algebraic_geometry.locally_ringed_space ⟷ Mathlib.Geometry.RingedSpace.LocallyRingedSpace

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

@@ -162,7 +162,7 @@ def forgetToSheafedSpace : LocallyRingedSpace ⥤ SheafedSpace CommRingCat
 #align algebraic_geometry.LocallyRingedSpace.forget_to_SheafedSpace AlgebraicGeometry.LocallyRingedSpace.forgetToSheafedSpace
 -/
 
-instance : Faithful forgetToSheafedSpace where
+instance : CategoryTheory.Functor.Faithful forgetToSheafedSpace where
 
 #print AlgebraicGeometry.LocallyRingedSpace.forgetToTop /-
 /-- The forgetful functor from `LocallyRingedSpace` to `Top`. -/
@@ -230,7 +230,7 @@ def isoOfSheafedSpaceIso {X Y : LocallyRingedSpace} (f : X.toSheafedSpace ≅ Y.
 #align algebraic_geometry.LocallyRingedSpace.iso_of_SheafedSpace_iso AlgebraicGeometry.LocallyRingedSpace.isoOfSheafedSpaceIso
 -/
 
-instance : ReflectsIsomorphisms forgetToSheafedSpace
+instance : CategoryTheory.Functor.ReflectsIsomorphisms forgetToSheafedSpace
     where reflects X Y f i :=
     {
       out :=

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

@@ -3,8 +3,8 @@ Copyright (c) 2020 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin
 -/
-import AlgebraicGeometry.RingedSpace
-import AlgebraicGeometry.Stalks
+import Geometry.RingedSpace.Basic
+import Geometry.RingedSpace.Stalks
 
 #align_import algebraic_geometry.locally_ringed_space from "leanprover-community/mathlib"@"af471b9e3ce868f296626d33189b4ce730fa4c00"
 

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

@@ -330,7 +330,7 @@ theorem preimage_basicOpen {X Y : LocallyRingedSpace} (f : X ⟶ Y) {U : Opens Y
     exact (PresheafedSpace.stalk_map f.1 _).isUnit_map hy
   · rintro ⟨y, hy : IsUnit _, rfl⟩
     erw [RingedSpace.mem_basic_open _ _ ⟨f.1.base y.1, y.2⟩]
-    rw [← PresheafedSpace.stalk_map_germ_apply] at hy 
+    rw [← PresheafedSpace.stalk_map_germ_apply] at hy
     exact (isUnit_map_iff (PresheafedSpace.stalk_map f.1 _) _).mp hy
 #align algebraic_geometry.LocallyRingedSpace.preimage_basic_open AlgebraicGeometry.LocallyRingedSpace.preimage_basicOpen
 -/

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

@@ -3,8 +3,8 @@ Copyright (c) 2020 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin
 -/
-import Mathbin.AlgebraicGeometry.RingedSpace
-import Mathbin.AlgebraicGeometry.Stalks
+import AlgebraicGeometry.RingedSpace
+import AlgebraicGeometry.Stalks
 
 #align_import algebraic_geometry.locally_ringed_space from "leanprover-community/mathlib"@"af471b9e3ce868f296626d33189b4ce730fa4c00"
 

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

@@ -2,15 +2,12 @@
 Copyright (c) 2020 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin
-
-! This file was ported from Lean 3 source module algebraic_geometry.locally_ringed_space
-! leanprover-community/mathlib commit af471b9e3ce868f296626d33189b4ce730fa4c00
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.AlgebraicGeometry.RingedSpace
 import Mathbin.AlgebraicGeometry.Stalks
 
+#align_import algebraic_geometry.locally_ringed_space from "leanprover-community/mathlib"@"af471b9e3ce868f296626d33189b4ce730fa4c00"
+
 /-!
 # The category of locally ringed spaces
 

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

@@ -109,6 +109,7 @@ noncomputable def stalk (X : LocallyRingedSpace) (x : X) : CommRingCat :=
 #align algebraic_geometry.LocallyRingedSpace.stalk AlgebraicGeometry.LocallyRingedSpace.stalk
 -/
 
+#print AlgebraicGeometry.LocallyRingedSpace.stalkMap /-
 /-- A morphism of locally ringed spaces `f : X ⟶ Y` induces
 a local ring homomorphism from `Y.stalk (f x)` to `X.stalk x` for any `x : X`.
 -/
@@ -116,6 +117,7 @@ noncomputable def stalkMap {X Y : LocallyRingedSpace} (f : X ⟶ Y) (x : X) :
     Y.stalk (f.1.1 x) ⟶ X.stalk x :=
   PresheafedSpace.stalkMap f.1 x
 #align algebraic_geometry.LocallyRingedSpace.stalk_map AlgebraicGeometry.LocallyRingedSpace.stalkMap
+-/
 
 instance {X Y : LocallyRingedSpace} (f : X ⟶ Y) (x : X) : IsLocalRingHom (stalkMap f x) :=
   f.2 x
@@ -153,6 +155,7 @@ instance : Category LocallyRingedSpace where
   id_comp' := by intros; ext1; simp [comp]
   assoc' := by intros; ext1; simp [comp]
 
+#print AlgebraicGeometry.LocallyRingedSpace.forgetToSheafedSpace /-
 /-- The forgetful functor from `LocallyRingedSpace` to `SheafedSpace CommRing`. -/
 @[simps]
 def forgetToSheafedSpace : LocallyRingedSpace ⥤ SheafedSpace CommRingCat
@@ -160,6 +163,7 @@ def forgetToSheafedSpace : LocallyRingedSpace ⥤ SheafedSpace CommRingCat
   obj X := X.toSheafedSpace
   map X Y f := f.1
 #align algebraic_geometry.LocallyRingedSpace.forget_to_SheafedSpace AlgebraicGeometry.LocallyRingedSpace.forgetToSheafedSpace
+-/
 
 instance : Faithful forgetToSheafedSpace where
 
@@ -171,23 +175,30 @@ def forgetToTop : LocallyRingedSpace ⥤ TopCat :=
 #align algebraic_geometry.LocallyRingedSpace.forget_to_Top AlgebraicGeometry.LocallyRingedSpace.forgetToTop
 -/
 
+#print AlgebraicGeometry.LocallyRingedSpace.comp_val /-
 @[simp]
 theorem comp_val {X Y Z : LocallyRingedSpace} (f : X ⟶ Y) (g : Y ⟶ Z) :
     (f ≫ g).val = f.val ≫ g.val :=
   rfl
 #align algebraic_geometry.LocallyRingedSpace.comp_val AlgebraicGeometry.LocallyRingedSpace.comp_val
+-/
 
+#print AlgebraicGeometry.LocallyRingedSpace.comp_val_c /-
 @[simp]
 theorem comp_val_c {X Y Z : LocallyRingedSpace.{u}} (f : X ⟶ Y) (g : Y ⟶ Z) :
     (f ≫ g).val.c = g.val.c ≫ (Presheaf.pushforward _ g.val.base).map f.val.c :=
   rfl
 #align algebraic_geometry.LocallyRingedSpace.comp_val_c AlgebraicGeometry.LocallyRingedSpace.comp_val_c
+-/
 
+#print AlgebraicGeometry.LocallyRingedSpace.comp_val_c_app /-
 theorem comp_val_c_app {X Y Z : LocallyRingedSpace} (f : X ⟶ Y) (g : Y ⟶ Z) (U : (Opens Z)ᵒᵖ) :
     (f ≫ g).val.c.app U = g.val.c.app U ≫ f.val.c.app (op <| (Opens.map g.val.base).obj U.unop) :=
   rfl
 #align algebraic_geometry.LocallyRingedSpace.comp_val_c_app AlgebraicGeometry.LocallyRingedSpace.comp_val_c_app
+-/
 
+#print AlgebraicGeometry.LocallyRingedSpace.homOfSheafedSpaceHomOfIsIso /-
 /-- Given two locally ringed spaces `X` and `Y`, an isomorphism between `X` and `Y` as _sheafed_
 spaces can be lifted to a morphism `X ⟶ Y` as locally ringed spaces.
 
@@ -203,7 +214,9 @@ def homOfSheafedSpaceHomOfIsIso {X Y : LocallyRingedSpace} (f : X.toSheafedSpace
     show IsLocalRingHom (PresheafedSpace.stalkMap (SheafedSpace.forgetToPresheafedSpace.map f) x) by
       infer_instance
 #align algebraic_geometry.LocallyRingedSpace.hom_of_SheafedSpace_hom_of_is_iso AlgebraicGeometry.LocallyRingedSpace.homOfSheafedSpaceHomOfIsIso
+-/
 
+#print AlgebraicGeometry.LocallyRingedSpace.isoOfSheafedSpaceIso /-
 /-- Given two locally ringed spaces `X` and `Y`, an isomorphism between `X` and `Y` as _sheafed_
 spaces can be lifted to an isomorphism `X ⟶ Y` as locally ringed spaces.
 
@@ -218,6 +231,7 @@ def isoOfSheafedSpaceIso {X Y : LocallyRingedSpace} (f : X.toSheafedSpace ≅ Y.
   hom_inv_id' := Hom.ext _ _ f.hom_inv_id
   inv_hom_id' := Hom.ext _ _ f.inv_hom_id
 #align algebraic_geometry.LocallyRingedSpace.iso_of_SheafedSpace_iso AlgebraicGeometry.LocallyRingedSpace.isoOfSheafedSpaceIso
+-/
 
 instance : ReflectsIsomorphisms forgetToSheafedSpace
     where reflects X Y f i :=
@@ -226,10 +240,13 @@ instance : ReflectsIsomorphisms forgetToSheafedSpace
         ⟨hom_of_SheafedSpace_hom_of_is_iso (CategoryTheory.inv (forget_to_SheafedSpace.map f)),
           hom.ext _ _ (is_iso.hom_inv_id _), hom.ext _ _ (is_iso.inv_hom_id _)⟩ }
 
+#print AlgebraicGeometry.LocallyRingedSpace.is_sheafedSpace_iso /-
 instance is_sheafedSpace_iso {X Y : LocallyRingedSpace} (f : X ⟶ Y) [IsIso f] : IsIso f.1 :=
   LocallyRingedSpace.forgetToSheafedSpace.map_isIso f
 #align algebraic_geometry.LocallyRingedSpace.is_SheafedSpace_iso AlgebraicGeometry.LocallyRingedSpace.is_sheafedSpace_iso
+-/
 
+#print AlgebraicGeometry.LocallyRingedSpace.restrict /-
 /-- The restriction of a locally ringed space along an open embedding.
 -/
 @[simps]
@@ -244,12 +261,15 @@ def restrict {U : TopCat} (X : LocallyRingedSpace) {f : U ⟶ X.toTopCat} (h : O
     exact (X.to_PresheafedSpace.restrict_stalk_iso h x).symm.commRingCatIsoToRingEquiv
   toSheafedSpace := X.toSheafedSpace.restrict h
 #align algebraic_geometry.LocallyRingedSpace.restrict AlgebraicGeometry.LocallyRingedSpace.restrict
+-/
 
+#print AlgebraicGeometry.LocallyRingedSpace.ofRestrict /-
 /-- The canonical map from the restriction to the supspace. -/
 def ofRestrict {U : TopCat} (X : LocallyRingedSpace) {f : U ⟶ X.toTopCat} (h : OpenEmbedding f) :
     X.restrict h ⟶ X :=
   ⟨X.toPresheafedSpace.of_restrict h, fun x => inferInstance⟩
 #align algebraic_geometry.LocallyRingedSpace.of_restrict AlgebraicGeometry.LocallyRingedSpace.ofRestrict
+-/
 
 #print AlgebraicGeometry.LocallyRingedSpace.restrictTopIso /-
 /-- The restriction of a locally ringed space `X` to the top subspace is isomorphic to `X` itself.
@@ -273,24 +293,33 @@ theorem Γ_def : Γ = forgetToSheafedSpace.op ⋙ SheafedSpace.Γ :=
 #align algebraic_geometry.LocallyRingedSpace.Γ_def AlgebraicGeometry.LocallyRingedSpace.Γ_def
 -/
 
+#print AlgebraicGeometry.LocallyRingedSpace.Γ_obj /-
 @[simp]
 theorem Γ_obj (X : LocallyRingedSpaceᵒᵖ) : Γ.obj X = (unop X).Presheaf.obj (op ⊤) :=
   rfl
 #align algebraic_geometry.LocallyRingedSpace.Γ_obj AlgebraicGeometry.LocallyRingedSpace.Γ_obj
+-/
 
+#print AlgebraicGeometry.LocallyRingedSpace.Γ_obj_op /-
 theorem Γ_obj_op (X : LocallyRingedSpace) : Γ.obj (op X) = X.Presheaf.obj (op ⊤) :=
   rfl
 #align algebraic_geometry.LocallyRingedSpace.Γ_obj_op AlgebraicGeometry.LocallyRingedSpace.Γ_obj_op
+-/
 
+#print AlgebraicGeometry.LocallyRingedSpace.Γ_map /-
 @[simp]
 theorem Γ_map {X Y : LocallyRingedSpaceᵒᵖ} (f : X ⟶ Y) : Γ.map f = f.unop.1.c.app (op ⊤) :=
   rfl
 #align algebraic_geometry.LocallyRingedSpace.Γ_map AlgebraicGeometry.LocallyRingedSpace.Γ_map
+-/
 
+#print AlgebraicGeometry.LocallyRingedSpace.Γ_map_op /-
 theorem Γ_map_op {X Y : LocallyRingedSpace} (f : X ⟶ Y) : Γ.map f.op = f.1.c.app (op ⊤) :=
   rfl
 #align algebraic_geometry.LocallyRingedSpace.Γ_map_op AlgebraicGeometry.LocallyRingedSpace.Γ_map_op
+-/
 
+#print AlgebraicGeometry.LocallyRingedSpace.preimage_basicOpen /-
 theorem preimage_basicOpen {X Y : LocallyRingedSpace} (f : X ⟶ Y) {U : Opens Y}
     (s : Y.Presheaf.obj (op U)) :
     (Opens.map f.1.base).obj (Y.toRingedSpace.basicOpen s) =
@@ -307,6 +336,7 @@ theorem preimage_basicOpen {X Y : LocallyRingedSpace} (f : X ⟶ Y) {U : Opens Y
     rw [← PresheafedSpace.stalk_map_germ_apply] at hy 
     exact (isUnit_map_iff (PresheafedSpace.stalk_map f.1 _) _).mp hy
 #align algebraic_geometry.LocallyRingedSpace.preimage_basic_open AlgebraicGeometry.LocallyRingedSpace.preimage_basicOpen
+-/
 
 #print AlgebraicGeometry.LocallyRingedSpace.basicOpen_zero /-
 -- This actually holds for all ringed spaces with nontrivial stalks.
@@ -320,10 +350,12 @@ theorem basicOpen_zero (X : LocallyRingedSpace) (U : Opens X.carrier) :
 #align algebraic_geometry.LocallyRingedSpace.basic_open_zero AlgebraicGeometry.LocallyRingedSpace.basicOpen_zero
 -/
 
+#print AlgebraicGeometry.LocallyRingedSpace.component_nontrivial /-
 instance component_nontrivial (X : LocallyRingedSpace) (U : Opens X.carrier) [hU : Nonempty U] :
     Nontrivial (X.Presheaf.obj <| op U) :=
   (X.toPresheafedSpace.Presheaf.germ hU.some).domain_nontrivial
 #align algebraic_geometry.LocallyRingedSpace.component_nontrivial AlgebraicGeometry.LocallyRingedSpace.component_nontrivial
+-/
 
 end LocallyRingedSpace
 

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin
 
 ! This file was ported from Lean 3 source module algebraic_geometry.locally_ringed_space
-! leanprover-community/mathlib commit f0c8bf9245297a541f468be517f1bde6195105e9
+! leanprover-community/mathlib commit af471b9e3ce868f296626d33189b4ce730fa4c00
 ! 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.Stalks
 /-!
 # The category of locally ringed spaces
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 We define (bundled) locally ringed spaces (as `SheafedSpace CommRing` along with the fact that the
 stalks are local rings), and morphisms between these (morphisms in `SheafedSpace` with
 `is_local_ring_hom` on the stalk maps).
@@ -34,6 +37,7 @@ open CategoryTheory.Category CategoryTheory.Functor
 
 namespace AlgebraicGeometry
 
+#print AlgebraicGeometry.LocallyRingedSpace /-
 /-- A `LocallyRingedSpace` is a topological space equipped with a sheaf of commutative rings
 such that all the stalks are local rings.
 
@@ -43,6 +47,7 @@ such that the morphisms induced on stalks are local ring homomorphisms. -/
 structure LocallyRingedSpace extends SheafedSpace CommRingCat where
   LocalRing : ∀ x, LocalRing (presheaf.stalk x)
 #align algebraic_geometry.LocallyRingedSpace AlgebraicGeometry.LocallyRingedSpace
+-/
 
 attribute [instance] LocallyRingedSpace.local_ring
 
@@ -50,17 +55,21 @@ namespace LocallyRingedSpace
 
 variable (X : LocallyRingedSpace)
 
+#print AlgebraicGeometry.LocallyRingedSpace.toRingedSpace /-
 /-- An alias for `to_SheafedSpace`, where the result type is a `RingedSpace`.
 This allows us to use dot-notation for the `RingedSpace` namespace.
  -/
 def toRingedSpace : RingedSpace :=
   X.toSheafedSpace
 #align algebraic_geometry.LocallyRingedSpace.to_RingedSpace AlgebraicGeometry.LocallyRingedSpace.toRingedSpace
+-/
 
+#print AlgebraicGeometry.LocallyRingedSpace.toTopCat /-
 /-- The underlying topological space of a locally ringed space. -/
-def toTop : TopCat :=
+def toTopCat : TopCat :=
   X.1.carrier
-#align algebraic_geometry.LocallyRingedSpace.to_Top AlgebraicGeometry.LocallyRingedSpace.toTop
+#align algebraic_geometry.LocallyRingedSpace.to_Top AlgebraicGeometry.LocallyRingedSpace.toTopCat
+-/
 
 instance : CoeSort LocallyRingedSpace (Type u) :=
   ⟨fun X : LocallyRingedSpace => (X.toTopCat : Type u)⟩
@@ -68,13 +77,16 @@ instance : CoeSort LocallyRingedSpace (Type u) :=
 instance (x : X) : LocalRing (X.toPresheafedSpace.stalk x) :=
   X.LocalRing x
 
+#print AlgebraicGeometry.LocallyRingedSpace.𝒪 /-
 -- PROJECT: how about a typeclass "has_structure_sheaf" to mediate the 𝒪 notation, rather
 -- than defining it over and over for PresheafedSpace, LRS, Scheme, etc.
 /-- The structure sheaf of a locally ringed space. -/
 def 𝒪 : Sheaf CommRingCat X.toTopCat :=
   X.toSheafedSpace.Sheaf
 #align algebraic_geometry.LocallyRingedSpace.𝒪 AlgebraicGeometry.LocallyRingedSpace.𝒪
+-/
 
+#print AlgebraicGeometry.LocallyRingedSpace.Hom /-
 /-- A morphism of locally ringed spaces is a morphism of ringed spaces
  such that the morphims induced on stalks are local ring homomorphisms. -/
 @[ext]
@@ -82,10 +94,12 @@ structure Hom (X Y : LocallyRingedSpace.{u}) : Type u where
   val : X.toSheafedSpace ⟶ Y.toSheafedSpace
   Prop : ∀ x, IsLocalRingHom (PresheafedSpace.stalkMap val x)
 #align algebraic_geometry.LocallyRingedSpace.hom AlgebraicGeometry.LocallyRingedSpace.Hom
+-/
 
 instance : Quiver LocallyRingedSpace :=
   ⟨Hom⟩
 
+#print AlgebraicGeometry.LocallyRingedSpace.stalk /-
 -- TODO perhaps we should make a bundled `LocalRing` and return one here?
 -- TODO define `sheaf.stalk` so we can write `X.𝒪.stalk` here?
 /-- The stalk of a locally ringed space, just as a `CommRing`.
@@ -93,6 +107,7 @@ instance : Quiver LocallyRingedSpace :=
 noncomputable def stalk (X : LocallyRingedSpace) (x : X) : CommRingCat :=
   X.Presheaf.stalk x
 #align algebraic_geometry.LocallyRingedSpace.stalk AlgebraicGeometry.LocallyRingedSpace.stalk
+-/
 
 /-- A morphism of locally ringed spaces `f : X ⟶ Y` induces
 a local ring homomorphism from `Y.stalk (f x)` to `X.stalk x` for any `x : X`.
@@ -109,21 +124,25 @@ instance {X Y : LocallyRingedSpace} (f : X ⟶ Y) (x : X) :
     IsLocalRingHom (PresheafedSpace.stalkMap f.1 x) :=
   f.2 x
 
+#print AlgebraicGeometry.LocallyRingedSpace.id /-
 /-- The identity morphism on a locally ringed space. -/
 @[simps]
 def id (X : LocallyRingedSpace) : Hom X X :=
   ⟨𝟙 _, fun x => by erw [PresheafedSpace.stalk_map.id]; apply isLocalRingHom_id⟩
 #align algebraic_geometry.LocallyRingedSpace.id AlgebraicGeometry.LocallyRingedSpace.id
+-/
 
 instance (X : LocallyRingedSpace) : Inhabited (Hom X X) :=
   ⟨id X⟩
 
+#print AlgebraicGeometry.LocallyRingedSpace.comp /-
 /-- Composition of morphisms of locally ringed spaces. -/
 def comp {X Y Z : LocallyRingedSpace} (f : Hom X Y) (g : Hom Y Z) : Hom X Z :=
   ⟨f.val ≫ g.val, fun x => by
     erw [PresheafedSpace.stalk_map.comp]
     exact @isLocalRingHom_comp _ _ _ _ _ _ _ _ (f.2 _) (g.2 _)⟩
 #align algebraic_geometry.LocallyRingedSpace.comp AlgebraicGeometry.LocallyRingedSpace.comp
+-/
 
 /-- The category of locally ringed spaces. -/
 instance : Category LocallyRingedSpace where
@@ -144,11 +163,13 @@ def forgetToSheafedSpace : LocallyRingedSpace ⥤ SheafedSpace CommRingCat
 
 instance : Faithful forgetToSheafedSpace where
 
+#print AlgebraicGeometry.LocallyRingedSpace.forgetToTop /-
 /-- The forgetful functor from `LocallyRingedSpace` to `Top`. -/
 @[simps]
 def forgetToTop : LocallyRingedSpace ⥤ TopCat :=
   forgetToSheafedSpace ⋙ SheafedSpace.forget _
 #align algebraic_geometry.LocallyRingedSpace.forget_to_Top AlgebraicGeometry.LocallyRingedSpace.forgetToTop
+-/
 
 @[simp]
 theorem comp_val {X Y Z : LocallyRingedSpace} (f : X ⟶ Y) (g : Y ⟶ Z) :
@@ -230,21 +251,27 @@ def ofRestrict {U : TopCat} (X : LocallyRingedSpace) {f : U ⟶ X.toTopCat} (h :
   ⟨X.toPresheafedSpace.of_restrict h, fun x => inferInstance⟩
 #align algebraic_geometry.LocallyRingedSpace.of_restrict AlgebraicGeometry.LocallyRingedSpace.ofRestrict
 
+#print AlgebraicGeometry.LocallyRingedSpace.restrictTopIso /-
 /-- The restriction of a locally ringed space `X` to the top subspace is isomorphic to `X` itself.
 -/
 def restrictTopIso (X : LocallyRingedSpace) : X.restrict (Opens.openEmbedding ⊤) ≅ X :=
   @isoOfSheafedSpaceIso (X.restrict (Opens.openEmbedding ⊤)) X X.toSheafedSpace.restrictTopIso
 #align algebraic_geometry.LocallyRingedSpace.restrict_top_iso AlgebraicGeometry.LocallyRingedSpace.restrictTopIso
+-/
 
+#print AlgebraicGeometry.LocallyRingedSpace.Γ /-
 /-- The global sections, notated Gamma.
 -/
 def Γ : LocallyRingedSpaceᵒᵖ ⥤ CommRingCat :=
   forgetToSheafedSpace.op ⋙ SheafedSpace.Γ
 #align algebraic_geometry.LocallyRingedSpace.Γ AlgebraicGeometry.LocallyRingedSpace.Γ
+-/
 
+#print AlgebraicGeometry.LocallyRingedSpace.Γ_def /-
 theorem Γ_def : Γ = forgetToSheafedSpace.op ⋙ SheafedSpace.Γ :=
   rfl
 #align algebraic_geometry.LocallyRingedSpace.Γ_def AlgebraicGeometry.LocallyRingedSpace.Γ_def
+-/
 
 @[simp]
 theorem Γ_obj (X : LocallyRingedSpaceᵒᵖ) : Γ.obj X = (unop X).Presheaf.obj (op ⊤) :=
@@ -281,6 +308,7 @@ theorem preimage_basicOpen {X Y : LocallyRingedSpace} (f : X ⟶ Y) {U : Opens Y
     exact (isUnit_map_iff (PresheafedSpace.stalk_map f.1 _) _).mp hy
 #align algebraic_geometry.LocallyRingedSpace.preimage_basic_open AlgebraicGeometry.LocallyRingedSpace.preimage_basicOpen
 
+#print AlgebraicGeometry.LocallyRingedSpace.basicOpen_zero /-
 -- This actually holds for all ringed spaces with nontrivial stalks.
 @[simp]
 theorem basicOpen_zero (X : LocallyRingedSpace) (U : Opens X.carrier) :
@@ -290,6 +318,7 @@ theorem basicOpen_zero (X : LocallyRingedSpace) (U : Opens X.carrier) :
     Set.setOf_false, Set.image_empty]
   rfl
 #align algebraic_geometry.LocallyRingedSpace.basic_open_zero AlgebraicGeometry.LocallyRingedSpace.basicOpen_zero
+-/
 
 instance component_nontrivial (X : LocallyRingedSpace) (U : Opens X.carrier) [hU : Nonempty U] :
     Nontrivial (X.Presheaf.obj <| op U) :=

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

@@ -130,9 +130,9 @@ instance : Category LocallyRingedSpace where
   Hom := Hom
   id := id
   comp X Y Z f g := comp f g
-  comp_id' := by intros ; ext1; simp [comp]
-  id_comp' := by intros ; ext1; simp [comp]
-  assoc' := by intros ; ext1; simp [comp]
+  comp_id' := by intros; ext1; simp [comp]
+  id_comp' := by intros; ext1; simp [comp]
+  assoc' := by intros; ext1; simp [comp]
 
 /-- The forgetful functor from `LocallyRingedSpace` to `SheafedSpace CommRing`. -/
 @[simps]
@@ -277,7 +277,7 @@ theorem preimage_basicOpen {X Y : LocallyRingedSpace} (f : X ⟶ Y) {U : Opens Y
     exact (PresheafedSpace.stalk_map f.1 _).isUnit_map hy
   · rintro ⟨y, hy : IsUnit _, rfl⟩
     erw [RingedSpace.mem_basic_open _ _ ⟨f.1.base y.1, y.2⟩]
-    rw [← PresheafedSpace.stalk_map_germ_apply] at hy
+    rw [← PresheafedSpace.stalk_map_germ_apply] at hy 
     exact (isUnit_map_iff (PresheafedSpace.stalk_map f.1 _) _).mp hy
 #align algebraic_geometry.LocallyRingedSpace.preimage_basic_open AlgebraicGeometry.LocallyRingedSpace.preimage_basicOpen
 

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

@@ -112,9 +112,7 @@ instance {X Y : LocallyRingedSpace} (f : X ⟶ Y) (x : X) :
 /-- The identity morphism on a locally ringed space. -/
 @[simps]
 def id (X : LocallyRingedSpace) : Hom X X :=
-  ⟨𝟙 _, fun x => by
-    erw [PresheafedSpace.stalk_map.id]
-    apply isLocalRingHom_id⟩
+  ⟨𝟙 _, fun x => by erw [PresheafedSpace.stalk_map.id]; apply isLocalRingHom_id⟩
 #align algebraic_geometry.LocallyRingedSpace.id AlgebraicGeometry.LocallyRingedSpace.id
 
 instance (X : LocallyRingedSpace) : Inhabited (Hom X X) :=
@@ -132,18 +130,9 @@ instance : Category LocallyRingedSpace where
   Hom := Hom
   id := id
   comp X Y Z f g := comp f g
-  comp_id' := by
-    intros
-    ext1
-    simp [comp]
-  id_comp' := by
-    intros
-    ext1
-    simp [comp]
-  assoc' := by
-    intros
-    ext1
-    simp [comp]
+  comp_id' := by intros ; ext1; simp [comp]
+  id_comp' := by intros ; ext1; simp [comp]
+  assoc' := by intros ; ext1; simp [comp]
 
 /-- The forgetful functor from `LocallyRingedSpace` to `SheafedSpace CommRing`. -/
 @[simps]

mathlib commit https://github.com/leanprover-community/mathlib/commit/e3fb84046afd187b710170887195d50bada934ee

@@ -231,7 +231,7 @@ def restrict {U : TopCat} (X : LocallyRingedSpace) {f : U ⟶ X.toTopCat} (h : O
     dsimp at *
     -- We show that the stalk of the restriction is isomorphic to the original stalk,
     apply @RingEquiv.localRing _ _ _ (X.local_ring (f x))
-    exact (X.to_PresheafedSpace.restrict_stalk_iso h x).symm.commRingIsoToRingEquiv
+    exact (X.to_PresheafedSpace.restrict_stalk_iso h x).symm.commRingCatIsoToRingEquiv
   toSheafedSpace := X.toSheafedSpace.restrict h
 #align algebraic_geometry.LocallyRingedSpace.restrict AlgebraicGeometry.LocallyRingedSpace.restrict
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/738054fa93d43512da144ec45ce799d18fd44248

@@ -4,13 +4,12 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin
 
 ! This file was ported from Lean 3 source module algebraic_geometry.locally_ringed_space
-! leanprover-community/mathlib commit d39590fc8728fbf6743249802486f8c91ffe07bc
+! leanprover-community/mathlib commit f0c8bf9245297a541f468be517f1bde6195105e9
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.AlgebraicGeometry.RingedSpace
 import Mathbin.AlgebraicGeometry.Stalks
-import Mathbin.Logic.Equiv.TransferInstance
 
 /-!
 # The category of locally ringed spaces

mathlib commit https://github.com/leanprover-community/mathlib/commit/9b2b58d6b14b895b2f375108e765cb47de71aebd

@@ -64,7 +64,7 @@ def toTop : TopCat :=
 #align algebraic_geometry.LocallyRingedSpace.to_Top AlgebraicGeometry.LocallyRingedSpace.toTop
 
 instance : CoeSort LocallyRingedSpace (Type u) :=
-  ⟨fun X : LocallyRingedSpace => (X.toTop : Type u)⟩
+  ⟨fun X : LocallyRingedSpace => (X.toTopCat : Type u)⟩
 
 instance (x : X) : LocalRing (X.toPresheafedSpace.stalk x) :=
   X.LocalRing x
@@ -72,7 +72,7 @@ instance (x : X) : LocalRing (X.toPresheafedSpace.stalk x) :=
 -- PROJECT: how about a typeclass "has_structure_sheaf" to mediate the 𝒪 notation, rather
 -- than defining it over and over for PresheafedSpace, LRS, Scheme, etc.
 /-- The structure sheaf of a locally ringed space. -/
-def 𝒪 : Sheaf CommRingCat X.toTop :=
+def 𝒪 : Sheaf CommRingCat X.toTopCat :=
   X.toSheafedSpace.Sheaf
 #align algebraic_geometry.LocallyRingedSpace.𝒪 AlgebraicGeometry.LocallyRingedSpace.𝒪
 
@@ -224,7 +224,7 @@ instance is_sheafedSpace_iso {X Y : LocallyRingedSpace} (f : X ⟶ Y) [IsIso f]
 /-- The restriction of a locally ringed space along an open embedding.
 -/
 @[simps]
-def restrict {U : TopCat} (X : LocallyRingedSpace) {f : U ⟶ X.toTop} (h : OpenEmbedding f) :
+def restrict {U : TopCat} (X : LocallyRingedSpace) {f : U ⟶ X.toTopCat} (h : OpenEmbedding f) :
     LocallyRingedSpace
     where
   LocalRing := by
@@ -237,7 +237,7 @@ def restrict {U : TopCat} (X : LocallyRingedSpace) {f : U ⟶ X.toTop} (h : Open
 #align algebraic_geometry.LocallyRingedSpace.restrict AlgebraicGeometry.LocallyRingedSpace.restrict
 
 /-- The canonical map from the restriction to the supspace. -/
-def ofRestrict {U : TopCat} (X : LocallyRingedSpace) {f : U ⟶ X.toTop} (h : OpenEmbedding f) :
+def ofRestrict {U : TopCat} (X : LocallyRingedSpace) {f : U ⟶ X.toTopCat} (h : OpenEmbedding f) :
     X.restrict h ⟶ X :=
   ⟨X.toPresheafedSpace.of_restrict h, fun x => inferInstance⟩
 #align algebraic_geometry.LocallyRingedSpace.of_restrict AlgebraicGeometry.LocallyRingedSpace.ofRestrict

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

Before this PR, Functor.Full contained the data of the preimage of maps by a full functor F. This PR makes Functor.Full a proposition. This is to prevent any diamond to appear.

The lemma Functor.image_preimage is also renamed Functor.map_preimage.

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

@@ -88,7 +88,7 @@ instance : Quiver LocallyRingedSpace :=
   ⟨Hom⟩
 
 @[ext] lemma Hom.ext' (X Y : LocallyRingedSpace) {f g : X ⟶ Y} (h : f.val = g.val) : f = g :=
-Hom.ext _ _ h
+  Hom.ext _ _ h
 
 -- TODO perhaps we should make a bundled `LocalRing` and return one here?
 -- TODO define `sheaf.stalk` so we can write `X.𝒪.stalk` here?
@@ -252,8 +252,9 @@ set_option linter.uppercaseLean3 false in
 
 /-- The restriction of a locally ringed space `X` to the top subspace is isomorphic to `X` itself.
 -/
-def restrictTopIso (X : LocallyRingedSpace) : X.restrict (Opens.openEmbedding ⊤) ≅ X :=
-  @isoOfSheafedSpaceIso (X.restrict (Opens.openEmbedding ⊤)) X X.toSheafedSpace.restrictTopIso
+def restrictTopIso (X : LocallyRingedSpace) :
+    X.restrict (Opens.openEmbedding ⊤) ≅ X :=
+  isoOfSheafedSpaceIso X.toSheafedSpace.restrictTopIso
 set_option linter.uppercaseLean3 false in
 #align algebraic_geometry.LocallyRingedSpace.restrict_top_iso AlgebraicGeometry.LocallyRingedSpace.restrictTopIso
 

These notions on functors are now Functor.Full, Functor.Faithful, Functor.EssSurj, Functor.IsEquivalence, Functor.ReflectsIsomorphisms. Deprecated aliases are introduced for the previous names.

@@ -154,7 +154,7 @@ def forgetToSheafedSpace : LocallyRingedSpace ⥤ SheafedSpace CommRingCat where
 set_option linter.uppercaseLean3 false in
 #align algebraic_geometry.LocallyRingedSpace.forget_to_SheafedSpace AlgebraicGeometry.LocallyRingedSpace.forgetToSheafedSpace
 
-instance : Faithful forgetToSheafedSpace where
+instance : forgetToSheafedSpace.Faithful where
   map_injective {_ _} _ _ h := Hom.ext _ _ h
 
 /-- The forgetful functor from `LocallyRingedSpace` to `Top`. -/
@@ -219,7 +219,7 @@ def isoOfSheafedSpaceIso {X Y : LocallyRingedSpace} (f : X.toSheafedSpace ≅ Y.
 set_option linter.uppercaseLean3 false in
 #align algebraic_geometry.LocallyRingedSpace.iso_of_SheafedSpace_iso AlgebraicGeometry.LocallyRingedSpace.isoOfSheafedSpaceIso
 
-instance : ReflectsIsomorphisms forgetToSheafedSpace where reflects {_ _} f i :=
+instance : forgetToSheafedSpace.ReflectsIsomorphisms where reflects {_ _} f i :=
   { out :=
       ⟨homOfSheafedSpaceHomOfIsIso (CategoryTheory.inv (forgetToSheafedSpace.map f)),
         Hom.ext _ _ (IsIso.hom_inv_id (I := i)), Hom.ext _ _ (IsIso.inv_hom_id (I := i))⟩ }

Classifies by adding issue number (#10754) to porting notes claiming added instance.

@@ -99,8 +99,8 @@ noncomputable def stalk (X : LocallyRingedSpace) (x : X) : CommRingCat :=
 set_option linter.uppercaseLean3 false in
 #align algebraic_geometry.LocallyRingedSpace.stalk AlgebraicGeometry.LocallyRingedSpace.stalk
 
--- Porting note: added this instance to help Lean realize stalks are local (so that `0 ≠ 1`
--- works below)
+-- Porting note (#10754): added this instance to help Lean realize stalks are local
+-- (so that `0 ≠ 1` works below)
 instance stalkLocal (x : X) : LocalRing <| X.stalk x := X.localRing x
 
 /-- A morphism of locally ringed spaces `f : X ⟶ Y` induces

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.

@@ -99,7 +99,7 @@ noncomputable def stalk (X : LocallyRingedSpace) (x : X) : CommRingCat :=
 set_option linter.uppercaseLean3 false in
 #align algebraic_geometry.LocallyRingedSpace.stalk AlgebraicGeometry.LocallyRingedSpace.stalk
 
--- Porting note : added this instance to help Lean realize stalks are local (so that `0 ≠ 1`
+-- Porting note: added this instance to help Lean realize stalks are local (so that `0 ≠ 1`
 -- works below)
 instance stalkLocal (x : X) : LocalRing <| X.stalk x := X.localRing x
 
@@ -171,7 +171,7 @@ theorem comp_val {X Y Z : LocallyRingedSpace} (f : X ⟶ Y) (g : Y ⟶ Z) :
 set_option linter.uppercaseLean3 false in
 #align algebraic_geometry.LocallyRingedSpace.comp_val AlgebraicGeometry.LocallyRingedSpace.comp_val
 
--- Porting note : complains that `(f ≫ g).val.c` can be further simplified
+-- Porting note: complains that `(f ≫ g).val.c` can be further simplified
 -- so changed to its simp normal form `(f.val ≫ g.val).c`
 @[simp]
 theorem comp_val_c {X Y Z : LocallyRingedSpace} (f : X ⟶ Y) (g : Y ⟶ Z) :

Co-Authored-By: newell <newell.jensen@gmail.com>

@@ -243,7 +243,7 @@ def restrict {U : TopCat} (X : LocallyRingedSpace) {f : U ⟶ X.toTopCat} (h : O
 set_option linter.uppercaseLean3 false in
 #align algebraic_geometry.LocallyRingedSpace.restrict AlgebraicGeometry.LocallyRingedSpace.restrict
 
-/-- The canonical map from the restriction to the supspace. -/
+/-- The canonical map from the restriction to the subspace. -/
 def ofRestrict {U : TopCat} (X : LocallyRingedSpace) {f : U ⟶ X.toTopCat} (h : OpenEmbedding f) :
     X.restrict h ⟶ X :=
   ⟨X.toPresheafedSpace.ofRestrict h, fun _ => inferInstance⟩

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) 2020 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin
 -/
-import Mathlib.AlgebraicGeometry.RingedSpace
-import Mathlib.AlgebraicGeometry.Stalks
+import Mathlib.Geometry.RingedSpace.Basic
+import Mathlib.Geometry.RingedSpace.Stalks
 
 #align_import algebraic_geometry.locally_ringed_space from "leanprover-community/mathlib"@"f0c8bf9245297a541f468be517f1bde6195105e9"
 

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

@@ -236,7 +236,6 @@ def restrict {U : TopCat} (X : LocallyRingedSpace) {f : U ⟶ X.toTopCat} (h : O
     LocallyRingedSpace where
   localRing := by
     intro x
-    dsimp at *
     -- We show that the stalk of the restriction is isomorphic to the original stalk,
     apply @RingEquiv.localRing _ _ _ (X.localRing (f x))
     exact (X.restrictStalkIso h x).symm.commRingCatIsoToRingEquiv

We remove all possible occurences of Type _ and Sort _ in favor of Type* and Sort*.

This has nice performance benefits.

@@ -59,7 +59,7 @@ def toTopCat : TopCat :=
 set_option linter.uppercaseLean3 false in
 #align algebraic_geometry.LocallyRingedSpace.to_Top AlgebraicGeometry.LocallyRingedSpace.toTopCat
 
-instance : CoeSort LocallyRingedSpace (Type _) :=
+instance : CoeSort LocallyRingedSpace (Type*) :=
   ⟨fun X : LocallyRingedSpace => (X.toTopCat : Type _)⟩
 
 instance (x : X) : LocalRing (X.stalk 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) 2020 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin
-
-! This file was ported from Lean 3 source module algebraic_geometry.locally_ringed_space
-! leanprover-community/mathlib commit f0c8bf9245297a541f468be517f1bde6195105e9
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.AlgebraicGeometry.RingedSpace
 import Mathlib.AlgebraicGeometry.Stalks
 
+#align_import algebraic_geometry.locally_ringed_space from "leanprover-community/mathlib"@"f0c8bf9245297a541f468be517f1bde6195105e9"
+
 /-!
 # The category of locally ringed spaces
 

Co-authored-by: Jujian Zhang <jujian.zhang1998@outlook.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -90,6 +90,9 @@ set_option linter.uppercaseLean3 false in
 instance : Quiver LocallyRingedSpace :=
   ⟨Hom⟩
 
+@[ext] lemma Hom.ext' (X Y : LocallyRingedSpace) {f g : X ⟶ Y} (h : f.val = g.val) : f = g :=
+Hom.ext _ _ h
+
 -- TODO perhaps we should make a bundled `LocalRing` and return one here?
 -- TODO define `sheaf.stalk` so we can write `X.𝒪.stalk` here?
 /-- The stalk of a locally ringed space, just as a `CommRing`.

@@ -19,9 +19,6 @@ stalks are local rings), and morphisms between these (morphisms in `SheafedSpace
 `is_local_ring_hom` on the stalk maps).
 -/
 
-
-universe v u
-
 open CategoryTheory
 
 open TopCat
@@ -65,8 +62,8 @@ def toTopCat : TopCat :=
 set_option linter.uppercaseLean3 false in
 #align algebraic_geometry.LocallyRingedSpace.to_Top AlgebraicGeometry.LocallyRingedSpace.toTopCat
 
-instance : CoeSort LocallyRingedSpace (Type u) :=
-  ⟨fun X : LocallyRingedSpace => (X.toTopCat : Type u)⟩
+instance : CoeSort LocallyRingedSpace (Type _) :=
+  ⟨fun X : LocallyRingedSpace => (X.toTopCat : Type _)⟩
 
 instance (x : X) : LocalRing (X.stalk x) :=
   X.localRing x
@@ -82,7 +79,7 @@ set_option linter.uppercaseLean3 false in
 /-- A morphism of locally ringed spaces is a morphism of ringed spaces
  such that the morphisms induced on stalks are local ring homomorphisms. -/
 @[ext]
-structure Hom (X Y : LocallyRingedSpace.{u}) : Type u where
+structure Hom (X Y : LocallyRingedSpace) : Type _ where
   /-- the underlying morphism between ringed spaces -/
   val : X.toSheafedSpace ⟶ Y.toSheafedSpace
   /-- the underlying morphism induces a local ring homomorphism on stalks -/
@@ -177,7 +174,7 @@ set_option linter.uppercaseLean3 false in
 -- Porting note : complains that `(f ≫ g).val.c` can be further simplified
 -- so changed to its simp normal form `(f.val ≫ g.val).c`
 @[simp]
-theorem comp_val_c {X Y Z : LocallyRingedSpace.{u}} (f : X ⟶ Y) (g : Y ⟶ Z) :
+theorem comp_val_c {X Y Z : LocallyRingedSpace} (f : X ⟶ Y) (g : Y ⟶ Z) :
     (f.1 ≫ g.1).c = g.val.c ≫ (Presheaf.pushforward _ g.val.base).map f.val.c :=
   rfl
 set_option linter.uppercaseLean3 false in

@@ -302,19 +302,12 @@ theorem preimage_basicOpen {X Y : LocallyRingedSpace} (f : X ⟶ Y) {U : Opens Y
   ext x
   constructor
   · rintro ⟨⟨y, hyU⟩, hy : IsUnit _, rfl : y = _⟩
-    erw [RingedSpace.mem_basicOpen _ _ ⟨x, show x ∈ (Opens.map f.1.base).obj U from hyU⟩]
-    have eq1 := PresheafedSpace.stalkMap_germ_apply _ _
-      ⟨x, show x ∈ (Opens.map f.1.base).obj U from hyU⟩
-    dsimp at eq1
-    -- Porting note : `rw` and `erw` can't rewrite `stalkMap_germ_apply`
-    rw [← eq1]
+    erw [RingedSpace.mem_basicOpen _ _ ⟨x, show x ∈ (Opens.map f.1.base).obj U from hyU⟩,
+      ← PresheafedSpace.stalkMap_germ_apply]
     exact (PresheafedSpace.stalkMap f.1 _).isUnit_map hy
   · rintro ⟨y, hy : IsUnit _, rfl⟩
     erw [RingedSpace.mem_basicOpen _ _ ⟨f.1.base y.1, y.2⟩]
-    have eq1 := PresheafedSpace.stalkMap_germ_apply _ _ y
-    dsimp at eq1
-    -- Porting note : `rw` and `erw` can't rewrite `stalkMap_germ_apply`
-    rw [← eq1] at hy
+    erw [← PresheafedSpace.stalkMap_germ_apply] at hy
     exact (isUnit_map_iff (PresheafedSpace.stalkMap f.1 _) _).mp hy
 set_option linter.uppercaseLean3 false in
 #align algebraic_geometry.LocallyRingedSpace.preimage_basic_open AlgebraicGeometry.LocallyRingedSpace.preimage_basicOpen

These are all doc fixes

@@ -80,7 +80,7 @@ set_option linter.uppercaseLean3 false in
 #align algebraic_geometry.LocallyRingedSpace.𝒪 AlgebraicGeometry.LocallyRingedSpace.𝒪
 
 /-- A morphism of locally ringed spaces is a morphism of ringed spaces
- such that the morphims induced on stalks are local ring homomorphisms. -/
+ such that the morphisms induced on stalks are local ring homomorphisms. -/
 @[ext]
 structure Hom (X Y : LocallyRingedSpace.{u}) : Type u where
   /-- the underlying morphism between ringed spaces -/

Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com> Co-authored-by: Johan Commelin <johan@commelin.net>