algebraic_geometry.pullbacks | Mathlib porting status

Changes since the initial port

The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.

Changes in mathlib3

7316286f

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

d0b19368

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -608,8 +608,8 @@ def gluedIsLimit : IsLimit (PullbackCone.mk _ _ (p_comm 𝒰 f g)) :=
   intro s
   refine' ⟨glued_lift 𝒰 f g s, glued_lift_p1 𝒰 f g s, glued_lift_p2 𝒰 f g s, _⟩
   intro m h₁ h₂
-  change m ≫ p1 𝒰 f g = _ at h₁ 
-  change m ≫ p2 𝒰 f g = _ at h₂ 
+  change m ≫ p1 𝒰 f g = _ at h₁
+  change m ≫ p2 𝒰 f g = _ at h₂
   apply (𝒰.pullback_cover s.fst).hom_ext
   intro i
   rw [open_cover.pullback_cover_map]
@@ -684,7 +684,7 @@ instance left_affine_comp_pullback_hasPullback {X Y Z : Scheme} (f : X ⟶ Z) (g
       pullback.condition.symm (pullback_cone.flip_is_limit <| pullback_is_pullback _ _)
       (pullback_cone.flip_is_limit <| pullback_is_pullback _ _)
   have : has_pullback (pullback.snd ≫ Z.affine_cover.map i : Xᵢ ⟶ _) g := ⟨⟨⟨_, this⟩⟩⟩
-  rw [← pullback.condition] at this 
+  rw [← pullback.condition] at this
   exact this
 #align algebraic_geometry.Scheme.pullback.left_affine_comp_pullback_has_pullback AlgebraicGeometry.Scheme.Pullback.left_affine_comp_pullback_hasPullback
 -/

d0b19368

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,10 +3,10 @@ Copyright (c) 2022 Andrew Yang. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Andrew Yang
 -/
-import Mathbin.AlgebraicGeometry.Gluing
-import Mathbin.CategoryTheory.Limits.Opposites
-import Mathbin.AlgebraicGeometry.AffineScheme
-import Mathbin.CategoryTheory.Limits.Shapes.Diagonal
+import AlgebraicGeometry.Gluing
+import CategoryTheory.Limits.Opposites
+import AlgebraicGeometry.AffineScheme
+import CategoryTheory.Limits.Shapes.Diagonal
 
 #align_import algebraic_geometry.pullbacks from "leanprover-community/mathlib"@"d0b1936853671209a866fa35b9e54949c81116e2"

d0b19368

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,17 +2,14 @@
 Copyright (c) 2022 Andrew Yang. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Andrew Yang
-
-! This file was ported from Lean 3 source module algebraic_geometry.pullbacks
-! leanprover-community/mathlib commit d0b1936853671209a866fa35b9e54949c81116e2
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.AlgebraicGeometry.Gluing
 import Mathbin.CategoryTheory.Limits.Opposites
 import Mathbin.AlgebraicGeometry.AffineScheme
 import Mathbin.CategoryTheory.Limits.Shapes.Diagonal
 
+#align_import algebraic_geometry.pullbacks from "leanprover-community/mathlib"@"d0b1936853671209a866fa35b9e54949c81116e2"
+
 /-!
 # Fibred products of schemes

d0b19368

bump to nightly-2023-07-04-01

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

05318d71

Diff

@@ -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.pullbacks
-! leanprover-community/mathlib commit 7316286ff2942aa14e540add9058c6b0aa1c8070
+! leanprover-community/mathlib commit d0b1936853671209a866fa35b9e54949c81116e2
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -16,6 +16,9 @@ import Mathbin.CategoryTheory.Limits.Shapes.Diagonal
 /-!
 # Fibred products of schemes
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file we construct the fibred product of schemes via gluing.
 We roughly follow [har77] Theorem 3.3.

7316286f

bump to nightly-2023-06-29-21

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

95e32410

Diff

@@ -45,11 +45,14 @@ variable {X Y Z : Scheme.{u}} (𝒰 : OpenCover.{u} X) (f : X ⟶ Z) (g : Y ⟶
 
 variable [∀ i, HasPullback (𝒰.map i ≫ f) g]
 
+#print AlgebraicGeometry.Scheme.Pullback.v /-
 /-- The intersection of `Uᵢ ×[Z] Y` and `Uⱼ ×[Z] Y` is given by (Uᵢ ×[Z] Y) ×[X] Uⱼ -/
 def v (i j : 𝒰.J) : Scheme :=
   pullback ((pullback.fst : pullback (𝒰.map i ≫ f) g ⟶ _) ≫ 𝒰.map i) (𝒰.map j)
 #align algebraic_geometry.Scheme.pullback.V AlgebraicGeometry.Scheme.Pullback.v
+-/
 
+#print AlgebraicGeometry.Scheme.Pullback.t /-
 /-- The canonical transition map `(Uᵢ ×[Z] Y) ×[X] Uⱼ ⟶ (Uⱼ ×[Z] Y) ×[X] Uᵢ` given by the fact
 that pullbacks are associative and symmetric. -/
 def t (i j : 𝒰.J) : v 𝒰 f g i j ⟶ v 𝒰 f g j i :=
@@ -67,7 +70,9 @@ def t (i j : 𝒰.J) : v 𝒰 f g i j ⟶ v 𝒰 f g j i :=
   rw [pullback_symmetry_hom_comp_snd_assoc, pullback.condition_assoc, category.comp_id]
   rw [category.comp_id, category.id_comp]
 #align algebraic_geometry.Scheme.pullback.t AlgebraicGeometry.Scheme.Pullback.t
+-/
 
+#print AlgebraicGeometry.Scheme.Pullback.t_fst_fst /-
 @[simp, reassoc]
 theorem t_fst_fst (i j : 𝒰.J) : t 𝒰 f g i j ≫ pullback.fst ≫ pullback.fst = pullback.snd :=
   by
@@ -76,7 +81,9 @@ theorem t_fst_fst (i j : 𝒰.J) : t 𝒰 f g i j ≫ pullback.fst ≫ pullback.
     pullback_assoc_hom_snd_fst, pullback.lift_fst_assoc, pullback_symmetry_hom_comp_snd,
     pullback_assoc_inv_fst_fst, pullback_symmetry_hom_comp_fst]
 #align algebraic_geometry.Scheme.pullback.t_fst_fst AlgebraicGeometry.Scheme.Pullback.t_fst_fst
+-/
 
+#print AlgebraicGeometry.Scheme.Pullback.t_fst_snd /-
 @[simp, reassoc]
 theorem t_fst_snd (i j : 𝒰.J) :
     t 𝒰 f g i j ≫ pullback.fst ≫ pullback.snd = pullback.fst ≫ pullback.snd :=
@@ -86,7 +93,9 @@ theorem t_fst_snd (i j : 𝒰.J) :
     pullback_symmetry_hom_comp_fst_assoc, pullback_assoc_hom_snd_snd, pullback.lift_snd,
     pullback_assoc_inv_snd]
 #align algebraic_geometry.Scheme.pullback.t_fst_snd AlgebraicGeometry.Scheme.Pullback.t_fst_snd
+-/
 
+#print AlgebraicGeometry.Scheme.Pullback.t_snd /-
 @[simp, reassoc]
 theorem t_snd (i j : 𝒰.J) : t 𝒰 f g i j ≫ pullback.snd = pullback.fst ≫ pullback.fst :=
   by
@@ -95,7 +104,9 @@ theorem t_snd (i j : 𝒰.J) : t 𝒰 f g i j ≫ pullback.snd = pullback.fst 
     pullback_symmetry_hom_comp_snd, pullback_assoc_hom_fst, pullback.lift_fst_assoc,
     pullback_symmetry_hom_comp_fst, pullback_assoc_inv_fst_snd]
 #align algebraic_geometry.Scheme.pullback.t_snd AlgebraicGeometry.Scheme.Pullback.t_snd
+-/
 
+#print AlgebraicGeometry.Scheme.Pullback.t_id /-
 theorem t_id (i : 𝒰.J) : t 𝒰 f g i i = 𝟙 _ :=
   by
   apply pullback.hom_ext <;> rw [category.id_comp]
@@ -104,12 +115,16 @@ theorem t_id (i : 𝒰.J) : t 𝒰 f g i i = 𝟙 _ :=
   · simp only [category.assoc, t_fst_snd]
   · rw [← cancel_mono (𝒰.map i)]; simp only [pullback.condition, t_snd, category.assoc]
 #align algebraic_geometry.Scheme.pullback.t_id AlgebraicGeometry.Scheme.Pullback.t_id
+-/
 
+#print AlgebraicGeometry.Scheme.Pullback.fV /-
 /-- The inclusion map of `V i j = (Uᵢ ×[Z] Y) ×[X] Uⱼ ⟶ Uᵢ ×[Z] Y`-/
 abbrev fV (i j : 𝒰.J) : v 𝒰 f g i j ⟶ pullback (𝒰.map i ≫ f) g :=
   pullback.fst
 #align algebraic_geometry.Scheme.pullback.fV AlgebraicGeometry.Scheme.Pullback.fV
+-/
 
+#print AlgebraicGeometry.Scheme.Pullback.t' /-
 /-- The map `((Xᵢ ×[Z] Y) ×[X] Xⱼ) ×[Xᵢ ×[Z] Y] ((Xᵢ ×[Z] Y) ×[X] Xₖ)` ⟶
   `((Xⱼ ×[Z] Y) ×[X] Xₖ) ×[Xⱼ ×[Z] Y] ((Xⱼ ×[Z] Y) ×[X] Xᵢ)` needed for gluing   -/
 def t' (i j k : 𝒰.J) :
@@ -122,11 +137,13 @@ def t' (i j k : 𝒰.J) :
   · simp only [← pullback.condition, category.comp_id, t_fst_fst_assoc]
   · simp only [category.comp_id, category.id_comp]
 #align algebraic_geometry.Scheme.pullback.t' AlgebraicGeometry.Scheme.Pullback.t'
+-/
 
 section
 
 end
 
+#print AlgebraicGeometry.Scheme.Pullback.t'_fst_fst_fst /-
 @[simp, reassoc]
 theorem t'_fst_fst_fst (i j k : 𝒰.J) :
     t' 𝒰 f g i j k ≫ pullback.fst ≫ pullback.fst ≫ pullback.fst = pullback.fst ≫ pullback.snd :=
@@ -136,7 +153,9 @@ theorem t'_fst_fst_fst (i j k : 𝒰.J) :
     pullback_right_pullback_fst_iso_inv_snd_fst_assoc, pullback.lift_fst_assoc, t_fst_fst,
     pullback_right_pullback_fst_iso_hom_fst_assoc]
 #align algebraic_geometry.Scheme.pullback.t'_fst_fst_fst AlgebraicGeometry.Scheme.Pullback.t'_fst_fst_fst
+-/
 
+#print AlgebraicGeometry.Scheme.Pullback.t'_fst_fst_snd /-
 @[simp, reassoc]
 theorem t'_fst_fst_snd (i j k : 𝒰.J) :
     t' 𝒰 f g i j k ≫ pullback.fst ≫ pullback.fst ≫ pullback.snd =
@@ -147,7 +166,9 @@ theorem t'_fst_fst_snd (i j k : 𝒰.J) :
     pullback_right_pullback_fst_iso_inv_snd_fst_assoc, pullback.lift_fst_assoc, t_fst_snd,
     pullback_right_pullback_fst_iso_hom_fst_assoc]
 #align algebraic_geometry.Scheme.pullback.t'_fst_fst_snd AlgebraicGeometry.Scheme.Pullback.t'_fst_fst_snd
+-/
 
+#print AlgebraicGeometry.Scheme.Pullback.t'_fst_snd /-
 @[simp, reassoc]
 theorem t'_fst_snd (i j k : 𝒰.J) :
     t' 𝒰 f g i j k ≫ pullback.fst ≫ pullback.snd = pullback.snd ≫ pullback.snd :=
@@ -157,7 +178,9 @@ theorem t'_fst_snd (i j k : 𝒰.J) :
     pullback_right_pullback_fst_iso_inv_snd_snd, pullback.lift_snd,
     pullback_right_pullback_fst_iso_hom_snd]
 #align algebraic_geometry.Scheme.pullback.t'_fst_snd AlgebraicGeometry.Scheme.Pullback.t'_fst_snd
+-/
 
+#print AlgebraicGeometry.Scheme.Pullback.t'_snd_fst_fst /-
 @[simp, reassoc]
 theorem t'_snd_fst_fst (i j k : 𝒰.J) :
     t' 𝒰 f g i j k ≫ pullback.snd ≫ pullback.fst ≫ pullback.fst = pullback.fst ≫ pullback.snd :=
@@ -167,7 +190,9 @@ theorem t'_snd_fst_fst (i j k : 𝒰.J) :
     pullback_right_pullback_fst_iso_inv_fst_assoc, pullback.lift_fst_assoc, t_fst_fst,
     pullback_right_pullback_fst_iso_hom_fst_assoc]
 #align algebraic_geometry.Scheme.pullback.t'_snd_fst_fst AlgebraicGeometry.Scheme.Pullback.t'_snd_fst_fst
+-/
 
+#print AlgebraicGeometry.Scheme.Pullback.t'_snd_fst_snd /-
 @[simp, reassoc]
 theorem t'_snd_fst_snd (i j k : 𝒰.J) :
     t' 𝒰 f g i j k ≫ pullback.snd ≫ pullback.fst ≫ pullback.snd =
@@ -178,7 +203,9 @@ theorem t'_snd_fst_snd (i j k : 𝒰.J) :
     pullback_right_pullback_fst_iso_inv_fst_assoc, pullback.lift_fst_assoc, t_fst_snd,
     pullback_right_pullback_fst_iso_hom_fst_assoc]
 #align algebraic_geometry.Scheme.pullback.t'_snd_fst_snd AlgebraicGeometry.Scheme.Pullback.t'_snd_fst_snd
+-/
 
+#print AlgebraicGeometry.Scheme.Pullback.t'_snd_snd /-
 @[simp, reassoc]
 theorem t'_snd_snd (i j k : 𝒰.J) :
     t' 𝒰 f g i j k ≫ pullback.snd ≫ pullback.snd = pullback.fst ≫ pullback.fst ≫ pullback.fst :=
@@ -188,25 +215,33 @@ theorem t'_snd_snd (i j k : 𝒰.J) :
     pullback_right_pullback_fst_iso_inv_fst_assoc, pullback.lift_fst_assoc, t_snd,
     pullback_right_pullback_fst_iso_hom_fst_assoc]
 #align algebraic_geometry.Scheme.pullback.t'_snd_snd AlgebraicGeometry.Scheme.Pullback.t'_snd_snd
+-/
 
+#print AlgebraicGeometry.Scheme.Pullback.cocycle_fst_fst_fst /-
 theorem cocycle_fst_fst_fst (i j k : 𝒰.J) :
     t' 𝒰 f g i j k ≫ t' 𝒰 f g j k i ≫ t' 𝒰 f g k i j ≫ pullback.fst ≫ pullback.fst ≫ pullback.fst =
       pullback.fst ≫ pullback.fst ≫ pullback.fst :=
   by simp only [t'_fst_fst_fst, t'_fst_snd, t'_snd_snd]
 #align algebraic_geometry.Scheme.pullback.cocycle_fst_fst_fst AlgebraicGeometry.Scheme.Pullback.cocycle_fst_fst_fst
+-/
 
+#print AlgebraicGeometry.Scheme.Pullback.cocycle_fst_fst_snd /-
 theorem cocycle_fst_fst_snd (i j k : 𝒰.J) :
     t' 𝒰 f g i j k ≫ t' 𝒰 f g j k i ≫ t' 𝒰 f g k i j ≫ pullback.fst ≫ pullback.fst ≫ pullback.snd =
       pullback.fst ≫ pullback.fst ≫ pullback.snd :=
   by simp only [t'_fst_fst_snd]
 #align algebraic_geometry.Scheme.pullback.cocycle_fst_fst_snd AlgebraicGeometry.Scheme.Pullback.cocycle_fst_fst_snd
+-/
 
+#print AlgebraicGeometry.Scheme.Pullback.cocycle_fst_snd /-
 theorem cocycle_fst_snd (i j k : 𝒰.J) :
     t' 𝒰 f g i j k ≫ t' 𝒰 f g j k i ≫ t' 𝒰 f g k i j ≫ pullback.fst ≫ pullback.snd =
       pullback.fst ≫ pullback.snd :=
   by simp only [t'_fst_snd, t'_snd_snd, t'_fst_fst_fst]
 #align algebraic_geometry.Scheme.pullback.cocycle_fst_snd AlgebraicGeometry.Scheme.Pullback.cocycle_fst_snd
+-/
 
+#print AlgebraicGeometry.Scheme.Pullback.cocycle_snd_fst_fst /-
 theorem cocycle_snd_fst_fst (i j k : 𝒰.J) :
     t' 𝒰 f g i j k ≫ t' 𝒰 f g j k i ≫ t' 𝒰 f g k i j ≫ pullback.snd ≫ pullback.fst ≫ pullback.fst =
       pullback.snd ≫ pullback.fst ≫ pullback.fst :=
@@ -214,19 +249,25 @@ theorem cocycle_snd_fst_fst (i j k : 𝒰.J) :
   rw [← cancel_mono (𝒰.map i)]
   simp only [pullback.condition_assoc, t'_snd_fst_fst, t'_fst_snd, t'_snd_snd]
 #align algebraic_geometry.Scheme.pullback.cocycle_snd_fst_fst AlgebraicGeometry.Scheme.Pullback.cocycle_snd_fst_fst
+-/
 
+#print AlgebraicGeometry.Scheme.Pullback.cocycle_snd_fst_snd /-
 theorem cocycle_snd_fst_snd (i j k : 𝒰.J) :
     t' 𝒰 f g i j k ≫ t' 𝒰 f g j k i ≫ t' 𝒰 f g k i j ≫ pullback.snd ≫ pullback.fst ≫ pullback.snd =
       pullback.snd ≫ pullback.fst ≫ pullback.snd :=
   by simp only [pullback.condition_assoc, t'_snd_fst_snd]
 #align algebraic_geometry.Scheme.pullback.cocycle_snd_fst_snd AlgebraicGeometry.Scheme.Pullback.cocycle_snd_fst_snd
+-/
 
+#print AlgebraicGeometry.Scheme.Pullback.cocycle_snd_snd /-
 theorem cocycle_snd_snd (i j k : 𝒰.J) :
     t' 𝒰 f g i j k ≫ t' 𝒰 f g j k i ≫ t' 𝒰 f g k i j ≫ pullback.snd ≫ pullback.snd =
       pullback.snd ≫ pullback.snd :=
   by simp only [t'_snd_snd, t'_fst_fst_fst, t'_fst_snd]
 #align algebraic_geometry.Scheme.pullback.cocycle_snd_snd AlgebraicGeometry.Scheme.Pullback.cocycle_snd_snd
+-/
 
+#print AlgebraicGeometry.Scheme.Pullback.cocycle /-
 -- `by tidy` should solve it, but it times out.
 theorem cocycle (i j k : 𝒰.J) : t' 𝒰 f g i j k ≫ t' 𝒰 f g j k i ≫ t' 𝒰 f g k i j = 𝟙 _ :=
   by
@@ -248,7 +289,9 @@ theorem cocycle (i j k : 𝒰.J) : t' 𝒰 f g i j k ≫ t' 𝒰 f g j k i ≫ t
     · simp_rw [category.assoc]
       exact cocycle_snd_snd 𝒰 f g i j k
 #align algebraic_geometry.Scheme.pullback.cocycle AlgebraicGeometry.Scheme.Pullback.cocycle
+-/
 
+#print AlgebraicGeometry.Scheme.Pullback.gluing /-
 /-- Given `Uᵢ ×[Z] Y`, this is the glued fibered product `X ×[Z] Y`. -/
 @[simps]
 def gluing : Scheme.GlueData.{u} where
@@ -270,7 +313,9 @@ def gluing : Scheme.GlueData.{u} where
         category.assoc]
   cocycle i j k := cocycle 𝒰 f g i j k
 #align algebraic_geometry.Scheme.pullback.gluing AlgebraicGeometry.Scheme.Pullback.gluing
+-/
 
+#print AlgebraicGeometry.Scheme.Pullback.p1 /-
 /-- The first projection from the glued scheme into `X`. -/
 def p1 : (gluing 𝒰 f g).glued ⟶ X :=
   by
@@ -284,7 +329,9 @@ def p1 : (gluing 𝒰 f g).glued ⟶ X :=
   rw [category.assoc]
   exact (t_fst_fst _ _ _ _ _).symm
 #align algebraic_geometry.Scheme.pullback.p1 AlgebraicGeometry.Scheme.Pullback.p1
+-/
 
+#print AlgebraicGeometry.Scheme.Pullback.p2 /-
 /-- The second projection from the glued scheme into `Y`. -/
 def p2 : (gluing 𝒰 f g).glued ⟶ Y :=
   by
@@ -295,7 +342,9 @@ def p2 : (gluing 𝒰 f g).glued ⟶ Y :=
   rw [category.assoc]
   exact (t_fst_snd _ _ _ _ _).symm
 #align algebraic_geometry.Scheme.pullback.p2 AlgebraicGeometry.Scheme.Pullback.p2
+-/
 
+#print AlgebraicGeometry.Scheme.Pullback.p_comm /-
 theorem p_comm : p1 𝒰 f g ≫ f = p2 𝒰 f g ≫ g :=
   by
   apply multicoequalizer.hom_ext
@@ -303,9 +352,11 @@ theorem p_comm : p1 𝒰 f g ≫ f = p2 𝒰 f g ≫ g :=
   erw [multicoequalizer.π_desc_assoc, multicoequalizer.π_desc_assoc]
   rw [category.assoc, pullback.condition]
 #align algebraic_geometry.Scheme.pullback.p_comm AlgebraicGeometry.Scheme.Pullback.p_comm
+-/
 
 variable (s : PullbackCone f g)
 
+#print AlgebraicGeometry.Scheme.Pullback.gluedLiftPullbackMap /-
 /-- (Implementation)
 The canonical map `(s.X ×[X] Uᵢ) ×[s.X] (s.X ×[X] Uⱼ) ⟶ (Uᵢ ×[Z] Y) ×[X] Uⱼ`
 
@@ -324,7 +375,9 @@ def gluedLiftPullbackMap (i j : 𝒰.J) :
   · simpa using pullback.condition
   · simp only [category.comp_id, category.id_comp]
 #align algebraic_geometry.Scheme.pullback.glued_lift_pullback_map AlgebraicGeometry.Scheme.Pullback.gluedLiftPullbackMap
+-/
 
+#print AlgebraicGeometry.Scheme.Pullback.gluedLiftPullbackMap_fst /-
 @[reassoc]
 theorem gluedLiftPullbackMap_fst (i j : 𝒰.J) :
     gluedLiftPullbackMap 𝒰 f g s i j ≫ pullback.fst =
@@ -336,7 +389,9 @@ theorem gluedLiftPullbackMap_fst (i j : 𝒰.J) :
   simp only [category.assoc, id.def, pullback.lift_fst,
     pullback_right_pullback_fst_iso_hom_fst_assoc]
 #align algebraic_geometry.Scheme.pullback.glued_lift_pullback_map_fst AlgebraicGeometry.Scheme.Pullback.gluedLiftPullbackMap_fst
+-/
 
+#print AlgebraicGeometry.Scheme.Pullback.gluedLiftPullbackMap_snd /-
 @[reassoc]
 theorem gluedLiftPullbackMap_snd (i j : 𝒰.J) :
     gluedLiftPullbackMap 𝒰 f g s i j ≫ pullback.snd = pullback.snd ≫ pullback.snd :=
@@ -345,7 +400,9 @@ theorem gluedLiftPullbackMap_snd (i j : 𝒰.J) :
   simp only [category.assoc, category.comp_id, id.def, pullback.lift_snd,
     pullback_right_pullback_fst_iso_hom_snd]
 #align algebraic_geometry.Scheme.pullback.glued_lift_pullback_map_snd AlgebraicGeometry.Scheme.Pullback.gluedLiftPullbackMap_snd
+-/
 
+#print AlgebraicGeometry.Scheme.Pullback.gluedLift /-
 /-- The lifted map `s.X ⟶ (gluing 𝒰 f g).glued` in order to show that `(gluing 𝒰 f g).glued` is
 indeed the pullback.
 
@@ -381,7 +438,9 @@ def gluedLift : s.pt ⟶ (gluing 𝒰 f g).glued :=
     rw [pullback_symmetry_hom_comp_snd_assoc, pullback_symmetry_hom_comp_snd_assoc]
     exact pullback.condition_assoc _
 #align algebraic_geometry.Scheme.pullback.glued_lift AlgebraicGeometry.Scheme.Pullback.gluedLift
+-/
 
+#print AlgebraicGeometry.Scheme.Pullback.gluedLift_p1 /-
 theorem gluedLift_p1 : gluedLift 𝒰 f g s ≫ p1 𝒰 f g = s.fst :=
   by
   rw [← cancel_epi (𝒰.pullback_cover s.fst).fromGlued]
@@ -395,7 +454,9 @@ theorem gluedLift_p1 : gluedLift 𝒰 f g s ≫ p1 𝒰 f g = s.fst :=
   erw [multicoequalizer.π_desc, pullback.lift_fst_assoc, pullback.condition, category.comp_id]
   rw [pullback_symmetry_hom_comp_fst_assoc]
 #align algebraic_geometry.Scheme.pullback.glued_lift_p1 AlgebraicGeometry.Scheme.Pullback.gluedLift_p1
+-/
 
+#print AlgebraicGeometry.Scheme.Pullback.gluedLift_p2 /-
 theorem gluedLift_p2 : gluedLift 𝒰 f g s ≫ p2 𝒰 f g = s.snd :=
   by
   rw [← cancel_epi (𝒰.pullback_cover s.fst).fromGlued]
@@ -410,7 +471,9 @@ theorem gluedLift_p2 : gluedLift 𝒰 f g s ≫ p2 𝒰 f g = s.snd :=
   rw [pullback_symmetry_hom_comp_snd_assoc]
   rfl
 #align algebraic_geometry.Scheme.pullback.glued_lift_p2 AlgebraicGeometry.Scheme.Pullback.gluedLift_p2
+-/
 
+#print AlgebraicGeometry.Scheme.Pullback.pullbackFstιToV /-
 /-- (Implementation)
 The canonical map `(W ×[X] Uᵢ) ×[W] (Uⱼ ×[Z] Y) ⟶ (Uⱼ ×[Z] Y) ×[X] Uᵢ = V j i` where `W` is
 the glued fibred product.
@@ -422,7 +485,9 @@ def pullbackFstιToV (i j : 𝒰.J) :
   (pullbackSymmetry _ _ ≪≫ pullbackRightPullbackFstIso (p1 𝒰 f g) (𝒰.map i) _).Hom ≫
     (pullback.congrHom (Multicoequalizer.π_desc _ _ _ _ _) rfl).Hom
 #align algebraic_geometry.Scheme.pullback.pullback_fst_ι_to_V AlgebraicGeometry.Scheme.Pullback.pullbackFstιToV
+-/
 
+#print AlgebraicGeometry.Scheme.Pullback.pullbackFstιToV_fst /-
 @[simp, reassoc]
 theorem pullbackFstιToV_fst (i j : 𝒰.J) : pullbackFstιToV 𝒰 f g i j ≫ pullback.fst = pullback.snd :=
   by
@@ -430,7 +495,9 @@ theorem pullbackFstιToV_fst (i j : 𝒰.J) : pullbackFstιToV 𝒰 f g i j ≫
   simp only [iso.trans_hom, pullback.congr_hom_hom, category.assoc, pullback.lift_fst,
     category.comp_id, pullback_right_pullback_fst_iso_hom_fst, pullback_symmetry_hom_comp_fst]
 #align algebraic_geometry.Scheme.pullback.pullback_fst_ι_to_V_fst AlgebraicGeometry.Scheme.Pullback.pullbackFstιToV_fst
+-/
 
+#print AlgebraicGeometry.Scheme.Pullback.pullbackFstιToV_snd /-
 @[simp, reassoc]
 theorem pullbackFstιToV_snd (i j : 𝒰.J) :
     pullbackFstιToV 𝒰 f g i j ≫ pullback.snd = pullback.fst ≫ pullback.snd :=
@@ -439,7 +506,9 @@ theorem pullbackFstιToV_snd (i j : 𝒰.J) :
   simp only [iso.trans_hom, pullback.congr_hom_hom, category.assoc, pullback.lift_snd,
     category.comp_id, pullback_right_pullback_fst_iso_hom_snd, pullback_symmetry_hom_comp_snd_assoc]
 #align algebraic_geometry.Scheme.pullback.pullback_fst_ι_to_V_snd AlgebraicGeometry.Scheme.Pullback.pullbackFstιToV_snd
+-/
 
+#print AlgebraicGeometry.Scheme.Pullback.lift_comp_ι /-
 /-- We show that the map `W ×[X] Uᵢ ⟶ Uᵢ ×[Z] Y ⟶ W` is the first projection, where the
 first map is given by the lift of `W ×[X] Uᵢ ⟶ Uᵢ` and `W ×[X] Uᵢ ⟶ W ⟶ Y`.
 
@@ -469,7 +538,9 @@ theorem lift_comp_ι (i : 𝒰.J) :
     · simp only [pullback_fst_ι_to_V_fst]
     · simp only [pullback_fst_ι_to_V_fst]
 #align algebraic_geometry.Scheme.pullback.lift_comp_ι AlgebraicGeometry.Scheme.Pullback.lift_comp_ι
+-/
 
+#print AlgebraicGeometry.Scheme.Pullback.pullbackP1Iso /-
 /-- The canonical isomorphism between `W ×[X] Uᵢ` and `Uᵢ ×[X] Y`. That is, the preimage of `Uᵢ` in
 `W` along `p1` is indeed `Uᵢ ×[X] Y`. -/
 def pullbackP1Iso (i : 𝒰.J) : pullback (p1 𝒰 f g) (𝒰.map i) ≅ pullback (𝒰.map i ≫ f) g :=
@@ -487,37 +558,49 @@ def pullbackP1Iso (i : 𝒰.J) : pullback (p1 𝒰 f g) (𝒰.map i) ≅ pullbac
     · simp only [category.assoc, pullback.lift_snd, pullback.lift_fst_assoc, category.id_comp]
       erw [multicoequalizer.π_desc]
 #align algebraic_geometry.Scheme.pullback.pullback_p1_iso AlgebraicGeometry.Scheme.Pullback.pullbackP1Iso
+-/
 
+#print AlgebraicGeometry.Scheme.Pullback.pullbackP1Iso_hom_fst /-
 @[simp, reassoc]
 theorem pullbackP1Iso_hom_fst (i : 𝒰.J) :
     (pullbackP1Iso 𝒰 f g i).Hom ≫ pullback.fst = pullback.snd := by delta pullback_p1_iso;
   simp only [pullback.lift_fst]
 #align algebraic_geometry.Scheme.pullback.pullback_p1_iso_hom_fst AlgebraicGeometry.Scheme.Pullback.pullbackP1Iso_hom_fst
+-/
 
+#print AlgebraicGeometry.Scheme.Pullback.pullbackP1Iso_hom_snd /-
 @[simp, reassoc]
 theorem pullbackP1Iso_hom_snd (i : 𝒰.J) :
     (pullbackP1Iso 𝒰 f g i).Hom ≫ pullback.snd = pullback.fst ≫ p2 𝒰 f g := by
   delta pullback_p1_iso; simp only [pullback.lift_snd]
 #align algebraic_geometry.Scheme.pullback.pullback_p1_iso_hom_snd AlgebraicGeometry.Scheme.Pullback.pullbackP1Iso_hom_snd
+-/
 
+#print AlgebraicGeometry.Scheme.Pullback.pullbackP1Iso_inv_fst /-
 @[simp, reassoc]
 theorem pullbackP1Iso_inv_fst (i : 𝒰.J) :
     (pullbackP1Iso 𝒰 f g i).inv ≫ pullback.fst = (gluing 𝒰 f g).ι i := by delta pullback_p1_iso;
   simp only [pullback.lift_fst]
 #align algebraic_geometry.Scheme.pullback.pullback_p1_iso_inv_fst AlgebraicGeometry.Scheme.Pullback.pullbackP1Iso_inv_fst
+-/
 
+#print AlgebraicGeometry.Scheme.Pullback.pullbackP1Iso_inv_snd /-
 @[simp, reassoc]
 theorem pullbackP1Iso_inv_snd (i : 𝒰.J) :
     (pullbackP1Iso 𝒰 f g i).inv ≫ pullback.snd = pullback.fst := by delta pullback_p1_iso;
   simp only [pullback.lift_snd]
 #align algebraic_geometry.Scheme.pullback.pullback_p1_iso_inv_snd AlgebraicGeometry.Scheme.Pullback.pullbackP1Iso_inv_snd
+-/
 
+#print AlgebraicGeometry.Scheme.Pullback.pullbackP1Iso_hom_ι /-
 @[simp, reassoc]
 theorem pullbackP1Iso_hom_ι (i : 𝒰.J) :
     (pullbackP1Iso 𝒰 f g i).Hom ≫ (gluing 𝒰 f g).ι i = pullback.fst := by
   rw [← pullback_p1_iso_inv_fst, iso.hom_inv_id_assoc]
 #align algebraic_geometry.Scheme.pullback.pullback_p1_iso_hom_ι AlgebraicGeometry.Scheme.Pullback.pullbackP1Iso_hom_ι
+-/
 
+#print AlgebraicGeometry.Scheme.Pullback.gluedIsLimit /-
 /-- The glued scheme (`(gluing 𝒰 f g).glued`) is indeed the pullback of `f` and `g`. -/
 def gluedIsLimit : IsLimit (PullbackCone.mk _ _ (p_comm 𝒰 f g)) :=
   by
@@ -550,11 +633,15 @@ def gluedIsLimit : IsLimit (PullbackCone.mk _ _ (p_comm 𝒰 f g)) :=
       pullback_symmetry_hom_comp_snd_assoc, pullback.lift_snd]
     rw [← pullback.condition_assoc, h₂]
 #align algebraic_geometry.Scheme.pullback.glued_is_limit AlgebraicGeometry.Scheme.Pullback.gluedIsLimit
+-/
 
+#print AlgebraicGeometry.Scheme.Pullback.hasPullback_of_cover /-
 theorem hasPullback_of_cover : HasPullback f g :=
   ⟨⟨⟨_, gluedIsLimit 𝒰 f g⟩⟩⟩
 #align algebraic_geometry.Scheme.pullback.has_pullback_of_cover AlgebraicGeometry.Scheme.Pullback.hasPullback_of_cover
+-/
 
+#print AlgebraicGeometry.Scheme.Pullback.affine_hasPullback /-
 instance affine_hasPullback {A B C : CommRingCat}
     (f : Spec.obj (Opposite.op A) ⟶ Spec.obj (Opposite.op C))
     (g : Spec.obj (Opposite.op B) ⟶ Spec.obj (Opposite.op C)) : HasPullback f g :=
@@ -563,20 +650,28 @@ instance affine_hasPullback {A B C : CommRingCat}
   exact
     ⟨⟨⟨_, is_limit_of_has_pullback_of_preserves_limit Spec (Spec.preimage f) (Spec.preimage g)⟩⟩⟩
 #align algebraic_geometry.Scheme.pullback.affine_has_pullback AlgebraicGeometry.Scheme.Pullback.affine_hasPullback
+-/
 
+#print AlgebraicGeometry.Scheme.Pullback.affine_affine_hasPullback /-
 theorem affine_affine_hasPullback {B C : CommRingCat} {X : Scheme}
     (f : X ⟶ Spec.obj (Opposite.op C)) (g : Spec.obj (Opposite.op B) ⟶ Spec.obj (Opposite.op C)) :
     HasPullback f g :=
   hasPullback_of_cover X.affineCover f g
 #align algebraic_geometry.Scheme.pullback.affine_affine_has_pullback AlgebraicGeometry.Scheme.Pullback.affine_affine_hasPullback
+-/
 
+#print AlgebraicGeometry.Scheme.Pullback.base_affine_hasPullback /-
 instance base_affine_hasPullback {C : CommRingCat} {X Y : Scheme} (f : X ⟶ Spec.obj (Opposite.op C))
     (g : Y ⟶ Spec.obj (Opposite.op C)) : HasPullback f g :=
   @hasPullback_symmetry _ _ _
     (@hasPullback_of_cover Y.affineCover g f fun i =>
       @hasPullback_symmetry _ _ _ <| affine_affine_hasPullback _ _)
 #align algebraic_geometry.Scheme.pullback.base_affine_has_pullback AlgebraicGeometry.Scheme.Pullback.base_affine_hasPullback
+-/
 
+/- warning: algebraic_geometry.Scheme.pullback.left_affine_comp_pullback_has_pullback clashes with algebraic_geometry.Scheme.pullback.left_affine_comp_pullback_HasPullback -> AlgebraicGeometry.Scheme.Pullback.left_affine_comp_pullback_hasPullback
+Case conversion may be inaccurate. Consider using '#align algebraic_geometry.Scheme.pullback.left_affine_comp_pullback_has_pullback AlgebraicGeometry.Scheme.Pullback.left_affine_comp_pullback_hasPullbackₓ'. -/
+#print AlgebraicGeometry.Scheme.Pullback.left_affine_comp_pullback_hasPullback /-
 instance left_affine_comp_pullback_hasPullback {X Y Z : Scheme} (f : X ⟶ Z) (g : Y ⟶ Z)
     (i : Z.affineCover.J) : HasPullback ((Z.affineCover.pullbackCover f).map i ≫ f) g :=
   by
@@ -592,6 +687,7 @@ instance left_affine_comp_pullback_hasPullback {X Y Z : Scheme} (f : X ⟶ Z) (g
   rw [← pullback.condition] at this 
   exact this
 #align algebraic_geometry.Scheme.pullback.left_affine_comp_pullback_has_pullback AlgebraicGeometry.Scheme.Pullback.left_affine_comp_pullback_hasPullback
+-/
 
 instance {X Y Z : Scheme} (f : X ⟶ Z) (g : Y ⟶ Z) : HasPullback f g :=
   hasPullback_of_cover (Z.affineCover.pullbackCover f) f g
@@ -607,6 +703,7 @@ instance {X Y Z : Scheme} (f : X ⟶ Z) (g : Y ⟶ Z) [IsAffine X] [IsAffine Y]
         (ΓSpec.adjunction.Unit.naturality f) (ΓSpec.adjunction.Unit.naturality g) ≫
       (PreservesPullback.iso Spec _ _).inv)
 
+#print AlgebraicGeometry.Scheme.Pullback.openCoverOfLeft /-
 /-- Given an open cover `{ Xᵢ }` of `X`, then `X ×[Z] Y` is covered by `Xᵢ ×[Z] Y`. -/
 @[simps J obj map]
 def openCoverOfLeft (𝒰 : OpenCover X) (f : X ⟶ Z) (g : Y ⟶ Z) : OpenCover (pullback f g) :=
@@ -628,7 +725,9 @@ def openCoverOfLeft (𝒰 : OpenCover X) (f : X ⟶ Z) (g : Y ⟶ Z) : OpenCover
     symm
     exact multicoequalizer.π_desc _ _ _ _ _
 #align algebraic_geometry.Scheme.pullback.open_cover_of_left AlgebraicGeometry.Scheme.Pullback.openCoverOfLeft
+-/
 
+#print AlgebraicGeometry.Scheme.Pullback.openCoverOfRight /-
 /-- Given an open cover `{ Yᵢ }` of `Y`, then `X ×[Z] Y` is covered by `X ×[Z] Yᵢ`. -/
 @[simps J obj map]
 def openCoverOfRight (𝒰 : OpenCover Y) (f : X ⟶ Z) (g : Y ⟶ Z) : OpenCover (pullback f g) :=
@@ -642,7 +741,9 @@ def openCoverOfRight (𝒰 : OpenCover Y) (f : X ⟶ Z) (g : Y ⟶ Z) : OpenCove
   dsimp [open_cover.bind]
   apply pullback.hom_ext <;> simp
 #align algebraic_geometry.Scheme.pullback.open_cover_of_right AlgebraicGeometry.Scheme.Pullback.openCoverOfRight
+-/
 
+#print AlgebraicGeometry.Scheme.Pullback.openCoverOfLeftRight /-
 /-- Given an open cover `{ Xᵢ }` of `X` and an open cover `{ Yⱼ }` of `Y`, then
 `X ×[Z] Y` is covered by `Xᵢ ×[Z] Yⱼ`. -/
 @[simps J obj map]
@@ -659,7 +760,9 @@ def openCoverOfLeftRight (𝒰X : X.OpenCover) (𝒰Y : Y.OpenCover) (f : X ⟶
   rintro ⟨i, j⟩
   apply pullback.hom_ext <;> simpa
 #align algebraic_geometry.Scheme.pullback.open_cover_of_left_right AlgebraicGeometry.Scheme.Pullback.openCoverOfLeftRight
+-/
 
+#print AlgebraicGeometry.Scheme.Pullback.openCoverOfBase' /-
 /-- (Implementation). Use `open_cover_of_base` instead. -/
 def openCoverOfBase' (𝒰 : OpenCover Z) (f : X ⟶ Z) (g : Y ⟶ Z) : OpenCover (pullback f g) :=
   by
@@ -681,7 +784,9 @@ def openCoverOfBase' (𝒰 : OpenCover Z) (f : X ⟶ Z) (g : Y ⟶ Z) : OpenCove
   · simp only [category.comp_id, category.id_comp]
   infer_instance
 #align algebraic_geometry.Scheme.pullback.open_cover_of_base' AlgebraicGeometry.Scheme.Pullback.openCoverOfBase'
+-/
 
+#print AlgebraicGeometry.Scheme.Pullback.openCoverOfBase /-
 /-- Given an open cover `{ Zᵢ }` of `Z`, then `X ×[Z] Y` is covered by `Xᵢ ×[Zᵢ] Yᵢ`, where
   `Xᵢ = X ×[Z] Zᵢ` and `Yᵢ = Y ×[Z] Zᵢ` is the preimage of `Zᵢ` in `X` and `Y`. -/
 @[simps J obj map]
@@ -706,6 +811,7 @@ def openCoverOfBase (𝒰 : OpenCover Z) (f : X ⟶ Z) (g : Y ⟶ Z) : OpenCover
       pullback.lift_fst, limit.iso_limit_cone_inv_π, pullback_cone.mk_π_app_right,
       pullback_symmetry_hom_comp_fst_assoc, pullback.lift_snd]
 #align algebraic_geometry.Scheme.pullback.open_cover_of_base AlgebraicGeometry.Scheme.Pullback.openCoverOfBase
+-/
 
 end Pullback

7316286f

bump to nightly-2023-06-22-19

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

d370f1be

Diff

@@ -715,8 +715,8 @@ namespace AlgebraicGeometry
 
 instance {X Y S X' Y' S' : Scheme} (f : X ⟶ S) (g : Y ⟶ S) (f' : X' ⟶ S') (g' : Y' ⟶ S')
     (i₁ : X ⟶ X') (i₂ : Y ⟶ Y') (i₃ : S ⟶ S') (e₁ : f ≫ i₃ = i₁ ≫ f') (e₂ : g ≫ i₃ = i₂ ≫ g')
-    [IsOpenImmersion i₁] [IsOpenImmersion i₂] [Mono i₃] :
-    IsOpenImmersion (pullback.map f g f' g' i₁ i₂ i₃ e₁ e₂) :=
+    [IsOpenImmersionCat i₁] [IsOpenImmersionCat i₂] [Mono i₃] :
+    IsOpenImmersionCat (pullback.map f g f' g' i₁ i₂ i₃ e₁ e₂) :=
   by
   rw [pullback_map_eq_pullback_fst_fst_iso_inv]
   infer_instance

7316286f

bump to nightly-2023-06-18-23

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

3b5e23dc

Diff

@@ -556,8 +556,8 @@ theorem hasPullback_of_cover : HasPullback f g :=
 #align algebraic_geometry.Scheme.pullback.has_pullback_of_cover AlgebraicGeometry.Scheme.Pullback.hasPullback_of_cover
 
 instance affine_hasPullback {A B C : CommRingCat}
-    (f : spec.obj (Opposite.op A) ⟶ spec.obj (Opposite.op C))
-    (g : spec.obj (Opposite.op B) ⟶ spec.obj (Opposite.op C)) : HasPullback f g :=
+    (f : Spec.obj (Opposite.op A) ⟶ Spec.obj (Opposite.op C))
+    (g : Spec.obj (Opposite.op B) ⟶ Spec.obj (Opposite.op C)) : HasPullback f g :=
   by
   rw [← Spec.image_preimage f, ← Spec.image_preimage g]
   exact
@@ -565,13 +565,13 @@ instance affine_hasPullback {A B C : CommRingCat}
 #align algebraic_geometry.Scheme.pullback.affine_has_pullback AlgebraicGeometry.Scheme.Pullback.affine_hasPullback
 
 theorem affine_affine_hasPullback {B C : CommRingCat} {X : Scheme}
-    (f : X ⟶ spec.obj (Opposite.op C)) (g : spec.obj (Opposite.op B) ⟶ spec.obj (Opposite.op C)) :
+    (f : X ⟶ Spec.obj (Opposite.op C)) (g : Spec.obj (Opposite.op B) ⟶ Spec.obj (Opposite.op C)) :
     HasPullback f g :=
   hasPullback_of_cover X.affineCover f g
 #align algebraic_geometry.Scheme.pullback.affine_affine_has_pullback AlgebraicGeometry.Scheme.Pullback.affine_affine_hasPullback
 
-instance base_affine_hasPullback {C : CommRingCat} {X Y : Scheme} (f : X ⟶ spec.obj (Opposite.op C))
-    (g : Y ⟶ spec.obj (Opposite.op C)) : HasPullback f g :=
+instance base_affine_hasPullback {C : CommRingCat} {X Y : Scheme} (f : X ⟶ Spec.obj (Opposite.op C))
+    (g : Y ⟶ Spec.obj (Opposite.op C)) : HasPullback f g :=
   @hasPullback_symmetry _ _ _
     (@hasPullback_of_cover Y.affineCover g f fun i =>
       @hasPullback_symmetry _ _ _ <| affine_affine_hasPullback _ _)
@@ -601,11 +601,11 @@ instance : HasPullbacks Scheme :=
 
 instance {X Y Z : Scheme} (f : X ⟶ Z) (g : Y ⟶ Z) [IsAffine X] [IsAffine Y] [IsAffine Z] :
     IsAffine (pullback f g) :=
-  isAffine_of_iso
-    (pullback.map f g (spec.map (Γ.map f.op).op) (spec.map (Γ.map g.op).op)
+  isAffineOfIso
+    (pullback.map f g (Spec.map (Γ.map f.op).op) (Spec.map (Γ.map g.op).op)
         (ΓSpec.adjunction.Unit.app X) (ΓSpec.adjunction.Unit.app Y) (ΓSpec.adjunction.Unit.app Z)
         (ΓSpec.adjunction.Unit.naturality f) (ΓSpec.adjunction.Unit.naturality g) ≫
-      (PreservesPullback.iso spec _ _).inv)
+      (PreservesPullback.iso Spec _ _).inv)
 
 /-- Given an open cover `{ Xᵢ }` of `X`, then `X ×[Z] Y` is covered by `Xᵢ ×[Z] Y`. -/
 @[simps J obj map]

7316286f

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -525,8 +525,8 @@ def gluedIsLimit : IsLimit (PullbackCone.mk _ _ (p_comm 𝒰 f g)) :=
   intro s
   refine' ⟨glued_lift 𝒰 f g s, glued_lift_p1 𝒰 f g s, glued_lift_p2 𝒰 f g s, _⟩
   intro m h₁ h₂
-  change m ≫ p1 𝒰 f g = _ at h₁
-  change m ≫ p2 𝒰 f g = _ at h₂
+  change m ≫ p1 𝒰 f g = _ at h₁ 
+  change m ≫ p2 𝒰 f g = _ at h₂ 
   apply (𝒰.pullback_cover s.fst).hom_ext
   intro i
   rw [open_cover.pullback_cover_map]
@@ -589,7 +589,7 @@ instance left_affine_comp_pullback_hasPullback {X Y Z : Scheme} (f : X ⟶ Z) (g
       pullback.condition.symm (pullback_cone.flip_is_limit <| pullback_is_pullback _ _)
       (pullback_cone.flip_is_limit <| pullback_is_pullback _ _)
   have : has_pullback (pullback.snd ≫ Z.affine_cover.map i : Xᵢ ⟶ _) g := ⟨⟨⟨_, this⟩⟩⟩
-  rw [← pullback.condition] at this
+  rw [← pullback.condition] at this 
   exact this
 #align algebraic_geometry.Scheme.pullback.left_affine_comp_pullback_has_pullback AlgebraicGeometry.Scheme.Pullback.left_affine_comp_pullback_hasPullback

7316286f

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -100,11 +100,9 @@ theorem t_id (i : 𝒰.J) : t 𝒰 f g i i = 𝟙 _ :=
   by
   apply pullback.hom_ext <;> rw [category.id_comp]
   apply pullback.hom_ext
-  · rw [← cancel_mono (𝒰.map i)]
-    simp only [pullback.condition, category.assoc, t_fst_fst]
+  · rw [← cancel_mono (𝒰.map i)]; simp only [pullback.condition, category.assoc, t_fst_fst]
   · simp only [category.assoc, t_fst_snd]
-  · rw [← cancel_mono (𝒰.map i)]
-    simp only [pullback.condition, t_snd, category.assoc]
+  · rw [← cancel_mono (𝒰.map i)]; simp only [pullback.condition, t_snd, category.assoc]
 #align algebraic_geometry.Scheme.pullback.t_id AlgebraicGeometry.Scheme.Pullback.t_id
 
 /-- The inclusion map of `V i j = (Uᵢ ×[Z] Y) ×[X] Uⱼ ⟶ Uᵢ ×[Z] Y`-/
@@ -492,33 +490,25 @@ def pullbackP1Iso (i : 𝒰.J) : pullback (p1 𝒰 f g) (𝒰.map i) ≅ pullbac
 
 @[simp, reassoc]
 theorem pullbackP1Iso_hom_fst (i : 𝒰.J) :
-    (pullbackP1Iso 𝒰 f g i).Hom ≫ pullback.fst = pullback.snd :=
-  by
-  delta pullback_p1_iso
+    (pullbackP1Iso 𝒰 f g i).Hom ≫ pullback.fst = pullback.snd := by delta pullback_p1_iso;
   simp only [pullback.lift_fst]
 #align algebraic_geometry.Scheme.pullback.pullback_p1_iso_hom_fst AlgebraicGeometry.Scheme.Pullback.pullbackP1Iso_hom_fst
 
 @[simp, reassoc]
 theorem pullbackP1Iso_hom_snd (i : 𝒰.J) :
-    (pullbackP1Iso 𝒰 f g i).Hom ≫ pullback.snd = pullback.fst ≫ p2 𝒰 f g :=
-  by
-  delta pullback_p1_iso
-  simp only [pullback.lift_snd]
+    (pullbackP1Iso 𝒰 f g i).Hom ≫ pullback.snd = pullback.fst ≫ p2 𝒰 f g := by
+  delta pullback_p1_iso; simp only [pullback.lift_snd]
 #align algebraic_geometry.Scheme.pullback.pullback_p1_iso_hom_snd AlgebraicGeometry.Scheme.Pullback.pullbackP1Iso_hom_snd
 
 @[simp, reassoc]
 theorem pullbackP1Iso_inv_fst (i : 𝒰.J) :
-    (pullbackP1Iso 𝒰 f g i).inv ≫ pullback.fst = (gluing 𝒰 f g).ι i :=
-  by
-  delta pullback_p1_iso
+    (pullbackP1Iso 𝒰 f g i).inv ≫ pullback.fst = (gluing 𝒰 f g).ι i := by delta pullback_p1_iso;
   simp only [pullback.lift_fst]
 #align algebraic_geometry.Scheme.pullback.pullback_p1_iso_inv_fst AlgebraicGeometry.Scheme.Pullback.pullbackP1Iso_inv_fst
 
 @[simp, reassoc]
 theorem pullbackP1Iso_inv_snd (i : 𝒰.J) :
-    (pullbackP1Iso 𝒰 f g i).inv ≫ pullback.snd = pullback.fst :=
-  by
-  delta pullback_p1_iso
+    (pullbackP1Iso 𝒰 f g i).inv ≫ pullback.snd = pullback.fst := by delta pullback_p1_iso;
   simp only [pullback.lift_snd]
 #align algebraic_geometry.Scheme.pullback.pullback_p1_iso_inv_snd AlgebraicGeometry.Scheme.Pullback.pullbackP1Iso_inv_snd
 
@@ -548,8 +538,7 @@ def gluedIsLimit : IsLimit (PullbackCone.mk _ _ (p_comm 𝒰 f g)) :=
     iso.trans_hom, category.assoc, pullback.congr_hom_hom, pullback.lift_fst_assoc,
     category.comp_id, pullback_right_pullback_fst_iso_hom_fst_assoc, pullback.condition]
   trans pullback.snd ≫ (pullback_p1_iso 𝒰 f g _).Hom ≫ (gluing 𝒰 f g).ι _
-  · congr 1
-    rw [← pullback_p1_iso_hom_ι]
+  · congr 1; rw [← pullback_p1_iso_hom_ι]
   simp_rw [← category.assoc]
   congr 1
   apply pullback.hom_ext

7316286f

bump to nightly-2023-05-23-03

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

ed98987c

Diff

@@ -68,7 +68,7 @@ def t (i j : 𝒰.J) : v 𝒰 f g i j ⟶ v 𝒰 f g j i :=
   rw [category.comp_id, category.id_comp]
 #align algebraic_geometry.Scheme.pullback.t AlgebraicGeometry.Scheme.Pullback.t
 
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem t_fst_fst (i j : 𝒰.J) : t 𝒰 f g i j ≫ pullback.fst ≫ pullback.fst = pullback.snd :=
   by
   delta t
@@ -77,7 +77,7 @@ theorem t_fst_fst (i j : 𝒰.J) : t 𝒰 f g i j ≫ pullback.fst ≫ pullback.
     pullback_assoc_inv_fst_fst, pullback_symmetry_hom_comp_fst]
 #align algebraic_geometry.Scheme.pullback.t_fst_fst AlgebraicGeometry.Scheme.Pullback.t_fst_fst
 
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem t_fst_snd (i j : 𝒰.J) :
     t 𝒰 f g i j ≫ pullback.fst ≫ pullback.snd = pullback.fst ≫ pullback.snd :=
   by
@@ -87,7 +87,7 @@ theorem t_fst_snd (i j : 𝒰.J) :
     pullback_assoc_inv_snd]
 #align algebraic_geometry.Scheme.pullback.t_fst_snd AlgebraicGeometry.Scheme.Pullback.t_fst_snd
 
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem t_snd (i j : 𝒰.J) : t 𝒰 f g i j ≫ pullback.snd = pullback.fst ≫ pullback.fst :=
   by
   delta t
@@ -129,7 +129,7 @@ section
 
 end
 
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem t'_fst_fst_fst (i j k : 𝒰.J) :
     t' 𝒰 f g i j k ≫ pullback.fst ≫ pullback.fst ≫ pullback.fst = pullback.fst ≫ pullback.snd :=
   by
@@ -139,7 +139,7 @@ theorem t'_fst_fst_fst (i j k : 𝒰.J) :
     pullback_right_pullback_fst_iso_hom_fst_assoc]
 #align algebraic_geometry.Scheme.pullback.t'_fst_fst_fst AlgebraicGeometry.Scheme.Pullback.t'_fst_fst_fst
 
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem t'_fst_fst_snd (i j k : 𝒰.J) :
     t' 𝒰 f g i j k ≫ pullback.fst ≫ pullback.fst ≫ pullback.snd =
       pullback.fst ≫ pullback.fst ≫ pullback.snd :=
@@ -150,7 +150,7 @@ theorem t'_fst_fst_snd (i j k : 𝒰.J) :
     pullback_right_pullback_fst_iso_hom_fst_assoc]
 #align algebraic_geometry.Scheme.pullback.t'_fst_fst_snd AlgebraicGeometry.Scheme.Pullback.t'_fst_fst_snd
 
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem t'_fst_snd (i j k : 𝒰.J) :
     t' 𝒰 f g i j k ≫ pullback.fst ≫ pullback.snd = pullback.snd ≫ pullback.snd :=
   by
@@ -160,7 +160,7 @@ theorem t'_fst_snd (i j k : 𝒰.J) :
     pullback_right_pullback_fst_iso_hom_snd]
 #align algebraic_geometry.Scheme.pullback.t'_fst_snd AlgebraicGeometry.Scheme.Pullback.t'_fst_snd
 
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem t'_snd_fst_fst (i j k : 𝒰.J) :
     t' 𝒰 f g i j k ≫ pullback.snd ≫ pullback.fst ≫ pullback.fst = pullback.fst ≫ pullback.snd :=
   by
@@ -170,7 +170,7 @@ theorem t'_snd_fst_fst (i j k : 𝒰.J) :
     pullback_right_pullback_fst_iso_hom_fst_assoc]
 #align algebraic_geometry.Scheme.pullback.t'_snd_fst_fst AlgebraicGeometry.Scheme.Pullback.t'_snd_fst_fst
 
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem t'_snd_fst_snd (i j k : 𝒰.J) :
     t' 𝒰 f g i j k ≫ pullback.snd ≫ pullback.fst ≫ pullback.snd =
       pullback.fst ≫ pullback.fst ≫ pullback.snd :=
@@ -181,7 +181,7 @@ theorem t'_snd_fst_snd (i j k : 𝒰.J) :
     pullback_right_pullback_fst_iso_hom_fst_assoc]
 #align algebraic_geometry.Scheme.pullback.t'_snd_fst_snd AlgebraicGeometry.Scheme.Pullback.t'_snd_fst_snd
 
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem t'_snd_snd (i j k : 𝒰.J) :
     t' 𝒰 f g i j k ≫ pullback.snd ≫ pullback.snd = pullback.fst ≫ pullback.fst ≫ pullback.fst :=
   by
@@ -327,7 +327,7 @@ def gluedLiftPullbackMap (i j : 𝒰.J) :
   · simp only [category.comp_id, category.id_comp]
 #align algebraic_geometry.Scheme.pullback.glued_lift_pullback_map AlgebraicGeometry.Scheme.Pullback.gluedLiftPullbackMap
 
-@[reassoc.1]
+@[reassoc]
 theorem gluedLiftPullbackMap_fst (i j : 𝒰.J) :
     gluedLiftPullbackMap 𝒰 f g s i j ≫ pullback.fst =
       pullback.fst ≫
@@ -339,7 +339,7 @@ theorem gluedLiftPullbackMap_fst (i j : 𝒰.J) :
     pullback_right_pullback_fst_iso_hom_fst_assoc]
 #align algebraic_geometry.Scheme.pullback.glued_lift_pullback_map_fst AlgebraicGeometry.Scheme.Pullback.gluedLiftPullbackMap_fst
 
-@[reassoc.1]
+@[reassoc]
 theorem gluedLiftPullbackMap_snd (i j : 𝒰.J) :
     gluedLiftPullbackMap 𝒰 f g s i j ≫ pullback.snd = pullback.snd ≫ pullback.snd :=
   by
@@ -425,7 +425,7 @@ def pullbackFstιToV (i j : 𝒰.J) :
     (pullback.congrHom (Multicoequalizer.π_desc _ _ _ _ _) rfl).Hom
 #align algebraic_geometry.Scheme.pullback.pullback_fst_ι_to_V AlgebraicGeometry.Scheme.Pullback.pullbackFstιToV
 
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem pullbackFstιToV_fst (i j : 𝒰.J) : pullbackFstιToV 𝒰 f g i j ≫ pullback.fst = pullback.snd :=
   by
   delta pullback_fst_ι_to_V
@@ -433,7 +433,7 @@ theorem pullbackFstιToV_fst (i j : 𝒰.J) : pullbackFstιToV 𝒰 f g i j ≫
     category.comp_id, pullback_right_pullback_fst_iso_hom_fst, pullback_symmetry_hom_comp_fst]
 #align algebraic_geometry.Scheme.pullback.pullback_fst_ι_to_V_fst AlgebraicGeometry.Scheme.Pullback.pullbackFstιToV_fst
 
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem pullbackFstιToV_snd (i j : 𝒰.J) :
     pullbackFstιToV 𝒰 f g i j ≫ pullback.snd = pullback.fst ≫ pullback.snd :=
   by
@@ -490,7 +490,7 @@ def pullbackP1Iso (i : 𝒰.J) : pullback (p1 𝒰 f g) (𝒰.map i) ≅ pullbac
       erw [multicoequalizer.π_desc]
 #align algebraic_geometry.Scheme.pullback.pullback_p1_iso AlgebraicGeometry.Scheme.Pullback.pullbackP1Iso
 
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem pullbackP1Iso_hom_fst (i : 𝒰.J) :
     (pullbackP1Iso 𝒰 f g i).Hom ≫ pullback.fst = pullback.snd :=
   by
@@ -498,7 +498,7 @@ theorem pullbackP1Iso_hom_fst (i : 𝒰.J) :
   simp only [pullback.lift_fst]
 #align algebraic_geometry.Scheme.pullback.pullback_p1_iso_hom_fst AlgebraicGeometry.Scheme.Pullback.pullbackP1Iso_hom_fst
 
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem pullbackP1Iso_hom_snd (i : 𝒰.J) :
     (pullbackP1Iso 𝒰 f g i).Hom ≫ pullback.snd = pullback.fst ≫ p2 𝒰 f g :=
   by
@@ -506,7 +506,7 @@ theorem pullbackP1Iso_hom_snd (i : 𝒰.J) :
   simp only [pullback.lift_snd]
 #align algebraic_geometry.Scheme.pullback.pullback_p1_iso_hom_snd AlgebraicGeometry.Scheme.Pullback.pullbackP1Iso_hom_snd
 
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem pullbackP1Iso_inv_fst (i : 𝒰.J) :
     (pullbackP1Iso 𝒰 f g i).inv ≫ pullback.fst = (gluing 𝒰 f g).ι i :=
   by
@@ -514,7 +514,7 @@ theorem pullbackP1Iso_inv_fst (i : 𝒰.J) :
   simp only [pullback.lift_fst]
 #align algebraic_geometry.Scheme.pullback.pullback_p1_iso_inv_fst AlgebraicGeometry.Scheme.Pullback.pullbackP1Iso_inv_fst
 
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem pullbackP1Iso_inv_snd (i : 𝒰.J) :
     (pullbackP1Iso 𝒰 f g i).inv ≫ pullback.snd = pullback.fst :=
   by
@@ -522,7 +522,7 @@ theorem pullbackP1Iso_inv_snd (i : 𝒰.J) :
   simp only [pullback.lift_snd]
 #align algebraic_geometry.Scheme.pullback.pullback_p1_iso_inv_snd AlgebraicGeometry.Scheme.Pullback.pullbackP1Iso_inv_snd
 
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem pullbackP1Iso_hom_ι (i : 𝒰.J) :
     (pullbackP1Iso 𝒰 f g i).Hom ≫ (gluing 𝒰 f g).ι i = pullback.fst := by
   rw [← pullback_p1_iso_inv_fst, iso.hom_inv_id_assoc]

7316286f

bump to nightly-2023-04-27-04

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

8f775de7

Diff

@@ -612,7 +612,7 @@ instance : HasPullbacks Scheme :=
 
 instance {X Y Z : Scheme} (f : X ⟶ Z) (g : Y ⟶ Z) [IsAffine X] [IsAffine Y] [IsAffine Z] :
     IsAffine (pullback f g) :=
-  isAffineOfIso
+  isAffine_of_iso
     (pullback.map f g (spec.map (Γ.map f.op).op) (spec.map (Γ.map g.op).op)
         (ΓSpec.adjunction.Unit.app X) (ΓSpec.adjunction.Unit.app Y) (ΓSpec.adjunction.Unit.app Z)
         (ΓSpec.adjunction.Unit.naturality f) (ΓSpec.adjunction.Unit.naturality g) ≫

7316286f

bump to nightly-2023-03-23-20

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

53b827ba

Diff

@@ -422,7 +422,7 @@ def pullbackFstιToV (i j : 𝒰.J) :
     pullback (pullback.fst : pullback (p1 𝒰 f g) (𝒰.map i) ⟶ _) ((gluing 𝒰 f g).ι j) ⟶
       v 𝒰 f g j i :=
   (pullbackSymmetry _ _ ≪≫ pullbackRightPullbackFstIso (p1 𝒰 f g) (𝒰.map i) _).Hom ≫
-    (pullback.congrHom (multicoequalizer.π_desc _ _ _ _ _) rfl).Hom
+    (pullback.congrHom (Multicoequalizer.π_desc _ _ _ _ _) rfl).Hom
 #align algebraic_geometry.Scheme.pullback.pullback_fst_ι_to_V AlgebraicGeometry.Scheme.Pullback.pullbackFstιToV
 
 @[simp, reassoc.1]

7316286f

bump to nightly-2023-02-28-22

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

1fb1623f

Diff

@@ -358,7 +358,7 @@ to glue these into a map `s.X ⟶ Uᵢ ×[Z] Y`, we need to show that the maps a
 `(s.fst ⁻¹' Uᵢ) ×[s.X] (s.fst ⁻¹' Uⱼ) ⟶ Uᵢ ×[Z] Y`. This is achieved by showing that both of these
 maps factors through `glued_lift_pullback_map`.
 -/
-def gluedLift : s.x ⟶ (gluing 𝒰 f g).glued :=
+def gluedLift : s.pt ⟶ (gluing 𝒰 f g).glued :=
   by
   fapply (𝒰.pullback_cover s.fst).glueMorphisms
   ·

7316286f

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

7316286f

chore: adapt to multiple goal linter 2 (#12361)

A PR analogous to #12338: reformatting proofs following the multiple goals linter of #12339.

fe96aa45

Diff

@@ -59,8 +59,8 @@ def t (i j : 𝒰.J) : v 𝒰 f g i j ⟶ v 𝒰 f g j i := by
   refine' _ ≫ (pullbackSymmetry _ _).hom
   refine' _ ≫ (pullbackAssoc _ _ _ _).hom
   refine' pullback.map _ _ _ _ (pullbackSymmetry _ _).hom (𝟙 _) (𝟙 _) _ _
-  rw [pullbackSymmetry_hom_comp_snd_assoc, pullback.condition_assoc, Category.comp_id]
-  rw [Category.comp_id, Category.id_comp]
+  · rw [pullbackSymmetry_hom_comp_snd_assoc, pullback.condition_assoc, Category.comp_id]
+  · rw [Category.comp_id, Category.id_comp]
 #align algebraic_geometry.Scheme.pullback.t AlgebraicGeometry.Scheme.Pullback.t
 
 @[simp, reassoc]
@@ -105,9 +105,9 @@ theorem t_snd (i j : 𝒰.J) : t 𝒰 f g i j ≫ pullback.snd = pullback.fst 
 
 theorem t_id (i : 𝒰.J) : t 𝒰 f g i i = 𝟙 _ := by
   apply pullback.hom_ext <;> rw [Category.id_comp]
-  apply pullback.hom_ext
-  · rw [← cancel_mono (𝒰.map i)]; simp only [pullback.condition, Category.assoc, t_fst_fst]
-  · simp only [Category.assoc, t_fst_snd]
+  · apply pullback.hom_ext
+    · rw [← cancel_mono (𝒰.map i)]; simp only [pullback.condition, Category.assoc, t_fst_fst]
+    · simp only [Category.assoc, t_fst_snd]
   · rw [← cancel_mono (𝒰.map i)]; simp only [pullback.condition, t_snd, Category.assoc]
 #align algebraic_geometry.Scheme.pullback.t_id AlgebraicGeometry.Scheme.Pullback.t_id
 
@@ -257,7 +257,7 @@ def gluing : Scheme.GlueData.{u} where
   t' i j k := t' 𝒰 f g i j k
   t_fac i j k := by
     apply pullback.hom_ext
-    apply pullback.hom_ext
+    on_goal 1 => apply pullback.hom_ext
     all_goals
       simp only [t'_snd_fst_fst, t'_snd_fst_snd, t'_snd_snd, t_fst_fst, t_fst_snd, t_snd,
         Category.assoc]
@@ -267,7 +267,7 @@ def gluing : Scheme.GlueData.{u} where
 /-- The first projection from the glued scheme into `X`. -/
 def p1 : (gluing 𝒰 f g).glued ⟶ X := by
   fapply Multicoequalizer.desc
-  exact fun i => pullback.fst ≫ 𝒰.map i
+  · exact fun i => pullback.fst ≫ 𝒰.map i
   rintro ⟨i, j⟩
   change pullback.fst ≫ _ ≫ 𝒰.map i = (_ ≫ _) ≫ _ ≫ 𝒰.map j
   -- Porting note (#11224): change `rw` to `erw`
@@ -281,7 +281,7 @@ def p1 : (gluing 𝒰 f g).glued ⟶ X := by
 /-- The second projection from the glued scheme into `Y`. -/
 def p2 : (gluing 𝒰 f g).glued ⟶ Y := by
   fapply Multicoequalizer.desc
-  exact fun i => pullback.snd
+  · exact fun i => pullback.snd
   rintro ⟨i, j⟩
   change pullback.fst ≫ _ = (_ ≫ _) ≫ _
   rw [Category.assoc]
@@ -468,10 +468,10 @@ theorem lift_comp_ι (i : 𝒰.J) :
 `W` along `p1` is indeed `Uᵢ ×[X] Y`. -/
 def pullbackP1Iso (i : 𝒰.J) : pullback (p1 𝒰 f g) (𝒰.map i) ≅ pullback (𝒰.map i ≫ f) g := by
   fconstructor
-  exact
-    pullback.lift pullback.snd (pullback.fst ≫ p2 𝒰 f g)
-      (by rw [← pullback.condition_assoc, Category.assoc, p_comm])
-  refine' pullback.lift ((gluing 𝒰 f g).ι i) pullback.fst (by erw [Multicoequalizer.π_desc])
+  · exact
+      pullback.lift pullback.snd (pullback.fst ≫ p2 𝒰 f g)
+        (by rw [← pullback.condition_assoc, Category.assoc, p_comm])
+  · refine' pullback.lift ((gluing 𝒰 f g).ι i) pullback.fst (by erw [Multicoequalizer.π_desc])
   · apply pullback.hom_ext
     · simpa using lift_comp_ι 𝒰 f g i
     · simp only [Category.assoc, pullback.lift_snd, pullback.lift_fst, Category.id_comp]

7316286f

chore: avoid id.def (adaptation for nightly-2024-03-27) (#11829)

Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com>

b8a0f589

Diff

@@ -71,7 +71,7 @@ theorem t_fst_fst (i j : 𝒰.J) : t 𝒰 f g i j ≫ pullback.fst ≫ pullback.
     hasPullback_assoc_symm (𝒰.map j) (𝒰.map i) (𝒰.map i ≫ f) g
   haveI : HasPullback (pullback.snd ≫ 𝒰.map j ≫ f) g :=
     hasPullback_assoc_symm (𝒰.map i) (𝒰.map j) (𝒰.map j ≫ f) g
-  simp only [Category.assoc, id.def, pullbackSymmetry_hom_comp_fst_assoc,
+  simp only [Category.assoc, id, pullbackSymmetry_hom_comp_fst_assoc,
     pullbackAssoc_hom_snd_fst, pullback.lift_fst_assoc, pullbackSymmetry_hom_comp_snd,
     pullbackAssoc_inv_fst_fst, pullbackSymmetry_hom_comp_fst]
 #align algebraic_geometry.Scheme.pullback.t_fst_fst AlgebraicGeometry.Scheme.Pullback.t_fst_fst
@@ -85,7 +85,7 @@ theorem t_fst_snd (i j : 𝒰.J) :
     hasPullback_assoc_symm (𝒰.map j) (𝒰.map i) (𝒰.map i ≫ f) g
   haveI : HasPullback (pullback.snd ≫ 𝒰.map j ≫ f) g :=
     hasPullback_assoc_symm (𝒰.map i) (𝒰.map j) (𝒰.map j ≫ f) g
-  simp only [pullbackSymmetry_hom_comp_snd_assoc, Category.comp_id, Category.assoc, id.def,
+  simp only [pullbackSymmetry_hom_comp_snd_assoc, Category.comp_id, Category.assoc, id,
     pullbackSymmetry_hom_comp_fst_assoc, pullbackAssoc_hom_snd_snd, pullback.lift_snd,
     pullbackAssoc_inv_snd]
 #align algebraic_geometry.Scheme.pullback.t_fst_snd AlgebraicGeometry.Scheme.Pullback.t_fst_snd
@@ -98,7 +98,7 @@ theorem t_snd (i j : 𝒰.J) : t 𝒰 f g i j ≫ pullback.snd = pullback.fst 
     hasPullback_assoc_symm (𝒰.map j) (𝒰.map i) (𝒰.map i ≫ f) g
   haveI : HasPullback (pullback.snd ≫ 𝒰.map j ≫ f) g :=
     hasPullback_assoc_symm (𝒰.map i) (𝒰.map j) (𝒰.map j ≫ f) g
-  simp only [pullbackSymmetry_hom_comp_snd_assoc, Category.assoc, id.def,
+  simp only [pullbackSymmetry_hom_comp_snd_assoc, Category.assoc, id,
     pullbackSymmetry_hom_comp_snd, pullbackAssoc_hom_fst, pullback.lift_fst_assoc,
     pullbackSymmetry_hom_comp_fst, pullbackAssoc_inv_fst_snd]
 #align algebraic_geometry.Scheme.pullback.t_snd AlgebraicGeometry.Scheme.Pullback.t_snd

7316286f

doc(Algebra,AlgebraicGeometry): remove mathlib3 names in doc comments (#11955)

Mostly automatic, with a few manual corrections.

11516514

Diff

@@ -669,7 +669,7 @@ def openCoverOfBase' (𝒰 : OpenCover Z) (f : X ⟶ Z) (g : Y ⟶ Z) : OpenCove
     -- Porting note: `simpa` failed, but this is indeed `rfl`
     rfl
   · simp only [Category.comp_id, Category.id_comp]
-  -- Porting note: this `IsIso` instance was `inferInstance`
+  -- Porting note: this `IsIso` instance was `infer_instance`
   · apply IsIso.comp_isIso
 #align algebraic_geometry.Scheme.pullback.open_cover_of_base' AlgebraicGeometry.Scheme.Pullback.openCoverOfBase'

7316286f

chore(*): remove empty lines between variable statements (#11418)

Empty lines were removed by executing the following Python script twice

import os
import re


# Loop through each file in the repository
for dir_path, dirs, files in os.walk('.'):
  for filename in files:
    if filename.endswith('.lean'):
      file_path = os.path.join(dir_path, filename)

      # Open the file and read its contents
      with open(file_path, 'r') as file:
        content = file.read()

      # Use a regular expression to replace sequences of "variable" lines separated by empty lines
      # with sequences without empty lines
      modified_content = re.sub(r'(variable.*\n)\n(variable(?! .* in))', r'\1\2', content)

      # Write the modified content back to the file
      with open(file_path, 'w') as file:
        file.write(modified_content)

75c86f04

Diff

@@ -38,9 +38,7 @@ namespace AlgebraicGeometry.Scheme
 namespace Pullback
 
 variable {C : Type u} [Category.{v} C]
-
 variable {X Y Z : Scheme.{u}} (𝒰 : OpenCover.{u} X) (f : X ⟶ Z) (g : Y ⟶ Z)
-
 variable [∀ i, HasPullback (𝒰.map i ≫ f) g]
 
 /-- The intersection of `Uᵢ ×[Z] Y` and `Uⱼ ×[Z] Y` is given by (Uᵢ ×[Z] Y) ×[X] Uⱼ -/

7316286f

chore: classify rw to erw porting notes (#11225)

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

change rw to erw

4d57cdd8

Diff

@@ -272,7 +272,7 @@ def p1 : (gluing 𝒰 f g).glued ⟶ X := by
   exact fun i => pullback.fst ≫ 𝒰.map i
   rintro ⟨i, j⟩
   change pullback.fst ≫ _ ≫ 𝒰.map i = (_ ≫ _) ≫ _ ≫ 𝒰.map j
-  -- Porting note: change `rw` to `erw`
+  -- Porting note (#11224): change `rw` to `erw`
   erw [pullback.condition]
   rw [← Category.assoc]
   congr 1

7316286f

style: reduce spacing variation in "porting note" comments (#10886)

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.

86b84c52

Diff

@@ -68,7 +68,7 @@ def t (i j : 𝒰.J) : v 𝒰 f g i j ⟶ v 𝒰 f g j i := by
 @[simp, reassoc]
 theorem t_fst_fst (i j : 𝒰.J) : t 𝒰 f g i j ≫ pullback.fst ≫ pullback.fst = pullback.snd := by
   delta t
-  -- Porting note : copied from previous definition, otherwise `simp` wouldn't work
+  -- Porting note: copied from previous definition, otherwise `simp` wouldn't work
   haveI : HasPullback (pullback.snd ≫ 𝒰.map i ≫ f) g :=
     hasPullback_assoc_symm (𝒰.map j) (𝒰.map i) (𝒰.map i ≫ f) g
   haveI : HasPullback (pullback.snd ≫ 𝒰.map j ≫ f) g :=
@@ -82,7 +82,7 @@ theorem t_fst_fst (i j : 𝒰.J) : t 𝒰 f g i j ≫ pullback.fst ≫ pullback.
 theorem t_fst_snd (i j : 𝒰.J) :
     t 𝒰 f g i j ≫ pullback.fst ≫ pullback.snd = pullback.fst ≫ pullback.snd := by
   delta t
-  -- Porting note : copied from previous definition, otherwise `simp` wouldn't work
+  -- Porting note: copied from previous definition, otherwise `simp` wouldn't work
   haveI : HasPullback (pullback.snd ≫ 𝒰.map i ≫ f) g :=
     hasPullback_assoc_symm (𝒰.map j) (𝒰.map i) (𝒰.map i ≫ f) g
   haveI : HasPullback (pullback.snd ≫ 𝒰.map j ≫ f) g :=
@@ -95,7 +95,7 @@ theorem t_fst_snd (i j : 𝒰.J) :
 @[simp, reassoc]
 theorem t_snd (i j : 𝒰.J) : t 𝒰 f g i j ≫ pullback.snd = pullback.fst ≫ pullback.fst := by
   delta t
-  -- Porting note : copied from previous definition, otherwise `simp` wouldn't work
+  -- Porting note: copied from previous definition, otherwise `simp` wouldn't work
   haveI : HasPullback (pullback.snd ≫ 𝒰.map i ≫ f) g :=
     hasPullback_assoc_symm (𝒰.map j) (𝒰.map i) (𝒰.map i ≫ f) g
   haveI : HasPullback (pullback.snd ≫ 𝒰.map j ≫ f) g :=
@@ -272,7 +272,7 @@ def p1 : (gluing 𝒰 f g).glued ⟶ X := by
   exact fun i => pullback.fst ≫ 𝒰.map i
   rintro ⟨i, j⟩
   change pullback.fst ≫ _ ≫ 𝒰.map i = (_ ≫ _) ≫ _ ≫ 𝒰.map j
-  -- Porting note : change `rw` to `erw`
+  -- Porting note: change `rw` to `erw`
   erw [pullback.condition]
   rw [← Category.assoc]
   congr 1
@@ -322,7 +322,7 @@ theorem gluedLiftPullbackMap_fst (i j : 𝒰.J) :
         (pullbackSymmetry _ _).hom ≫
           pullback.map _ _ _ _ (𝟙 _) s.snd f (Category.id_comp _).symm s.condition := by
   delta gluedLiftPullbackMap
-  -- Porting note : the original set of simp lemma is not sufficient, but as this is terminal
+  -- Porting note: the original set of simp lemma is not sufficient, but as this is terminal
   -- I just let `simp` do its work
   simp
 #align algebraic_geometry.Scheme.pullback.glued_lift_pullback_map_fst AlgebraicGeometry.Scheme.Pullback.gluedLiftPullbackMap_fst
@@ -331,7 +331,7 @@ theorem gluedLiftPullbackMap_fst (i j : 𝒰.J) :
 theorem gluedLiftPullbackMap_snd (i j : 𝒰.J) :
     gluedLiftPullbackMap 𝒰 f g s i j ≫ pullback.snd = pullback.snd ≫ pullback.snd := by
   delta gluedLiftPullbackMap
-  -- Porting note : the original set of simp lemma is not sufficient, but as this is terminal
+  -- Porting note: the original set of simp lemma is not sufficient, but as this is terminal
   -- I just let `simp` do its work
   simp
 #align algebraic_geometry.Scheme.pullback.glued_lift_pullback_map_snd AlgebraicGeometry.Scheme.Pullback.gluedLiftPullbackMap_snd
@@ -378,7 +378,7 @@ theorem gluedLift_p1 : gluedLift 𝒰 f g s ≫ p1 𝒰 f g = s.fst := by
   simp_rw [← Category.assoc]
   rw [(𝒰.pullbackCover s.fst).ι_glueMorphisms]
   simp_rw [Category.assoc]
-  -- Porting note : `Category.comp_id` is no longer necessary, don't know where `𝟙 _` has gone
+  -- Porting note: `Category.comp_id` is no longer necessary, don't know where `𝟙 _` has gone
   erw [Multicoequalizer.π_desc, pullback.lift_fst_assoc, pullback.condition]
   rw [pullbackSymmetry_hom_comp_snd_assoc]
   rfl
@@ -416,7 +416,7 @@ theorem pullbackFstιToV_fst (i j : 𝒰.J) :
   delta pullbackFstιToV
   simp only [Iso.trans_hom, pullback.congrHom_hom, Category.assoc, pullback.lift_fst,
     Category.comp_id]
-  -- Porting note : `pullbackRightPullbackFstIso_hom_fst` is not used in `simp` even though
+  -- Porting note: `pullbackRightPullbackFstIso_hom_fst` is not used in `simp` even though
   -- instructed, forcing `pullbackSymmetry_hom_comp_fst` to be manually `rw`ed as well.
   erw [pullbackRightPullbackFstIso_hom_fst]
   rw [pullbackSymmetry_hom_comp_fst]
@@ -428,7 +428,7 @@ theorem pullbackFstιToV_snd (i j : 𝒰.J) :
   delta pullbackFstιToV
   simp only [Iso.trans_hom, pullback.congrHom_hom, Category.assoc, pullback.lift_snd,
     Category.comp_id]
-  -- Porting note : `pullbackRightPullbackFstIso_hom_snd` is not used in `simp` even though
+  -- Porting note: `pullbackRightPullbackFstIso_hom_snd` is not used in `simp` even though
   -- instructed, forcing `pullbackSymmetry_hom_comp_snd_assoc` to be manually `rw`ed as well.
   erw [pullbackRightPullbackFstIso_hom_snd]
   rw [pullbackSymmetry_hom_comp_snd_assoc]
@@ -453,7 +453,7 @@ theorem lift_comp_ι (i : 𝒰.J) :
     congr 1
     rw [gluing_f, gluing_t]
     apply pullback.hom_ext <;> simp_rw [Category.assoc]
-    -- Porting note : in the following two bullet points, `rfl` was not necessary
+    -- Porting note: in the following two bullet points, `rfl` was not necessary
     · rw [t_fst_fst, pullback.lift_fst, pullbackFstιToV_snd]; rfl
     · rw [t_fst_snd, pullback.lift_snd, pullbackFstιToV_fst_assoc, pullback.condition_assoc]
       erw [Multicoequalizer.π_desc]
@@ -461,7 +461,7 @@ theorem lift_comp_ι (i : 𝒰.J) :
   · rw [pullback.condition, ← Category.assoc]
     congr 1
     apply pullback.hom_ext
-    -- Porting note : in the following two bullet points, `rfl` was not necessary
+    -- Porting note: in the following two bullet points, `rfl` was not necessary
     · simp only [pullbackFstιToV_fst]; rfl
     · simp only [pullbackFstιToV_fst]; rfl
 #align algebraic_geometry.Scheme.pullback.lift_comp_ι AlgebraicGeometry.Scheme.Pullback.lift_comp_ι
@@ -668,10 +668,10 @@ def openCoverOfBase' (𝒰 : OpenCover Z) (f : X ⟶ Z) (g : Y ⟶ Z) : OpenCove
       (f := (pullbackSymmetry _ _).hom ≫
         (limit.isoLimitCone ⟨_, this⟩).inv ≫ pullback.map _ _ _ _ (𝟙 _) (𝟙 _) (𝟙 _) _ _) ?_
   · simp only [Category.comp_id, Category.id_comp, ← pullback.condition]
-    -- Porting note : `simpa` failed, but this is indeed `rfl`
+    -- Porting note: `simpa` failed, but this is indeed `rfl`
     rfl
   · simp only [Category.comp_id, Category.id_comp]
-  -- Porting note : this `IsIso` instance was `inferInstance`
+  -- Porting note: this `IsIso` instance was `inferInstance`
   · apply IsIso.comp_isIso
 #align algebraic_geometry.Scheme.pullback.open_cover_of_base' AlgebraicGeometry.Scheme.Pullback.openCoverOfBase'
 
@@ -689,7 +689,7 @@ def openCoverOfBase (𝒰 : OpenCover Z) (f : X ⟶ Z) (g : Y ⟶ Z) : OpenCover
           pullback.condition.symm)
       ((Equiv.prodPUnit 𝒰.J).symm.trans (Equiv.sigmaEquivProd 𝒰.J PUnit).symm) fun _ => Iso.refl _
   intro i
-  -- Porting note : deviated from original proof a bit so that it won't timeout.
+  -- Porting note: deviated from original proof a bit so that it won't timeout.
   rw [Iso.refl_hom, Category.id_comp, openCoverOfBase'_map]
   apply pullback.hom_ext <;> dsimp <;>
   · simp only [limit.lift_π, PullbackCone.mk_pt, PullbackCone.mk_π_app, Category.assoc,
@@ -711,7 +711,7 @@ instance Scheme.pullback_map_isOpenImmersion {X Y S X' Y' S' : Scheme}
     [IsOpenImmersion i₁] [IsOpenImmersion i₂] [Mono i₃] :
     IsOpenImmersion (pullback.map f g f' g' i₁ i₂ i₃ e₁ e₂) := by
   rw [pullback_map_eq_pullbackFstFstIso_inv]
-  -- Porting note : was automatic
+  -- Porting note: was automatic
   exact PresheafedSpace.IsOpenImmersion.comp _ (hg := PresheafedSpace.IsOpenImmersion.comp _ _)
 
 end AlgebraicGeometry

7316286f

feat(CategoryTheory): characterization of epi/mono with limits (#9989)

In this PR, it is shown that monomorphisms can be characterized in terms of pullback squares. Future applications of this include the fact that if a family of functors reflects isomorphisms, it shall also reflect monomorphisms and epimorphisms (provided suitable limits/colimits exist).

23bf9fba

Diff

@@ -578,8 +578,8 @@ instance left_affine_comp_pullback_hasPullback {X Y Z : Scheme} (f : X ⟶ Z) (g
   have :=
     bigSquareIsPullback (pullback.fst : W ⟶ _) (pullback.fst : Yᵢ ⟶ _) (pullback.snd : Xᵢ ⟶ _)
       (Z.affineCover.map i) pullback.snd pullback.snd g pullback.condition.symm
-      pullback.condition.symm (PullbackCone.flipIsLimit <| pullbackIsPullback _ _)
-      (PullbackCone.flipIsLimit <| pullbackIsPullback _ _)
+      pullback.condition.symm (PullbackCone.isLimitOfFlip <| pullbackIsPullback _ _)
+      (PullbackCone.isLimitOfFlip <| pullbackIsPullback _ _)
   have : HasPullback (pullback.snd ≫ Z.affineCover.map i : Xᵢ ⟶ _) g := ⟨⟨⟨_, this⟩⟩⟩
   rw [← pullback.condition] at this
   exact this
@@ -661,8 +661,8 @@ def openCoverOfBase' (𝒰 : OpenCover Z) (f : X ⟶ Z) (g : Y ⟶ Z) : OpenCove
   have :=
     bigSquareIsPullback (pullback.fst : W ⟶ _) (pullback.fst : Yᵢ ⟶ _) (pullback.snd : Xᵢ ⟶ _)
       (𝒰.map i) pullback.snd pullback.snd g pullback.condition.symm pullback.condition.symm
-      (PullbackCone.flipIsLimit <| pullbackIsPullback _ _)
-      (PullbackCone.flipIsLimit <| pullbackIsPullback _ _)
+      (PullbackCone.isLimitOfFlip <| pullbackIsPullback _ _)
+      (PullbackCone.isLimitOfFlip <| pullbackIsPullback _ _)
   refine'
     @openCoverOfIsIso
       (f := (pullbackSymmetry _ _).hom ≫

7316286f

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

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

89aa3a3b

Diff

@@ -2,17 +2,14 @@
 Copyright (c) 2022 Andrew Yang. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Andrew Yang
-
-! This file was ported from Lean 3 source module algebraic_geometry.pullbacks
-! leanprover-community/mathlib commit 7316286ff2942aa14e540add9058c6b0aa1c8070
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.AlgebraicGeometry.Gluing
 import Mathlib.CategoryTheory.Limits.Opposites
 import Mathlib.AlgebraicGeometry.AffineScheme
 import Mathlib.CategoryTheory.Limits.Shapes.Diagonal
 
+#align_import algebraic_geometry.pullbacks from "leanprover-community/mathlib"@"7316286ff2942aa14e540add9058c6b0aa1c8070"
+
 /-!
 # Fibred products of schemes

7316286f

chore: fix focusing dots (#5708)

This PR is the result of running

find . -type f -name "*.lean" -exec sed -i -E 's/^( +)\. /\1· /' {} \;
find . -type f -name "*.lean" -exec sed -i -E 'N;s/^( +·)\n +(.*)$/\1 \2/;P;D' {} \;

which firstly replaces . focusing dots with · and secondly removes isolated instances of such dots, unifying them with the following line. A new rule is placed in the style linter to verify this.

cb02d09e

Diff

@@ -675,7 +675,7 @@ def openCoverOfBase' (𝒰 : OpenCover Z) (f : X ⟶ Z) (g : Y ⟶ Z) : OpenCove
     rfl
   · simp only [Category.comp_id, Category.id_comp]
   -- Porting note : this `IsIso` instance was `inferInstance`
-  . apply IsIso.comp_isIso
+  · apply IsIso.comp_isIso
 #align algebraic_geometry.Scheme.pullback.open_cover_of_base' AlgebraicGeometry.Scheme.Pullback.openCoverOfBase'
 
 /-- Given an open cover `{ Zᵢ }` of `Z`, then `X ×[Z] Y` is covered by `Xᵢ ×[Zᵢ] Yᵢ`, where
@@ -695,7 +695,7 @@ def openCoverOfBase (𝒰 : OpenCover Z) (f : X ⟶ Z) (g : Y ⟶ Z) : OpenCover
   -- Porting note : deviated from original proof a bit so that it won't timeout.
   rw [Iso.refl_hom, Category.id_comp, openCoverOfBase'_map]
   apply pullback.hom_ext <;> dsimp <;>
-  . simp only [limit.lift_π, PullbackCone.mk_pt, PullbackCone.mk_π_app, Category.assoc,
+  · simp only [limit.lift_π, PullbackCone.mk_pt, PullbackCone.mk_π_app, Category.assoc,
       limit.lift_π_assoc, cospan_left, Category.comp_id, limit.isoLimitCone_inv_π,
       limit.isoLimitCone_inv_π_assoc, pullbackSymmetry_hom_comp_fst_assoc,
       pullbackSymmetry_hom_comp_snd_assoc]

7316286f

chore: tidy various files (#5628)

3282e2f7

Diff

@@ -305,7 +305,7 @@ variable (s : PullbackCone f g)
 /-- (Implementation)
 The canonical map `(s.X ×[X] Uᵢ) ×[s.X] (s.X ×[X] Uⱼ) ⟶ (Uᵢ ×[Z] Y) ×[X] Uⱼ`
 
-This is used in `glued_lift`. -/
+This is used in `gluedLift`. -/
 def gluedLiftPullbackMap (i j : 𝒰.J) :
     pullback ((𝒰.pullbackCover s.fst).map i) ((𝒰.pullbackCover s.fst).map j) ⟶
       (gluing 𝒰 f g).V ⟨i, j⟩ := by
@@ -326,7 +326,7 @@ theorem gluedLiftPullbackMap_fst (i j : 𝒰.J) :
           pullback.map _ _ _ _ (𝟙 _) s.snd f (Category.id_comp _).symm s.condition := by
   delta gluedLiftPullbackMap
   -- Porting note : the original set of simp lemma is not sufficient, but as this is terminal
-  -- I just let `simp` does it work
+  -- I just let `simp` do its work
   simp
 #align algebraic_geometry.Scheme.pullback.glued_lift_pullback_map_fst AlgebraicGeometry.Scheme.Pullback.gluedLiftPullbackMap_fst
 
@@ -335,7 +335,7 @@ theorem gluedLiftPullbackMap_snd (i j : 𝒰.J) :
     gluedLiftPullbackMap 𝒰 f g s i j ≫ pullback.snd = pullback.snd ≫ pullback.snd := by
   delta gluedLiftPullbackMap
   -- Porting note : the original set of simp lemma is not sufficient, but as this is terminal
-  -- I just let `simp` does it work
+  -- I just let `simp` do its work
   simp
 #align algebraic_geometry.Scheme.pullback.glued_lift_pullback_map_snd AlgebraicGeometry.Scheme.Pullback.gluedLiftPullbackMap_snd
 
@@ -347,7 +347,7 @@ Given a pullback cone `s`, we have the maps `s.fst ⁻¹' Uᵢ ⟶ Uᵢ` and
 
 to glue these into a map `s.X ⟶ Uᵢ ×[Z] Y`, we need to show that the maps agree on
 `(s.fst ⁻¹' Uᵢ) ×[s.X] (s.fst ⁻¹' Uⱼ) ⟶ Uᵢ ×[Z] Y`. This is achieved by showing that both of these
-maps factors through `glued_lift_pullback_map`.
+maps factors through `gluedLiftPullbackMap`.
 -/
 def gluedLift : s.pt ⟶ (gluing 𝒰 f g).glued := by
   fapply (𝒰.pullbackCover s.fst).glueMorphisms
@@ -540,8 +540,7 @@ def gluedIsLimit : IsLimit (PullbackCone.mk _ _ (p_comm 𝒰 f g)) := by
   simp_rw [← Category.assoc]
   congr 1
   apply pullback.hom_ext
-  ·
-    simp only [Category.comp_id, pullbackRightPullbackFstIso_hom_snd, Category.assoc,
+  · simp only [Category.comp_id, pullbackRightPullbackFstIso_hom_snd, Category.assoc,
       pullbackP1Iso_hom_fst, pullback.lift_snd, pullback.lift_fst, pullbackSymmetry_hom_comp_fst]
   · simp only [Category.comp_id, pullbackRightPullbackFstIso_hom_fst_assoc,
       pullbackP1Iso_hom_snd, Category.assoc, pullback.lift_fst_assoc,
@@ -654,7 +653,7 @@ def openCoverOfLeftRight (𝒰X : X.OpenCover) (𝒰Y : Y.OpenCover) (f : X ⟶
   apply pullback.hom_ext <;> simp
 #align algebraic_geometry.Scheme.pullback.open_cover_of_left_right AlgebraicGeometry.Scheme.Pullback.openCoverOfLeftRight
 
-/-- (Implementation). Use `open_cover_of_base` instead. -/
+/-- (Implementation). Use `openCoverOfBase` instead. -/
 @[simps! map]
 def openCoverOfBase' (𝒰 : OpenCover Z) (f : X ⟶ Z) (g : Y ⟶ Z) : OpenCover (pullback f g) := by
   apply (openCoverOfLeft (𝒰.pullbackCover f) f g).bind

7316286f

feat: port AlgebraicGeometry.Morphisms.Basic (#5599)

Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com>

f68e3bd1

Diff

@@ -595,7 +595,8 @@ instance {X Y Z : Scheme} (f : X ⟶ Z) (g : Y ⟶ Z) : HasPullback f g :=
 instance : HasPullbacks Scheme :=
   hasPullbacks_of_hasLimit_cospan _
 
-instance {X Y Z : Scheme} (f : X ⟶ Z) (g : Y ⟶ Z) [IsAffine X] [IsAffine Y] [IsAffine Z] :
+instance isAffine_of_isAffine_isAffine_isAffine {X Y Z : Scheme}
+    (f : X ⟶ Z) (g : Y ⟶ Z) [IsAffine X] [IsAffine Y] [IsAffine Z] :
     IsAffine (pullback f g) :=
   isAffineOfIso
     (pullback.map f g (Spec.map (Γ.map f.op).op) (Spec.map (Γ.map g.op).op)
@@ -708,7 +709,8 @@ end AlgebraicGeometry.Scheme
 
 namespace AlgebraicGeometry
 
-instance {X Y S X' Y' S' : Scheme} (f : X ⟶ S) (g : Y ⟶ S) (f' : X' ⟶ S') (g' : Y' ⟶ S')
+instance Scheme.pullback_map_isOpenImmersion {X Y S X' Y' S' : Scheme}
+    (f : X ⟶ S) (g : Y ⟶ S) (f' : X' ⟶ S') (g' : Y' ⟶ S')
     (i₁ : X ⟶ X') (i₂ : Y ⟶ Y') (i₃ : S ⟶ S') (e₁ : f ≫ i₃ = i₁ ≫ f') (e₂ : g ≫ i₃ = i₂ ≫ g')
     [IsOpenImmersion i₁] [IsOpenImmersion i₂] [Mono i₃] :
     IsOpenImmersion (pullback.map f g f' g' i₁ i₂ i₃ e₁ e₂) := by

7316286f

feat: port AlgebraicGeometry.Pullbacks (#5583)

Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

80d2e74b

`algebraic_geometry.pullbacks` ⟷ `Mathlib.AlgebraicGeometry.Pullbacks`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 11 + 931

algebraic_geometry.pullbacks ⟷ Mathlib.AlgebraicGeometry.Pullbacks

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 11 + 931

`algebraic_geometry.pullbacks` ⟷ `Mathlib.AlgebraicGeometry.Pullbacks`