicity was left a blank and proved in the end
   -- but Lean 4 doesn't like this any more, so the proof is restructured
   rw [← @cancel_mono (f := (componentwiseDiagram 𝖣.diagram.multispan _).map
     (Quiver.Hom.op (WalkingMultispan.Hom.snd (i, j))) ≫ 𝟙 _) _ _ (by
@@ -474,7 +474,7 @@ theorem π_ιInvApp_π (i j : D.J) (U : Opens (D.U i).carrier) :
   rw [congr_app (D.t_id _), id_c_app]
   simp_rw [Category.assoc]
   rw [← Functor.map_comp_assoc]
-  -- Porting note : change `rw` to `erw`
+  -- Porting note: change `rw` to `erw`
   erw [IsOpenImmersion.inv_naturality_assoc]
   erw [IsOpenImmersion.app_invApp_assoc]
   iterate 3 rw [← Functor.map_comp_assoc]
@@ -538,7 +538,7 @@ def vPullbackConeIsLimit (i j : D.J) : IsLimit (𝖣.vPullbackCone i j) :=
         replace this := reassoc_of% this
         exact this _
       rw [← Set.image_subset_iff, ← Set.image_univ, ← Set.image_comp, Set.image_univ]
-      -- Porting note : change `rw` to `erw`
+      -- Porting note: change `rw` to `erw`
       erw [← coe_comp]
       rw [this, coe_comp, ← Set.image_univ, Set.image_comp]
       exact Set.image_subset_range _ _
@@ -579,7 +579,7 @@ such that
 We can then glue the spaces `U i` together by identifying `V i j` with `V j i`, such
 that the `U i`'s are open subspaces of the glued space.
 -/
--- Porting note : removed
+-- Porting note: removed
 -- @[nolint has_nonempty_instance]
 structure GlueData extends CategoryTheory.GlueData (SheafedSpace.{u, v, v} C) where
   f_open : ∀ i j, SheafedSpace.IsOpenImmersion (f i j)
@@ -615,7 +615,7 @@ theorem ι_isoPresheafedSpace_inv (i : D.J) :
 
 instance ιIsOpenImmersion (i : D.J) : IsOpenImmersion (𝖣.ι i) := by
   rw [← D.ι_isoPresheafedSpace_inv]
-  -- Porting note : was `inferInstance`
+  -- Porting note: was `inferInstance`
   refine PresheafedSpace.IsOpenImmersion.comp (hf := ?_) (hg := inferInstance)
   apply PresheafedSpace.GlueData.ιIsOpenImmersion
 #align algebraic_geometry.SheafedSpace.glue_data.ι_IsOpenImmersion AlgebraicGeometry.SheafedSpaceₓ.GlueData.ιIsOpenImmersion
@@ -660,7 +660,7 @@ such that
 We can then glue the spaces `U i` together by identifying `V i j` with `V j i`, such
 that the `U i`'s are open subspaces of the glued space.
 -/
--- Porting note : removed
+-- Porting note: removed
 -- @[nolint has_nonempty_instance]
 structure GlueData extends CategoryTheory.GlueData LocallyRingedSpace where
   f_open : ∀ i j, LocallyRingedSpace.IsOpenImmersion (f i j)
@@ -693,7 +693,7 @@ theorem ι_isoSheafedSpace_inv (i : D.J) :
 instance ι_isOpenImmersion (i : D.J) : IsOpenImmersion (𝖣.ι i) := by
   delta IsOpenImmersion; rw [← D.ι_isoSheafedSpace_inv]
   apply (config := { allowSynthFailures := true }) PresheafedSpace.IsOpenImmersion.comp
-  -- Porting note : this was automatic
+  -- Porting note: this was automatic
   exact (D.toSheafedSpaceGlueData).ιIsOpenImmersion i
 #align algebraic_geometry.LocallyRingedSpace.glue_data.ι_IsOpenImmersion AlgebraicGeometry.LocallyRingedSpace.GlueData.ι_isOpenImmersion
 

Co-authored-by: Moritz Firsching <firsching@google.com>

@@ -191,7 +191,7 @@ theorem snd_invApp_t_app' (i j k : D.J) (U : Opens (pullback (D.f i j) (D.f i k)
     dsimp only [Functor.op, Opens.map, IsOpenMap.functor, unop_op, Opens.coe_mk]
     congr
     have := (𝖣.t_fac k i j).symm
-    rw [←IsIso.inv_comp_eq] at this
+    rw [← IsIso.inv_comp_eq] at this
     replace this := (congr_arg ((PresheafedSpace.Hom.base ·)) this).symm
     replace this := congr_arg (ContinuousMap.toFun ·) this
     dsimp at this
@@ -201,14 +201,14 @@ theorem snd_invApp_t_app' (i j k : D.J) (U : Opens (pullback (D.f i j) (D.f i k)
     erw [this, Set.image_comp, Set.image_comp, Set.preimage_image_eq]
     swap
     · refine Function.HasLeftInverse.injective ⟨(D.t i k).base, fun x => ?_⟩
-      rw [←comp_apply, ←comp_base, D.t_inv, id_base, id_apply]
+      rw [← comp_apply, ← comp_base, D.t_inv, id_base, id_apply]
     refine congr_arg (_ '' ·) ?_
     refine congr_fun ?_ _
     refine Set.image_eq_preimage_of_inverse ?_ ?_
     · intro x
-      rw [←comp_apply, ←comp_base, IsIso.inv_hom_id, id_base, id_apply]
+      rw [← comp_apply, ← comp_base, IsIso.inv_hom_id, id_base, id_apply]
     · intro x
-      rw [←comp_apply, ←comp_base, IsIso.hom_inv_id, id_base, id_apply]
+      rw [← comp_apply, ← comp_base, IsIso.hom_inv_id, id_base, id_apply]
   · rw [← IsIso.eq_inv_comp, IsOpenImmersion.inv_invApp, Category.assoc,
       (D.t' k i j).c.naturality_assoc]
     simp_rw [← Category.assoc]
@@ -267,7 +267,7 @@ theorem ι_image_preimage_eq (i j : D.J) (U : Opens (D.U i).carrier) :
     change (D.t i j ≫ D.t j i).base '' _ = _
     rw [𝖣.t_inv]
     simp
-  · rw [←coe_comp, ← TopCat.mono_iff_injective]
+  · rw [← coe_comp, ← TopCat.mono_iff_injective]
     infer_instance
 #align algebraic_geometry.PresheafedSpace.glue_data.ι_image_preimage_eq AlgebraicGeometry.PresheafedSpace.GlueData.ι_image_preimage_eq
 
@@ -426,9 +426,9 @@ theorem ιInvApp_π {i : D.J} (U : Opens (D.U i).carrier) :
     · exact h2.symm
     · have := D.ι_gluedIso_inv (PresheafedSpace.forget _) i
       dsimp at this
-      rw [←this, coe_comp]
+      rw [← this, coe_comp]
       refine Function.Injective.comp ?_ (TopCat.GlueData.ι_injective D.toTopGlueData i)
-      rw [←TopCat.mono_iff_injective]
+      rw [← TopCat.mono_iff_injective]
       infer_instance
   delta ιInvApp
   rw [limit.lift_π]

This reverts commit f3695eb2.

@@ -195,8 +195,10 @@ theorem snd_invApp_t_app' (i j k : D.J) (U : Opens (pullback (D.f i j) (D.f i k)
     replace this := (congr_arg ((PresheafedSpace.Hom.base ·)) this).symm
     replace this := congr_arg (ContinuousMap.toFun ·) this
     dsimp at this
-    rw [coe_comp, coe_comp] at this
-    rw [this, Set.image_comp, Set.image_comp, Set.preimage_image_eq]
+    -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
+    erw [coe_comp, coe_comp] at this
+    -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
+    erw [this, Set.image_comp, Set.image_comp, Set.preimage_image_eq]
     swap
     · refine Function.HasLeftInverse.injective ⟨(D.t i k).base, fun x => ?_⟩
       rw [←comp_apply, ←comp_base, D.t_inv, id_base, id_apply]

This reverts commit 26eb2b0a.

@@ -195,10 +195,8 @@ theorem snd_invApp_t_app' (i j k : D.J) (U : Opens (pullback (D.f i j) (D.f i k)
     replace this := (congr_arg ((PresheafedSpace.Hom.base ·)) this).symm
     replace this := congr_arg (ContinuousMap.toFun ·) this
     dsimp at this
-    -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
-    erw [coe_comp, coe_comp] at this
-    -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
-    erw [this, Set.image_comp, Set.image_comp, Set.preimage_image_eq]
+    rw [coe_comp, coe_comp] at this
+    rw [this, Set.image_comp, Set.image_comp, Set.preimage_image_eq]
     swap
     · refine Function.HasLeftInverse.injective ⟨(D.t i k).base, fun x => ?_⟩
       rw [←comp_apply, ←comp_base, D.t_inv, id_base, id_apply]

This includes all the changes from #7606.

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

@@ -195,8 +195,10 @@ theorem snd_invApp_t_app' (i j k : D.J) (U : Opens (pullback (D.f i j) (D.f i k)
     replace this := (congr_arg ((PresheafedSpace.Hom.base ·)) this).symm
     replace this := congr_arg (ContinuousMap.toFun ·) this
     dsimp at this
-    rw [coe_comp, coe_comp] at this
-    rw [this, Set.image_comp, Set.image_comp, Set.preimage_image_eq]
+    -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
+    erw [coe_comp, coe_comp] at this
+    -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
+    erw [this, Set.image_comp, Set.image_comp, Set.preimage_image_eq]
     swap
     · refine Function.HasLeftInverse.injective ⟨(D.t i k).base, fun x => ?_⟩
       rw [←comp_apply, ←comp_base, D.t_inv, id_base, id_apply]

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.

@@ -4,8 +4,8 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Andrew Yang
 -/
 import Mathlib.Topology.Gluing
-import Mathlib.AlgebraicGeometry.OpenImmersion.Basic
-import Mathlib.AlgebraicGeometry.LocallyRingedSpace.HasColimits
+import Mathlib.Geometry.RingedSpace.OpenImmersion
+import Mathlib.Geometry.RingedSpace.LocallyRingedSpace.HasColimits
 
 #align_import algebraic_geometry.presheafed_space.gluing from "leanprover-community/mathlib"@"533f62f4dd62a5aad24a04326e6e787c8f7e98b1"
 

@@ -42,7 +42,7 @@ Analogous results are also provided for `SheafedSpace` and `LocallyRingedSpace`.
 Almost the whole file is dedicated to showing tht `ι i` is an open immersion. The fact that
 this is an open embedding of topological spaces follows from `Mathlib/Topology/Gluing.lean`, and it
 remains to construct `Γ(𝒪_{U_i}, U) ⟶ Γ(𝒪_X, ι i '' U)` for each `U ⊆ U i`.
-Since `Γ(𝒪_X, ι i '' U)` is the the limit of `diagram_over_open`, the components of the structure
+Since `Γ(𝒪_X, ι i '' U)` is the limit of `diagram_over_open`, the components of the structure
 sheafs of the spaces in the gluing diagram, we need to construct a map
 `ιInvApp_π_app : Γ(𝒪_{U_i}, U) ⟶ Γ(𝒪_V, U_V)` for each `V` in the gluing diagram.
 

@@ -192,15 +192,15 @@ theorem snd_invApp_t_app' (i j k : D.J) (U : Opens (pullback (D.f i j) (D.f i k)
     congr
     have := (𝖣.t_fac k i j).symm
     rw [←IsIso.inv_comp_eq] at this
-    replace this := (congr_arg ((PresheafedSpace.Hom.base .)) this).symm
-    replace this := congr_arg (ContinuousMap.toFun .) this
+    replace this := (congr_arg ((PresheafedSpace.Hom.base ·)) this).symm
+    replace this := congr_arg (ContinuousMap.toFun ·) this
     dsimp at this
     rw [coe_comp, coe_comp] at this
     rw [this, Set.image_comp, Set.image_comp, Set.preimage_image_eq]
     swap
     · refine Function.HasLeftInverse.injective ⟨(D.t i k).base, fun x => ?_⟩
       rw [←comp_apply, ←comp_base, D.t_inv, id_base, id_apply]
-    refine congr_arg (_ '' .) ?_
+    refine congr_arg (_ '' ·) ?_
     refine congr_fun ?_ _
     refine Set.image_eq_preimage_of_inverse ?_ ?_
     · intro x
@@ -258,7 +258,7 @@ theorem ι_image_preimage_eq (i j : D.J) (U : Opens (D.U i).carrier) :
   · refine' Eq.trans (D.toTopGlueData.preimage_image_eq_image' _ _ _) _
     dsimp
     rw [coe_comp, Set.image_comp]
-    refine congr_arg (_ '' .) ?_
+    refine congr_arg (_ '' ·) ?_
     rw [Set.eq_preimage_iff_image_eq, ← Set.image_comp]
     swap
     · apply CategoryTheory.ConcreteCategory.bijective_of_isIso
@@ -315,7 +315,7 @@ theorem opensImagePreimageMap_app_assoc (i j k : D.J) (U : Opens (D.U i).carrier
         (π₂⁻¹ j, i, k) (unop _) ≫
           (D.V (j, k)).presheaf.map
             (eqToHom (opensImagePreimageMap_app' D i j k U).choose) ≫ f' := by
-  simpa only [Category.assoc] using congr_arg (. ≫ f') (opensImagePreimageMap_app D i j k U)
+  simpa only [Category.assoc] using congr_arg (· ≫ f') (opensImagePreimageMap_app D i j k U)
 #align algebraic_geometry.PresheafedSpace.glue_data.opens_image_preimage_map_app_assoc AlgebraicGeometry.PresheafedSpace.GlueData.opensImagePreimageMap_app_assoc
 
 /-- (Implementation) Given an open subset of one of the spaces `U ⊆ Uᵢ`, the sheaf component of
@@ -345,9 +345,9 @@ def ιInvAppπApp {i : D.J} (U : Opens (D.U i).carrier) (j) :
     rw [Set.preimage_preimage]
     change (D.f j k ≫ 𝖣.ι j).base ⁻¹' _ = _
     -- Porting note : used to be `congr 3`
-    refine congr_arg (. ⁻¹' _) ?_
-    convert congr_arg (ContinuousMap.toFun (α := D.V ⟨j, k⟩) (β := D.glued) .) ?_
-    refine congr_arg (PresheafedSpace.Hom.base (C := C) .) ?_
+    refine congr_arg (· ⁻¹' _) ?_
+    convert congr_arg (ContinuousMap.toFun (α := D.V ⟨j, k⟩) (β := D.glued) ·) ?_
+    refine congr_arg (PresheafedSpace.Hom.base (C := C) ·) ?_
     exact colimit.w 𝖣.diagram.multispan (WalkingMultispan.Hom.fst (j, k))
   · exact D.opensImagePreimageMap i j U
 #align algebraic_geometry.PresheafedSpace.glue_data.ι_inv_app_π_app AlgebraicGeometry.PresheafedSpace.GlueData.ιInvAppπApp
@@ -406,7 +406,7 @@ def ιInvApp {i : D.J} (U : Opens (D.U i).carrier) :
               IsOpenImmersion.inv_naturality_assoc, IsOpenImmersion.app_invApp_assoc]
             repeat' erw [← (D.V (j, k)).presheaf.map_comp]
             -- Porting note : was just `congr`
-            exact congr_arg ((D.V (j, k)).presheaf.map .) rfl } }
+            exact congr_arg ((D.V (j, k)).presheaf.map ·) rfl } }
 #align algebraic_geometry.PresheafedSpace.glue_data.ι_inv_app AlgebraicGeometry.PresheafedSpace.GlueData.ιInvApp
 
 /-- `ιInvApp` is the left inverse of `D.ι i` on `U`. -/

• depends on: #5966

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

@@ -2,16 +2,13 @@
 Copyright (c) 2021 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.presheafed_space.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.Topology.Gluing
 import Mathlib.AlgebraicGeometry.OpenImmersion.Basic
 import Mathlib.AlgebraicGeometry.LocallyRingedSpace.HasColimits
 
+#align_import algebraic_geometry.presheafed_space.gluing from "leanprover-community/mathlib"@"533f62f4dd62a5aad24a04326e6e787c8f7e98b1"
+
 /-!
 # Gluing Structured spaces
 

Grepping for [^ .:{-] [^ :] and reviewing the results. Once I started I couldn't stop. :-)

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

@@ -356,7 +356,7 @@ def ιInvAppπApp {i : D.J} (U : Opens (D.U i).carrier) (j) :
 #align algebraic_geometry.PresheafedSpace.glue_data.ι_inv_app_π_app AlgebraicGeometry.PresheafedSpace.GlueData.ιInvAppπApp
 
 -- Porting note : time out started in `erw [... congr_app (pullbackSymmetry_hom_comp_snd _ _)]` and
--- the last congr has a very difficult `rfl : eqToHom _ ≫  eqToHom _ ≫ ... = eqToHom ... `
+-- the last congr has a very difficult `rfl : eqToHom _ ≫ eqToHom _ ≫ ... = eqToHom ... `
 set_option maxHeartbeats 600000 in
 /-- (Implementation) The natural map `Γ(𝒪_{U_i}, U) ⟶ Γ(𝒪_X, 𝖣.ι i '' U)`.
 This forms the inverse of `(𝖣.ι i).c.app (op U)`. -/

@@ -23,19 +23,19 @@ provided.
 
 ## Main definitions
 
-* `algebraic_geometry.PresheafedSpace.glue_data`: A structure containing the family of gluing data.
-* `Category_theory.glue_data.glued`: The glued presheafed space.
+* `AlgebraicGeometry.PresheafedSpace.GlueData`: A structure containing the family of gluing data.
+* `CategoryTheory.GlueData.glued`: The glued presheafed space.
     This is defined as the multicoequalizer of `∐ V i j ⇉ ∐ U i`, so that the general colimit API
     can be used.
-* `Category_theory.glue_data.ι`: The immersion `ι i : U i ⟶ glued` for each `i : J`.
+* `CategoryTheory.GlueData.ι`: The immersion `ι i : U i ⟶ glued` for each `i : J`.
 
 ## Main results
 
-* `algebraic_geometry.PresheafedSpace.glue_data.ι_IsOpenImmersion`: The map `ι i : U i ⟶ glued`
+* `AlgebraicGeometry.PresheafedSpace.GlueData.ιIsOpenImmersion`: The map `ι i : U i ⟶ glued`
   is an open immersion for each `i : J`.
-* `algebraic_geometry.PresheafedSpace.glue_data.ι_jointly_surjective` : The underlying maps of
+* `AlgebraicGeometry.PresheafedSpace.GlueData.ι_jointly_surjective` : The underlying maps of
   `ι i : U i ⟶ glued` are jointly surjective.
-* `algebraic_geometry.PresheafedSpace.glue_data.V_pullback_cone_is_limit` : `V i j` is the pullback
+* `AlgebraicGeometry.PresheafedSpace.GlueData.vPullbackConeIsLimit` : `V i j` is the pullback
   (intersection) of `U i` and `U j` over the glued space.
 
 Analogous results are also provided for `SheafedSpace` and `LocallyRingedSpace`.
@@ -43,8 +43,8 @@ Analogous results are also provided for `SheafedSpace` and `LocallyRingedSpace`.
 ## Implementation details
 
 Almost the whole file is dedicated to showing tht `ι i` is an open immersion. The fact that
-this is an open embedding of topological spaces follows from `topology.gluing.lean`, and it remains
-to construct `Γ(𝒪_{U_i}, U) ⟶ Γ(𝒪_X, ι i '' U)` for each `U ⊆ U i`.
+this is an open embedding of topological spaces follows from `Mathlib/Topology/Gluing.lean`, and it
+remains to construct `Γ(𝒪_{U_i}, U) ⟶ Γ(𝒪_X, ι i '' U)` for each `U ⊆ U i`.
 Since `Γ(𝒪_X, ι i '' U)` is the the limit of `diagram_over_open`, the components of the structure
 sheafs of the spaces in the gluing diagram, we need to construct a map
 `ιInvApp_π_app : Γ(𝒪_{U_i}, U) ⟶ Γ(𝒪_V, U_V)` for each `V` in the gluing diagram.

Co-authored-by: Johan Commelin <johan@commelin.net> Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>