algebraic_geometry.presheafed_space.has_colimits ⟷ Mathlib.Geometry.RingedSpace.PresheafedSpace.HasColimits

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

@@ -3,8 +3,8 @@ Copyright (c) 2020 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
 -/
-import AlgebraicGeometry.PresheafedSpace
-import Topology.Category.Top.Limits.Basic
+import Geometry.RingedSpace.PresheafedSpace
+import Topology.Category.TopCat.Limits.Basic
 import Topology.Sheaves.Limits
 
 #align_import algebraic_geometry.presheafed_space.has_colimits from "leanprover-community/mathlib"@"0b7c740e25651db0ba63648fbae9f9d6f941e31b"

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

@@ -266,7 +266,7 @@ def descCApp (F : J ⥤ PresheafedSpace.{v} C) (s : Cocone F) (U : (Opens ↥s.p
       functor.congr_obj
         (congr_arg opens.map (colimit.ι_desc ((PresheafedSpace.forget C).mapCocone s) (unop j)))
         (unop U)
-    simp only [opens.map_comp_obj_unop] at w 
+    simp only [opens.map_comp_obj_unop] at w
     replace w := congr_arg op w
     have w' := nat_trans.congr (F.map f.unop).c w
     rw [w']
@@ -293,7 +293,7 @@ theorem desc_c_naturality (F : J ⥤ PresheafedSpace.{v} C) (s : Cocone F)
     functor.congr_hom
       (congr_arg opens.map (colimit.ι_desc ((PresheafedSpace.forget C).mapCocone s) (unop j)))
       i.unop
-  simp only [opens.map_comp_map] at w 
+  simp only [opens.map_comp_map] at w
   replace w := congr_arg Quiver.Hom.op w
   rw [w]
   dsimp; simp

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

@@ -3,9 +3,9 @@ Copyright (c) 2020 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
 -/
-import Mathbin.AlgebraicGeometry.PresheafedSpace
-import Mathbin.Topology.Category.Top.Limits.Basic
-import Mathbin.Topology.Sheaves.Limits
+import AlgebraicGeometry.PresheafedSpace
+import Topology.Category.Top.Limits.Basic
+import Topology.Sheaves.Limits
 
 #align_import algebraic_geometry.presheafed_space.has_colimits from "leanprover-community/mathlib"@"0b7c740e25651db0ba63648fbae9f9d6f941e31b"
 

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

@@ -2,16 +2,13 @@
 Copyright (c) 2020 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
-
-! This file was ported from Lean 3 source module algebraic_geometry.presheafed_space.has_colimits
-! leanprover-community/mathlib commit 0b7c740e25651db0ba63648fbae9f9d6f941e31b
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.AlgebraicGeometry.PresheafedSpace
 import Mathbin.Topology.Category.Top.Limits.Basic
 import Mathbin.Topology.Sheaves.Limits
 
+#align_import algebraic_geometry.presheafed_space.has_colimits from "leanprover-community/mathlib"@"0b7c740e25651db0ba63648fbae9f9d6f941e31b"
+
 /-!
 # `PresheafedSpace C` has colimits.
 

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

@@ -354,7 +354,7 @@ def colimitCoconeIsColimit (F : J ⥤ PresheafedSpace.{v} C) : IsColimit (colimi
     fapply PresheafedSpace.ext
     -- could `ext` please not reorder goals?
     · exact t
-    · ext (U j); dsimp [desc, desc_c_app]
+    · ext U j; dsimp [desc, desc_c_app]
       simp only [limit.lift_π, eq_to_hom_op, eq_to_hom_map, assoc,
         limit_obj_iso_limit_comp_evaluation_inv_π_app]
       rw [PresheafedSpace.congr_app (w (unop j)).symm U]

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

@@ -71,6 +71,7 @@ attribute [local simp] eq_to_hom_map
 
 attribute [local tidy] tactic.auto_cases_opens
 
+#print AlgebraicGeometry.PresheafedSpace.map_id_c_app /-
 @[simp]
 theorem map_id_c_app (F : J ⥤ PresheafedSpace.{v} C) (j) (U) :
     (F.map (𝟙 j)).c.app (op U) =
@@ -82,7 +83,9 @@ theorem map_id_c_app (F : J ⥤ PresheafedSpace.{v} C) (j) (U) :
   simp [PresheafedSpace.congr_app (F.map_id j)]
   rfl
 #align algebraic_geometry.PresheafedSpace.map_id_c_app AlgebraicGeometry.PresheafedSpace.map_id_c_app
+-/
 
+#print AlgebraicGeometry.PresheafedSpace.map_comp_c_app /-
 @[simp]
 theorem map_comp_c_app (F : J ⥤ PresheafedSpace.{v} C) {j₁ j₂ j₃} (f : j₁ ⟶ j₂) (g : j₂ ⟶ j₃) (U) :
     (F.map (f ≫ g)).c.app (op U) =
@@ -96,7 +99,9 @@ theorem map_comp_c_app (F : J ⥤ PresheafedSpace.{v} C) {j₁ j₂ j₃} (f : j
   simp only [PresheafedSpace.congr_app (F.map_comp f g)]
   dsimp; simp; dsimp; simp
 #align algebraic_geometry.PresheafedSpace.map_comp_c_app AlgebraicGeometry.PresheafedSpace.map_comp_c_app
+-/
 
+#print AlgebraicGeometry.PresheafedSpace.componentwiseDiagram /-
 -- See note [dsimp, simp]
 /-- Given a diagram of `PresheafedSpace C`s, its colimit is computed by pushing the sheaves onto
 the colimit of the underlying spaces, and taking componentwise limit.
@@ -122,9 +127,11 @@ def componentwiseDiagram (F : J ⥤ PresheafedSpace.{v} C) [HasColimit F]
     erw [← (F.obj (unop k)).Presheaf.map_comp]
     congr
 #align algebraic_geometry.PresheafedSpace.componentwise_diagram AlgebraicGeometry.PresheafedSpace.componentwiseDiagram
+-/
 
 variable [HasColimitsOfShape J TopCat.{v}]
 
+#print AlgebraicGeometry.PresheafedSpace.pushforwardDiagramToColimit /-
 /-- Given a diagram of presheafed spaces,
 we can push all the presheaves forward to the colimit `X` of the underlying topological spaces,
 obtaining a diagram in `(presheaf C X)ᵒᵖ`.
@@ -170,9 +177,11 @@ def pushforwardDiagramToColimit (F : J ⥤ PresheafedSpace.{v} C) :
     swap
     · simp; rfl
 #align algebraic_geometry.PresheafedSpace.pushforward_diagram_to_colimit AlgebraicGeometry.PresheafedSpace.pushforwardDiagramToColimit
+-/
 
 variable [∀ X : TopCat.{v}, HasLimitsOfShape Jᵒᵖ (X.Presheaf C)]
 
+#print AlgebraicGeometry.PresheafedSpace.colimit /-
 /-- Auxiliary definition for `PresheafedSpace.has_colimits`.
 -/
 def colimit (F : J ⥤ PresheafedSpace.{v} C) : PresheafedSpace C
@@ -180,19 +189,25 @@ def colimit (F : J ⥤ PresheafedSpace.{v} C) : PresheafedSpace C
   carrier := colimit (F ⋙ PresheafedSpace.forget C)
   Presheaf := limit (pushforwardDiagramToColimit F).leftOp
 #align algebraic_geometry.PresheafedSpace.colimit AlgebraicGeometry.PresheafedSpace.colimit
+-/
 
+#print AlgebraicGeometry.PresheafedSpace.colimit_carrier /-
 @[simp]
 theorem colimit_carrier (F : J ⥤ PresheafedSpace.{v} C) :
     (colimit F).carrier = Limits.colimit (F ⋙ PresheafedSpace.forget C) :=
   rfl
 #align algebraic_geometry.PresheafedSpace.colimit_carrier AlgebraicGeometry.PresheafedSpace.colimit_carrier
+-/
 
+#print AlgebraicGeometry.PresheafedSpace.colimit_presheaf /-
 @[simp]
 theorem colimit_presheaf (F : J ⥤ PresheafedSpace.{v} C) :
     (colimit F).Presheaf = limit (pushforwardDiagramToColimit F).leftOp :=
   rfl
 #align algebraic_geometry.PresheafedSpace.colimit_presheaf AlgebraicGeometry.PresheafedSpace.colimit_presheaf
+-/
 
+#print AlgebraicGeometry.PresheafedSpace.colimitCocone /-
 /-- Auxiliary definition for `PresheafedSpace.has_colimits`.
 -/
 @[simps]
@@ -221,11 +236,13 @@ def colimitCocone (F : J ⥤ PresheafedSpace.{v} C) : Cocone F
           simp only [id_comp]
           simpa }
 #align algebraic_geometry.PresheafedSpace.colimit_cocone AlgebraicGeometry.PresheafedSpace.colimitCocone
+-/
 
 variable [HasLimitsOfShape Jᵒᵖ C]
 
 namespace ColimitCoconeIsColimit
 
+#print AlgebraicGeometry.PresheafedSpace.ColimitCoconeIsColimit.descCApp /-
 /-- Auxiliary definition for `PresheafedSpace.colimit_cocone_is_colimit`.
 -/
 def descCApp (F : J ⥤ PresheafedSpace.{v} C) (s : Cocone F) (U : (Opens ↥s.pt.carrier)ᵒᵖ) :
@@ -258,7 +275,9 @@ def descCApp (F : J ⥤ PresheafedSpace.{v} C) (s : Cocone F) (U : (Opens ↥s.p
     rw [w']
     dsimp; simp; dsimp; simp
 #align algebraic_geometry.PresheafedSpace.colimit_cocone_is_colimit.desc_c_app AlgebraicGeometry.PresheafedSpace.ColimitCoconeIsColimit.descCApp
+-/
 
+#print AlgebraicGeometry.PresheafedSpace.ColimitCoconeIsColimit.desc_c_naturality /-
 theorem desc_c_naturality (F : J ⥤ PresheafedSpace.{v} C) (s : Cocone F)
     {U V : (Opens ↥s.pt.carrier)ᵒᵖ} (i : U ⟶ V) :
     s.pt.Presheaf.map i ≫ descCApp F s V =
@@ -282,7 +301,9 @@ theorem desc_c_naturality (F : J ⥤ PresheafedSpace.{v} C) (s : Cocone F)
   rw [w]
   dsimp; simp
 #align algebraic_geometry.PresheafedSpace.colimit_cocone_is_colimit.desc_c_naturality AlgebraicGeometry.PresheafedSpace.ColimitCoconeIsColimit.desc_c_naturality
+-/
 
+#print AlgebraicGeometry.PresheafedSpace.ColimitCoconeIsColimit.desc /-
 /-- Auxiliary definition for `PresheafedSpace.colimit_cocone_is_colimit`.
 -/
 def desc (F : J ⥤ PresheafedSpace.{v} C) (s : Cocone F) : colimit F ⟶ s.pt
@@ -292,7 +313,9 @@ def desc (F : J ⥤ PresheafedSpace.{v} C) (s : Cocone F) : colimit F ⟶ s.pt
     { app := fun U => descCApp F s U
       naturality' := fun U V i => desc_c_naturality F s i }
 #align algebraic_geometry.PresheafedSpace.colimit_cocone_is_colimit.desc AlgebraicGeometry.PresheafedSpace.ColimitCoconeIsColimit.desc
+-/
 
+#print AlgebraicGeometry.PresheafedSpace.ColimitCoconeIsColimit.desc_fac /-
 theorem desc_fac (F : J ⥤ PresheafedSpace.{v} C) (s : Cocone F) (j : J) :
     (colimitCocone F).ι.app j ≫ desc F s = s.ι.app j :=
   by
@@ -302,11 +325,13 @@ theorem desc_fac (F : J ⥤ PresheafedSpace.{v} C) (s : Cocone F) (j : J) :
     dsimp [desc, desc_c_app]
     simpa
 #align algebraic_geometry.PresheafedSpace.colimit_cocone_is_colimit.desc_fac AlgebraicGeometry.PresheafedSpace.ColimitCoconeIsColimit.desc_fac
+-/
 
 end ColimitCoconeIsColimit
 
 open ColimitCoconeIsColimit
 
+#print AlgebraicGeometry.PresheafedSpace.colimitCoconeIsColimit /-
 /-- Auxiliary definition for `PresheafedSpace.has_colimits`.
 -/
 def colimitCoconeIsColimit (F : J ⥤ PresheafedSpace.{v} C) : IsColimit (colimitCocone F)
@@ -338,6 +363,7 @@ def colimitCoconeIsColimit (F : J ⥤ PresheafedSpace.{v} C) : IsColimit (colimi
       rw [nat_trans.congr (limit.π (pushforward_diagram_to_colimit F).leftOp j) w]
       simp
 #align algebraic_geometry.PresheafedSpace.colimit_cocone_is_colimit AlgebraicGeometry.PresheafedSpace.colimitCoconeIsColimit
+-/
 
 instance : HasColimitsOfShape J (PresheafedSpace.{v} C)
     where HasColimit F :=
@@ -364,6 +390,7 @@ instance [HasLimits C] : HasColimits (PresheafedSpace.{v} C)
           { Cocone := colimit_cocone F
             IsColimit := colimit_cocone_is_colimit F } }
 
+#print AlgebraicGeometry.PresheafedSpace.forgetPreservesColimits /-
 /-- The underlying topological space of a colimit of presheaved spaces is
 the colimit of the underlying topological spaces.
 -/
@@ -378,7 +405,9 @@ instance forgetPreservesColimits [HasLimits C] : PreservesColimits (PresheafedSp
             · rfl
             · intro j; dsimp; simp) }
 #align algebraic_geometry.PresheafedSpace.forget_preserves_colimits AlgebraicGeometry.PresheafedSpace.forgetPreservesColimits
+-/
 
+#print AlgebraicGeometry.PresheafedSpace.colimitPresheafObjIsoComponentwiseLimit /-
 /-- The components of the colimit of a diagram of `PresheafedSpace C` is obtained
 via taking componentwise limits.
 -/
@@ -408,7 +437,9 @@ def colimitPresheafObjIsoComponentwiseLimit (F : J ⥤ PresheafedSpace.{v} C) [H
       (F.obj (unop Y)).Presheaf.map_comp]
     congr
 #align algebraic_geometry.PresheafedSpace.colimit_presheaf_obj_iso_componentwise_limit AlgebraicGeometry.PresheafedSpace.colimitPresheafObjIsoComponentwiseLimit
+-/
 
+#print AlgebraicGeometry.PresheafedSpace.colimitPresheafObjIsoComponentwiseLimit_inv_ι_app /-
 @[simp]
 theorem colimitPresheafObjIsoComponentwiseLimit_inv_ι_app (F : J ⥤ PresheafedSpace.{v} C)
     (U : Opens (Limits.colimit F).carrier) (j : J) :
@@ -429,7 +460,9 @@ theorem colimitPresheafObjIsoComponentwiseLimit_inv_ι_app (F : J ⥤ Presheafed
   iterate 2 erw [← (F.obj j).Presheaf.map_comp]
   congr
 #align algebraic_geometry.PresheafedSpace.colimit_presheaf_obj_iso_componentwise_limit_inv_ι_app AlgebraicGeometry.PresheafedSpace.colimitPresheafObjIsoComponentwiseLimit_inv_ι_app
+-/
 
+#print AlgebraicGeometry.PresheafedSpace.colimitPresheafObjIsoComponentwiseLimit_hom_π /-
 @[simp]
 theorem colimitPresheafObjIsoComponentwiseLimit_hom_π (F : J ⥤ PresheafedSpace.{v} C)
     (U : Opens (Limits.colimit F).carrier) (j : J) :
@@ -437,6 +470,7 @@ theorem colimitPresheafObjIsoComponentwiseLimit_hom_π (F : J ⥤ PresheafedSpac
       (colimit.ι F j).c.app (op U) :=
   by rw [← iso.eq_inv_comp, colimit_presheaf_obj_iso_componentwise_limit_inv_ι_app]
 #align algebraic_geometry.PresheafedSpace.colimit_presheaf_obj_iso_componentwise_limit_hom_π AlgebraicGeometry.PresheafedSpace.colimitPresheafObjIsoComponentwiseLimit_hom_π
+-/
 
 end PresheafedSpace
 

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

@@ -252,7 +252,7 @@ def descCApp (F : J ⥤ PresheafedSpace.{v} C) (s : Cocone F) (U : (Opens ↥s.p
       functor.congr_obj
         (congr_arg opens.map (colimit.ι_desc ((PresheafedSpace.forget C).mapCocone s) (unop j)))
         (unop U)
-    simp only [opens.map_comp_obj_unop] at w
+    simp only [opens.map_comp_obj_unop] at w 
     replace w := congr_arg op w
     have w' := nat_trans.congr (F.map f.unop).c w
     rw [w']
@@ -277,7 +277,7 @@ theorem desc_c_naturality (F : J ⥤ PresheafedSpace.{v} C) (s : Cocone F)
     functor.congr_hom
       (congr_arg opens.map (colimit.ι_desc ((PresheafedSpace.forget C).mapCocone s) (unop j)))
       i.unop
-  simp only [opens.map_comp_map] at w
+  simp only [opens.map_comp_map] at w 
   replace w := congr_arg Quiver.Hom.op w
   rw [w]
   dsimp; simp

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

@@ -71,9 +71,6 @@ attribute [local simp] eq_to_hom_map
 
 attribute [local tidy] tactic.auto_cases_opens
 
-/- warning: algebraic_geometry.PresheafedSpace.map_id_c_app -> AlgebraicGeometry.PresheafedSpace.map_id_c_app is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.map_id_c_app AlgebraicGeometry.PresheafedSpace.map_id_c_appₓ'. -/
 @[simp]
 theorem map_id_c_app (F : J ⥤ PresheafedSpace.{v} C) (j) (U) :
     (F.map (𝟙 j)).c.app (op U) =
@@ -86,9 +83,6 @@ theorem map_id_c_app (F : J ⥤ PresheafedSpace.{v} C) (j) (U) :
   rfl
 #align algebraic_geometry.PresheafedSpace.map_id_c_app AlgebraicGeometry.PresheafedSpace.map_id_c_app
 
-/- warning: algebraic_geometry.PresheafedSpace.map_comp_c_app -> AlgebraicGeometry.PresheafedSpace.map_comp_c_app is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.map_comp_c_app AlgebraicGeometry.PresheafedSpace.map_comp_c_appₓ'. -/
 @[simp]
 theorem map_comp_c_app (F : J ⥤ PresheafedSpace.{v} C) {j₁ j₂ j₃} (f : j₁ ⟶ j₂) (g : j₂ ⟶ j₃) (U) :
     (F.map (f ≫ g)).c.app (op U) =
@@ -103,12 +97,6 @@ theorem map_comp_c_app (F : J ⥤ PresheafedSpace.{v} C) {j₁ j₂ j₃} (f : j
   dsimp; simp; dsimp; simp
 #align algebraic_geometry.PresheafedSpace.map_comp_c_app AlgebraicGeometry.PresheafedSpace.map_comp_c_app
 
-/- warning: algebraic_geometry.PresheafedSpace.componentwise_diagram -> AlgebraicGeometry.PresheafedSpace.componentwiseDiagram is a dubious translation:
-lean 3 declaration is
-  forall {J : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} J] {C : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u3, u4} C] (F : CategoryTheory.Functor.{u1, u3, u2, max u4 (succ u3)} J _inst_1 (AlgebraicGeometry.PresheafedSpace.{u3, u3, u4} C _inst_2) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{u3, u4} C _inst_2)) [_inst_3 : CategoryTheory.Limits.HasColimit.{u1, u2, u3, max u4 (succ u3)} J _inst_1 (AlgebraicGeometry.PresheafedSpace.{u3, u3, u4} C _inst_2) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{u3, u4} C _inst_2) F], (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} (AlgebraicGeometry.PresheafedSpace.carrier.{u3, u3, u4} C _inst_2 (CategoryTheory.Limits.colimit.{u1, u2, u3, max u4 (succ u3)} J _inst_1 (AlgebraicGeometry.PresheafedSpace.{u3, u3, u4} C _inst_2) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{u3, u4} C _inst_2) F _inst_3))) (TopCat.topologicalSpace.{u3} (AlgebraicGeometry.PresheafedSpace.carrier.{u3, u3, u4} C _inst_2 (CategoryTheory.Limits.colimit.{u1, u2, u3, max u4 (succ u3)} J _inst_1 (AlgebraicGeometry.PresheafedSpace.{u3, u3, u4} C _inst_2) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{u3, u4} C _inst_2) F _inst_3)))) -> (CategoryTheory.Functor.{u1, u3, u2, u4} (Opposite.{succ u2} J) (CategoryTheory.Category.opposite.{u1, u2} J _inst_1) C _inst_2)
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.componentwise_diagram AlgebraicGeometry.PresheafedSpace.componentwiseDiagramₓ'. -/
 -- See note [dsimp, simp]
 /-- Given a diagram of `PresheafedSpace C`s, its colimit is computed by pushing the sheaves onto
 the colimit of the underlying spaces, and taking componentwise limit.
@@ -137,12 +125,6 @@ def componentwiseDiagram (F : J ⥤ PresheafedSpace.{v} C) [HasColimit F]
 
 variable [HasColimitsOfShape J TopCat.{v}]
 
-/- warning: algebraic_geometry.PresheafedSpace.pushforward_diagram_to_colimit -> AlgebraicGeometry.PresheafedSpace.pushforwardDiagramToColimit is a dubious translation:
-lean 3 declaration is
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 /-- Given a diagram of presheafed spaces,
 we can push all the presheaves forward to the colimit `X` of the underlying topological spaces,
 obtaining a diagram in `(presheaf C X)ᵒᵖ`.
@@ -191,12 +173,6 @@ def pushforwardDiagramToColimit (F : J ⥤ PresheafedSpace.{v} C) :
 
 variable [∀ X : TopCat.{v}, HasLimitsOfShape Jᵒᵖ (X.Presheaf C)]
 
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 /-- Auxiliary definition for `PresheafedSpace.has_colimits`.
 -/
 def colimit (F : J ⥤ PresheafedSpace.{v} C) : PresheafedSpace C
@@ -205,33 +181,18 @@ def colimit (F : J ⥤ PresheafedSpace.{v} C) : PresheafedSpace C
   Presheaf := limit (pushforwardDiagramToColimit F).leftOp
 #align algebraic_geometry.PresheafedSpace.colimit AlgebraicGeometry.PresheafedSpace.colimit
 
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 @[simp]
 theorem colimit_carrier (F : J ⥤ PresheafedSpace.{v} C) :
     (colimit F).carrier = Limits.colimit (F ⋙ PresheafedSpace.forget C) :=
   rfl
 #align algebraic_geometry.PresheafedSpace.colimit_carrier AlgebraicGeometry.PresheafedSpace.colimit_carrier
 
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 @[simp]
 theorem colimit_presheaf (F : J ⥤ PresheafedSpace.{v} C) :
     (colimit F).Presheaf = limit (pushforwardDiagramToColimit F).leftOp :=
   rfl
 #align algebraic_geometry.PresheafedSpace.colimit_presheaf AlgebraicGeometry.PresheafedSpace.colimit_presheaf
 
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 /-- Auxiliary definition for `PresheafedSpace.has_colimits`.
 -/
 @[simps]
@@ -265,9 +226,6 @@ variable [HasLimitsOfShape Jᵒᵖ C]
 
 namespace ColimitCoconeIsColimit
 
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 /-- Auxiliary definition for `PresheafedSpace.colimit_cocone_is_colimit`.
 -/
 def descCApp (F : J ⥤ PresheafedSpace.{v} C) (s : Cocone F) (U : (Opens ↥s.pt.carrier)ᵒᵖ) :
@@ -301,9 +259,6 @@ def descCApp (F : J ⥤ PresheafedSpace.{v} C) (s : Cocone F) (U : (Opens ↥s.p
     dsimp; simp; dsimp; simp
 #align algebraic_geometry.PresheafedSpace.colimit_cocone_is_colimit.desc_c_app AlgebraicGeometry.PresheafedSpace.ColimitCoconeIsColimit.descCApp
 
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 theorem desc_c_naturality (F : J ⥤ PresheafedSpace.{v} C) (s : Cocone F)
     {U V : (Opens ↥s.pt.carrier)ᵒᵖ} (i : U ⟶ V) :
     s.pt.Presheaf.map i ≫ descCApp F s V =
@@ -328,12 +283,6 @@ theorem desc_c_naturality (F : J ⥤ PresheafedSpace.{v} C) (s : Cocone F)
   dsimp; simp
 #align algebraic_geometry.PresheafedSpace.colimit_cocone_is_colimit.desc_c_naturality AlgebraicGeometry.PresheafedSpace.ColimitCoconeIsColimit.desc_c_naturality
 
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-Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.colimit_cocone_is_colimit.desc AlgebraicGeometry.PresheafedSpace.ColimitCoconeIsColimit.descₓ'. -/
 /-- Auxiliary definition for `PresheafedSpace.colimit_cocone_is_colimit`.
 -/
 def desc (F : J ⥤ PresheafedSpace.{v} C) (s : Cocone F) : colimit F ⟶ s.pt
@@ -344,9 +293,6 @@ def desc (F : J ⥤ PresheafedSpace.{v} C) (s : Cocone F) : colimit F ⟶ s.pt
       naturality' := fun U V i => desc_c_naturality F s i }
 #align algebraic_geometry.PresheafedSpace.colimit_cocone_is_colimit.desc AlgebraicGeometry.PresheafedSpace.ColimitCoconeIsColimit.desc
 
-/- warning: algebraic_geometry.PresheafedSpace.colimit_cocone_is_colimit.desc_fac -> AlgebraicGeometry.PresheafedSpace.ColimitCoconeIsColimit.desc_fac is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.colimit_cocone_is_colimit.desc_fac AlgebraicGeometry.PresheafedSpace.ColimitCoconeIsColimit.desc_facₓ'. -/
 theorem desc_fac (F : J ⥤ PresheafedSpace.{v} C) (s : Cocone F) (j : J) :
     (colimitCocone F).ι.app j ≫ desc F s = s.ι.app j :=
   by
@@ -361,12 +307,6 @@ end ColimitCoconeIsColimit
 
 open ColimitCoconeIsColimit
 
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-Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.colimit_cocone_is_colimit AlgebraicGeometry.PresheafedSpace.colimitCoconeIsColimitₓ'. -/
 /-- Auxiliary definition for `PresheafedSpace.has_colimits`.
 -/
 def colimitCoconeIsColimit (F : J ⥤ PresheafedSpace.{v} C) : IsColimit (colimitCocone F)
@@ -424,12 +364,6 @@ instance [HasLimits C] : HasColimits (PresheafedSpace.{v} C)
           { Cocone := colimit_cocone F
             IsColimit := colimit_cocone_is_colimit F } }
 
-/- warning: algebraic_geometry.PresheafedSpace.forget_preserves_colimits -> AlgebraicGeometry.PresheafedSpace.forgetPreservesColimits is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.forget_preserves_colimits AlgebraicGeometry.PresheafedSpace.forgetPreservesColimitsₓ'. -/
 /-- The underlying topological space of a colimit of presheaved spaces is
 the colimit of the underlying topological spaces.
 -/
@@ -445,9 +379,6 @@ instance forgetPreservesColimits [HasLimits C] : PreservesColimits (PresheafedSp
             · intro j; dsimp; simp) }
 #align algebraic_geometry.PresheafedSpace.forget_preserves_colimits AlgebraicGeometry.PresheafedSpace.forgetPreservesColimits
 
-/- warning: algebraic_geometry.PresheafedSpace.colimit_presheaf_obj_iso_componentwise_limit -> AlgebraicGeometry.PresheafedSpace.colimitPresheafObjIsoComponentwiseLimit is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.colimit_presheaf_obj_iso_componentwise_limit AlgebraicGeometry.PresheafedSpace.colimitPresheafObjIsoComponentwiseLimitₓ'. -/
 /-- The components of the colimit of a diagram of `PresheafedSpace C` is obtained
 via taking componentwise limits.
 -/
@@ -478,9 +409,6 @@ def colimitPresheafObjIsoComponentwiseLimit (F : J ⥤ PresheafedSpace.{v} C) [H
     congr
 #align algebraic_geometry.PresheafedSpace.colimit_presheaf_obj_iso_componentwise_limit AlgebraicGeometry.PresheafedSpace.colimitPresheafObjIsoComponentwiseLimit
 
-/- warning: algebraic_geometry.PresheafedSpace.colimit_presheaf_obj_iso_componentwise_limit_inv_ι_app -> AlgebraicGeometry.PresheafedSpace.colimitPresheafObjIsoComponentwiseLimit_inv_ι_app is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.colimit_presheaf_obj_iso_componentwise_limit_inv_ι_app AlgebraicGeometry.PresheafedSpace.colimitPresheafObjIsoComponentwiseLimit_inv_ι_appₓ'. -/
 @[simp]
 theorem colimitPresheafObjIsoComponentwiseLimit_inv_ι_app (F : J ⥤ PresheafedSpace.{v} C)
     (U : Opens (Limits.colimit F).carrier) (j : J) :
@@ -502,9 +430,6 @@ theorem colimitPresheafObjIsoComponentwiseLimit_inv_ι_app (F : J ⥤ Presheafed
   congr
 #align algebraic_geometry.PresheafedSpace.colimit_presheaf_obj_iso_componentwise_limit_inv_ι_app AlgebraicGeometry.PresheafedSpace.colimitPresheafObjIsoComponentwiseLimit_inv_ι_app
 
-/- warning: algebraic_geometry.PresheafedSpace.colimit_presheaf_obj_iso_componentwise_limit_hom_π -> AlgebraicGeometry.PresheafedSpace.colimitPresheafObjIsoComponentwiseLimit_hom_π is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.colimit_presheaf_obj_iso_componentwise_limit_hom_π AlgebraicGeometry.PresheafedSpace.colimitPresheafObjIsoComponentwiseLimit_hom_πₓ'. -/
 @[simp]
 theorem colimitPresheafObjIsoComponentwiseLimit_hom_π (F : J ⥤ PresheafedSpace.{v} C)
     (U : Opens (Limits.colimit F).carrier) (j : J) :

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

@@ -78,12 +78,7 @@ Case conversion may be inaccurate. Consider using '#align algebraic_geometry.Pre
 theorem map_id_c_app (F : J ⥤ PresheafedSpace.{v} C) (j) (U) :
     (F.map (𝟙 j)).c.app (op U) =
       (Pushforward.id (F.obj j).Presheaf).inv.app (op U) ≫
-        (pushforwardEq
-                (by
-                  simp
-                  rfl)
-                (F.obj j).Presheaf).Hom.app
-          (op U) :=
+        (pushforwardEq (by simp; rfl) (F.obj j).Presheaf).Hom.app (op U) :=
   by
   cases U
   dsimp
@@ -100,12 +95,7 @@ theorem map_comp_c_app (F : J ⥤ PresheafedSpace.{v} C) {j₁ j₂ j₃} (f : j
       (F.map g).c.app (op U) ≫
         (pushforwardMap (F.map g).base (F.map f).c).app (op U) ≫
           (Pushforward.comp (F.obj j₁).Presheaf (F.map f).base (F.map g).base).inv.app (op U) ≫
-            (pushforwardEq
-                    (by
-                      rw [F.map_comp]
-                      rfl)
-                    _).Hom.app
-              _ :=
+            (pushforwardEq (by rw [F.map_comp]; rfl) _).Hom.app _ :=
   by
   cases U
   dsimp
@@ -131,11 +121,7 @@ def componentwiseDiagram (F : J ⥤ PresheafedSpace.{v} C) [HasColimit F]
   obj j := (F.obj (unop j)).Presheaf.obj (op ((Opens.map (colimit.ι F (unop j)).base).obj U))
   map j k f :=
     (F.map f.unop).c.app _ ≫
-      (F.obj (unop k)).Presheaf.map
-        (eqToHom
-          (by
-            rw [← colimit.w F f.unop, comp_base]
-            rfl))
+      (F.obj (unop k)).Presheaf.map (eqToHom (by rw [← colimit.w F f.unop, comp_base]; rfl))
   map_comp' i j k f g := by
     cases U
     dsimp
@@ -200,8 +186,7 @@ def pushforwardDiagramToColimit (F : J ⥤ PresheafedSpace.{v} C) :
       exact colimit.w (F ⋙ PresheafedSpace.forget C) g
     -- Finally, the original goal is now easy:
     swap
-    · simp
-      rfl
+    · simp; rfl
 #align algebraic_geometry.PresheafedSpace.pushforward_diagram_to_colimit AlgebraicGeometry.PresheafedSpace.pushforwardDiagramToColimit
 
 variable [∀ X : TopCat.{v}, HasLimitsOfShape Jᵒᵖ (X.Presheaf C)]
@@ -313,10 +298,7 @@ def descCApp (F : J ⥤ PresheafedSpace.{v} C) (s : Cocone F) (U : (Opens ↥s.p
     replace w := congr_arg op w
     have w' := nat_trans.congr (F.map f.unop).c w
     rw [w']
-    dsimp
-    simp
-    dsimp
-    simp
+    dsimp; simp; dsimp; simp
 #align algebraic_geometry.PresheafedSpace.colimit_cocone_is_colimit.desc_c_app AlgebraicGeometry.PresheafedSpace.ColimitCoconeIsColimit.descCApp
 
 /- warning: algebraic_geometry.PresheafedSpace.colimit_cocone_is_colimit.desc_c_naturality -> AlgebraicGeometry.PresheafedSpace.ColimitCoconeIsColimit.desc_c_naturality is a dubious translation:
@@ -398,10 +380,8 @@ def colimitCoconeIsColimit (F : J ⥤ PresheafedSpace.{v} C) : IsColimit (colimi
       m.base =
         colimit.desc (F ⋙ PresheafedSpace.forget C) ((PresheafedSpace.forget C).mapCocone s) :=
       by
-      apply CategoryTheory.Limits.colimit.hom_ext
-      intro j
-      apply ContinuousMap.ext
-      intro x
+      apply CategoryTheory.Limits.colimit.hom_ext; intro j
+      apply ContinuousMap.ext; intro x
       dsimp
       simp only [colimit.ι_desc_apply, map_cocone_ι_app]
       rw [← w j]
@@ -409,8 +389,7 @@ def colimitCoconeIsColimit (F : J ⥤ PresheafedSpace.{v} C) : IsColimit (colimi
     fapply PresheafedSpace.ext
     -- could `ext` please not reorder goals?
     · exact t
-    · ext (U j)
-      dsimp [desc, desc_c_app]
+    · ext (U j); dsimp [desc, desc_c_app]
       simp only [limit.lift_π, eq_to_hom_op, eq_to_hom_map, assoc,
         limit_obj_iso_limit_comp_evaluation_inv_π_app]
       rw [PresheafedSpace.congr_app (w (unop j)).symm U]
@@ -433,9 +412,7 @@ instance : PreservesColimitsOfShape J (PresheafedSpace.forget C)
         apply is_colimit.of_iso_colimit (colimit.is_colimit _)
         fapply cocones.ext
         · rfl
-        · intro j
-          dsimp
-          simp)
+        · intro j; dsimp; simp)
 
 /-- When `C` has limits, the category of presheaved spaces with values in `C` itself has colimits.
 -/
@@ -465,9 +442,7 @@ instance forgetPreservesColimits [HasLimits C] : PreservesColimits (PresheafedSp
             apply is_colimit.of_iso_colimit (colimit.is_colimit _)
             fapply cocones.ext
             · rfl
-            · intro j
-              dsimp
-              simp) }
+            · intro j; dsimp; simp) }
 #align algebraic_geometry.PresheafedSpace.forget_preserves_colimits AlgebraicGeometry.PresheafedSpace.forgetPreservesColimits
 
 /- warning: algebraic_geometry.PresheafedSpace.colimit_presheaf_obj_iso_componentwise_limit -> AlgebraicGeometry.PresheafedSpace.colimitPresheafObjIsoComponentwiseLimit is a dubious translation:

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
 
 ! This file was ported from Lean 3 source module algebraic_geometry.presheafed_space.has_colimits
-! leanprover-community/mathlib commit 178a32653e369dce2da68dc6b2694e385d484ef1
+! leanprover-community/mathlib commit 0b7c740e25651db0ba63648fbae9f9d6f941e31b
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.Topology.Sheaves.Limits
 /-!
 # `PresheafedSpace C` has colimits.
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 If `C` has limits, then the category `PresheafedSpace C` has colimits,
 and the forgetful functor to `Top` preserves these colimits.
 
@@ -69,10 +72,7 @@ attribute [local simp] eq_to_hom_map
 attribute [local tidy] tactic.auto_cases_opens
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.map_id_c_app AlgebraicGeometry.PresheafedSpace.map_id_c_appₓ'. -/
 @[simp]
 theorem map_id_c_app (F : J ⥤ PresheafedSpace.{v} C) (j) (U) :
@@ -92,10 +92,7 @@ theorem map_id_c_app (F : J ⥤ PresheafedSpace.{v} C) (j) (U) :
 #align algebraic_geometry.PresheafedSpace.map_id_c_app AlgebraicGeometry.PresheafedSpace.map_id_c_app
 
 /- warning: algebraic_geometry.PresheafedSpace.map_comp_c_app -> AlgebraicGeometry.PresheafedSpace.map_comp_c_app is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.map_comp_c_app AlgebraicGeometry.PresheafedSpace.map_comp_c_appₓ'. -/
 @[simp]
 theorem map_comp_c_app (F : J ⥤ PresheafedSpace.{v} C) {j₁ j₂ j₃} (f : j₁ ⟶ j₂) (g : j₂ ⟶ j₃) (U) :
@@ -236,10 +233,7 @@ theorem colimit_carrier (F : J ⥤ PresheafedSpace.{v} C) :
 #align algebraic_geometry.PresheafedSpace.colimit_carrier AlgebraicGeometry.PresheafedSpace.colimit_carrier
 
 /- warning: algebraic_geometry.PresheafedSpace.colimit_presheaf -> AlgebraicGeometry.PresheafedSpace.colimit_presheaf is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.colimit_presheaf AlgebraicGeometry.PresheafedSpace.colimit_presheafₓ'. -/
 @[simp]
 theorem colimit_presheaf (F : J ⥤ PresheafedSpace.{v} C) :
@@ -287,10 +281,7 @@ variable [HasLimitsOfShape Jᵒᵖ C]
 namespace ColimitCoconeIsColimit
 
 /- warning: algebraic_geometry.PresheafedSpace.colimit_cocone_is_colimit.desc_c_app -> AlgebraicGeometry.PresheafedSpace.ColimitCoconeIsColimit.descCApp is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.colimit_cocone_is_colimit.desc_c_app AlgebraicGeometry.PresheafedSpace.ColimitCoconeIsColimit.descCAppₓ'. -/
 /-- Auxiliary definition for `PresheafedSpace.colimit_cocone_is_colimit`.
 -/
@@ -329,10 +320,7 @@ def descCApp (F : J ⥤ PresheafedSpace.{v} C) (s : Cocone F) (U : (Opens ↥s.p
 #align algebraic_geometry.PresheafedSpace.colimit_cocone_is_colimit.desc_c_app AlgebraicGeometry.PresheafedSpace.ColimitCoconeIsColimit.descCApp
 
 /- warning: algebraic_geometry.PresheafedSpace.colimit_cocone_is_colimit.desc_c_naturality -> AlgebraicGeometry.PresheafedSpace.ColimitCoconeIsColimit.desc_c_naturality is a dubious translation:
-lean 3 declaration is
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(AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{u4, u3, u3} C _inst_2) TopCat.{u3} instTopCatLargeCategory.{u3} (AlgebraicGeometry.PresheafedSpace.forget.{u4, u3, u3} C _inst_2) F s)) (AlgebraicGeometry.PresheafedSpace.presheaf.{u4, u3, u3} C _inst_2 (CategoryTheory.Limits.Cocone.pt.{u1, u3, u2, max u4 (succ u3)} J _inst_1 (AlgebraicGeometry.PresheafedSpace.{u4, u3, u3} C _inst_2) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{u4, u3, u3} C _inst_2) F (AlgebraicGeometry.PresheafedSpace.colimitCocone.{u1, u2, u3, u4} J _inst_1 C _inst_2 _inst_3 (fun (X : TopCat.{u3}) => _inst_4 X) F))))) U V i))
+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.colimit_cocone_is_colimit.desc_c_naturality AlgebraicGeometry.PresheafedSpace.ColimitCoconeIsColimit.desc_c_naturalityₓ'. -/
 theorem desc_c_naturality (F : J ⥤ PresheafedSpace.{v} C) (s : Cocone F)
     {U V : (Opens ↥s.pt.carrier)ᵒᵖ} (i : U ⟶ V) :
@@ -375,10 +363,7 @@ def desc (F : J ⥤ PresheafedSpace.{v} C) (s : Cocone F) : colimit F ⟶ s.pt
 #align algebraic_geometry.PresheafedSpace.colimit_cocone_is_colimit.desc AlgebraicGeometry.PresheafedSpace.ColimitCoconeIsColimit.desc
 
 /- warning: algebraic_geometry.PresheafedSpace.colimit_cocone_is_colimit.desc_fac -> AlgebraicGeometry.PresheafedSpace.ColimitCoconeIsColimit.desc_fac is a dubious translation:
-lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.colimit_cocone_is_colimit.desc_fac AlgebraicGeometry.PresheafedSpace.ColimitCoconeIsColimit.desc_facₓ'. -/
 theorem desc_fac (F : J ⥤ PresheafedSpace.{v} C) (s : Cocone F) (j : J) :
     (colimitCocone F).ι.app j ≫ desc F s = s.ι.app j :=
@@ -486,10 +471,7 @@ instance forgetPreservesColimits [HasLimits C] : PreservesColimits (PresheafedSp
 #align algebraic_geometry.PresheafedSpace.forget_preserves_colimits AlgebraicGeometry.PresheafedSpace.forgetPreservesColimits
 
 /- warning: algebraic_geometry.PresheafedSpace.colimit_presheaf_obj_iso_componentwise_limit -> AlgebraicGeometry.PresheafedSpace.colimitPresheafObjIsoComponentwiseLimit is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.colimit_presheaf_obj_iso_componentwise_limit AlgebraicGeometry.PresheafedSpace.colimitPresheafObjIsoComponentwiseLimitₓ'. -/
 /-- The components of the colimit of a diagram of `PresheafedSpace C` is obtained
 via taking componentwise limits.
@@ -522,10 +504,7 @@ def colimitPresheafObjIsoComponentwiseLimit (F : J ⥤ PresheafedSpace.{v} C) [H
 #align algebraic_geometry.PresheafedSpace.colimit_presheaf_obj_iso_componentwise_limit AlgebraicGeometry.PresheafedSpace.colimitPresheafObjIsoComponentwiseLimit
 
 /- warning: algebraic_geometry.PresheafedSpace.colimit_presheaf_obj_iso_componentwise_limit_inv_ι_app -> AlgebraicGeometry.PresheafedSpace.colimitPresheafObjIsoComponentwiseLimit_inv_ι_app is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.colimit_presheaf_obj_iso_componentwise_limit_inv_ι_app AlgebraicGeometry.PresheafedSpace.colimitPresheafObjIsoComponentwiseLimit_inv_ι_appₓ'. -/
 @[simp]
 theorem colimitPresheafObjIsoComponentwiseLimit_inv_ι_app (F : J ⥤ PresheafedSpace.{v} C)
@@ -549,10 +528,7 @@ theorem colimitPresheafObjIsoComponentwiseLimit_inv_ι_app (F : J ⥤ Presheafed
 #align algebraic_geometry.PresheafedSpace.colimit_presheaf_obj_iso_componentwise_limit_inv_ι_app AlgebraicGeometry.PresheafedSpace.colimitPresheafObjIsoComponentwiseLimit_inv_ι_app
 
 /- warning: algebraic_geometry.PresheafedSpace.colimit_presheaf_obj_iso_componentwise_limit_hom_π -> AlgebraicGeometry.PresheafedSpace.colimitPresheafObjIsoComponentwiseLimit_hom_π is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.colimit_presheaf_obj_iso_componentwise_limit_hom_π AlgebraicGeometry.PresheafedSpace.colimitPresheafObjIsoComponentwiseLimit_hom_πₓ'. -/
 @[simp]
 theorem colimitPresheafObjIsoComponentwiseLimit_hom_π (F : J ⥤ PresheafedSpace.{v} C)

mathlib commit https://github.com/leanprover-community/mathlib/commit/ef95945cd48c932c9e034872bd25c3c220d9c946

@@ -68,6 +68,12 @@ attribute [local simp] eq_to_hom_map
 
 attribute [local tidy] tactic.auto_cases_opens
 
+/- warning: algebraic_geometry.PresheafedSpace.map_id_c_app -> AlgebraicGeometry.PresheafedSpace.map_id_c_app is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.map_id_c_app AlgebraicGeometry.PresheafedSpace.map_id_c_appₓ'. -/
 @[simp]
 theorem map_id_c_app (F : J ⥤ PresheafedSpace.{v} C) (j) (U) :
     (F.map (𝟙 j)).c.app (op U) =
@@ -85,6 +91,12 @@ theorem map_id_c_app (F : J ⥤ PresheafedSpace.{v} C) (j) (U) :
   rfl
 #align algebraic_geometry.PresheafedSpace.map_id_c_app AlgebraicGeometry.PresheafedSpace.map_id_c_app
 
+/- warning: algebraic_geometry.PresheafedSpace.map_comp_c_app -> AlgebraicGeometry.PresheafedSpace.map_comp_c_app is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.map_comp_c_app AlgebraicGeometry.PresheafedSpace.map_comp_c_appₓ'. -/
 @[simp]
 theorem map_comp_c_app (F : J ⥤ PresheafedSpace.{v} C) {j₁ j₂ j₃} (f : j₁ ⟶ j₂) (g : j₂ ⟶ j₃) (U) :
     (F.map (f ≫ g)).c.app (op U) =
@@ -104,6 +116,12 @@ theorem map_comp_c_app (F : J ⥤ PresheafedSpace.{v} C) {j₁ j₂ j₃} (f : j
   dsimp; simp; dsimp; simp
 #align algebraic_geometry.PresheafedSpace.map_comp_c_app AlgebraicGeometry.PresheafedSpace.map_comp_c_app
 
+/- warning: algebraic_geometry.PresheafedSpace.componentwise_diagram -> AlgebraicGeometry.PresheafedSpace.componentwiseDiagram is a dubious translation:
+lean 3 declaration is
+  forall {J : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} J] {C : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u3, u4} C] (F : CategoryTheory.Functor.{u1, u3, u2, max u4 (succ u3)} J _inst_1 (AlgebraicGeometry.PresheafedSpace.{u3, u3, u4} C _inst_2) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{u3, u4} C _inst_2)) [_inst_3 : CategoryTheory.Limits.HasColimit.{u1, u2, u3, max u4 (succ u3)} J _inst_1 (AlgebraicGeometry.PresheafedSpace.{u3, u3, u4} C _inst_2) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{u3, u4} C _inst_2) F], (TopologicalSpace.Opens.{u3} (coeSort.{succ (succ u3), succ (succ u3)} TopCat.{u3} Type.{u3} TopCat.hasCoeToSort.{u3} (AlgebraicGeometry.PresheafedSpace.carrier.{u3, u3, u4} C _inst_2 (CategoryTheory.Limits.colimit.{u1, u2, u3, max u4 (succ u3)} J _inst_1 (AlgebraicGeometry.PresheafedSpace.{u3, u3, u4} C _inst_2) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{u3, u4} C _inst_2) F _inst_3))) (TopCat.topologicalSpace.{u3} (AlgebraicGeometry.PresheafedSpace.carrier.{u3, u3, u4} C _inst_2 (CategoryTheory.Limits.colimit.{u1, u2, u3, max u4 (succ u3)} J _inst_1 (AlgebraicGeometry.PresheafedSpace.{u3, u3, u4} C _inst_2) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{u3, u4} C _inst_2) F _inst_3)))) -> (CategoryTheory.Functor.{u1, u3, u2, u4} (Opposite.{succ u2} J) (CategoryTheory.Category.opposite.{u1, u2} J _inst_1) C _inst_2)
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.componentwise_diagram AlgebraicGeometry.PresheafedSpace.componentwiseDiagramₓ'. -/
 -- See note [dsimp, simp]
 /-- Given a diagram of `PresheafedSpace C`s, its colimit is computed by pushing the sheaves onto
 the colimit of the underlying spaces, and taking componentwise limit.
@@ -136,6 +154,12 @@ def componentwiseDiagram (F : J ⥤ PresheafedSpace.{v} C) [HasColimit F]
 
 variable [HasColimitsOfShape J TopCat.{v}]
 
+/- warning: algebraic_geometry.PresheafedSpace.pushforward_diagram_to_colimit -> AlgebraicGeometry.PresheafedSpace.pushforwardDiagramToColimit is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.pushforward_diagram_to_colimit AlgebraicGeometry.PresheafedSpace.pushforwardDiagramToColimitₓ'. -/
 /-- Given a diagram of presheafed spaces,
 we can push all the presheaves forward to the colimit `X` of the underlying topological spaces,
 obtaining a diagram in `(presheaf C X)ᵒᵖ`.
@@ -185,6 +209,12 @@ def pushforwardDiagramToColimit (F : J ⥤ PresheafedSpace.{v} C) :
 
 variable [∀ X : TopCat.{v}, HasLimitsOfShape Jᵒᵖ (X.Presheaf C)]
 
+/- warning: algebraic_geometry.PresheafedSpace.colimit -> AlgebraicGeometry.PresheafedSpace.colimit is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.colimit AlgebraicGeometry.PresheafedSpace.colimitₓ'. -/
 /-- Auxiliary definition for `PresheafedSpace.has_colimits`.
 -/
 def colimit (F : J ⥤ PresheafedSpace.{v} C) : PresheafedSpace C
@@ -193,18 +223,36 @@ def colimit (F : J ⥤ PresheafedSpace.{v} C) : PresheafedSpace C
   Presheaf := limit (pushforwardDiagramToColimit F).leftOp
 #align algebraic_geometry.PresheafedSpace.colimit AlgebraicGeometry.PresheafedSpace.colimit
 
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 @[simp]
 theorem colimit_carrier (F : J ⥤ PresheafedSpace.{v} C) :
     (colimit F).carrier = Limits.colimit (F ⋙ PresheafedSpace.forget C) :=
   rfl
 #align algebraic_geometry.PresheafedSpace.colimit_carrier AlgebraicGeometry.PresheafedSpace.colimit_carrier
 
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+Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.colimit_presheaf AlgebraicGeometry.PresheafedSpace.colimit_presheafₓ'. -/
 @[simp]
 theorem colimit_presheaf (F : J ⥤ PresheafedSpace.{v} C) :
     (colimit F).Presheaf = limit (pushforwardDiagramToColimit F).leftOp :=
   rfl
 #align algebraic_geometry.PresheafedSpace.colimit_presheaf AlgebraicGeometry.PresheafedSpace.colimit_presheaf
 
+/- warning: algebraic_geometry.PresheafedSpace.colimit_cocone -> AlgebraicGeometry.PresheafedSpace.colimitCocone is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.colimit_cocone AlgebraicGeometry.PresheafedSpace.colimitCoconeₓ'. -/
 /-- Auxiliary definition for `PresheafedSpace.has_colimits`.
 -/
 @[simps]
@@ -238,6 +286,12 @@ variable [HasLimitsOfShape Jᵒᵖ C]
 
 namespace ColimitCoconeIsColimit
 
+/- warning: algebraic_geometry.PresheafedSpace.colimit_cocone_is_colimit.desc_c_app -> AlgebraicGeometry.PresheafedSpace.ColimitCoconeIsColimit.descCApp is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.colimit_cocone_is_colimit.desc_c_app AlgebraicGeometry.PresheafedSpace.ColimitCoconeIsColimit.descCAppₓ'. -/
 /-- Auxiliary definition for `PresheafedSpace.colimit_cocone_is_colimit`.
 -/
 def descCApp (F : J ⥤ PresheafedSpace.{v} C) (s : Cocone F) (U : (Opens ↥s.pt.carrier)ᵒᵖ) :
@@ -274,6 +328,12 @@ def descCApp (F : J ⥤ PresheafedSpace.{v} C) (s : Cocone F) (U : (Opens ↥s.p
     simp
 #align algebraic_geometry.PresheafedSpace.colimit_cocone_is_colimit.desc_c_app AlgebraicGeometry.PresheafedSpace.ColimitCoconeIsColimit.descCApp
 
+/- warning: algebraic_geometry.PresheafedSpace.colimit_cocone_is_colimit.desc_c_naturality -> AlgebraicGeometry.PresheafedSpace.ColimitCoconeIsColimit.desc_c_naturality is a dubious translation:
+lean 3 declaration is
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(AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{u4, u3, u3} C _inst_2) TopCat.{u3} instTopCatLargeCategory.{u3} (AlgebraicGeometry.PresheafedSpace.forget.{u4, u3, u3} C _inst_2) F s)) (AlgebraicGeometry.PresheafedSpace.presheaf.{u4, u3, u3} C _inst_2 (CategoryTheory.Limits.Cocone.pt.{u1, u3, u2, max u4 (succ u3)} J _inst_1 (AlgebraicGeometry.PresheafedSpace.{u4, u3, u3} C _inst_2) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{u4, u3, u3} C _inst_2) F (AlgebraicGeometry.PresheafedSpace.colimitCocone.{u1, u2, u3, u4} J _inst_1 C _inst_2 _inst_3 (fun (X : TopCat.{u3}) => _inst_4 X) F))))) U V i))
+Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.colimit_cocone_is_colimit.desc_c_naturality AlgebraicGeometry.PresheafedSpace.ColimitCoconeIsColimit.desc_c_naturalityₓ'. -/
 theorem desc_c_naturality (F : J ⥤ PresheafedSpace.{v} C) (s : Cocone F)
     {U V : (Opens ↥s.pt.carrier)ᵒᵖ} (i : U ⟶ V) :
     s.pt.Presheaf.map i ≫ descCApp F s V =
@@ -298,6 +358,12 @@ theorem desc_c_naturality (F : J ⥤ PresheafedSpace.{v} C) (s : Cocone F)
   dsimp; simp
 #align algebraic_geometry.PresheafedSpace.colimit_cocone_is_colimit.desc_c_naturality AlgebraicGeometry.PresheafedSpace.ColimitCoconeIsColimit.desc_c_naturality
 
+/- warning: algebraic_geometry.PresheafedSpace.colimit_cocone_is_colimit.desc -> AlgebraicGeometry.PresheafedSpace.ColimitCoconeIsColimit.desc is a dubious translation:
+lean 3 declaration is
+  forall {J : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} J] {C : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u3, u4} C] [_inst_3 : CategoryTheory.Limits.HasColimitsOfShape.{u1, u2, u3, succ u3} J _inst_1 TopCat.{u3} TopCat.largeCategory.{u3}] [_inst_4 : forall (X : TopCat.{u3}), CategoryTheory.Limits.HasLimitsOfShape.{u1, u2, u3, max u4 u3} (Opposite.{succ u2} J) (CategoryTheory.Category.opposite.{u1, u2} J _inst_1) (TopCat.Presheaf.{u3, u3, u4} C _inst_2 X) (TopCat.Presheaf.category.{u3, u3, u4} C _inst_2 X)] [_inst_5 : CategoryTheory.Limits.HasLimitsOfShape.{u1, u2, u3, u4} (Opposite.{succ u2} J) (CategoryTheory.Category.opposite.{u1, u2} J _inst_1) C _inst_2] (F : CategoryTheory.Functor.{u1, u3, u2, max u4 (succ u3)} J _inst_1 (AlgebraicGeometry.PresheafedSpace.{u3, u3, u4} C _inst_2) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{u3, u4} C _inst_2)) (s : CategoryTheory.Limits.Cocone.{u1, u3, u2, max u4 (succ u3)} J _inst_1 (AlgebraicGeometry.PresheafedSpace.{u3, u3, u4} C _inst_2) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{u3, u4} C _inst_2) F), Quiver.Hom.{succ u3, max u4 (succ u3)} (AlgebraicGeometry.PresheafedSpace.{u3, u3, u4} C _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{u3, max u4 (succ u3)} (AlgebraicGeometry.PresheafedSpace.{u3, u3, u4} C _inst_2) (CategoryTheory.Category.toCategoryStruct.{u3, max u4 (succ u3)} (AlgebraicGeometry.PresheafedSpace.{u3, u3, u4} C _inst_2) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{u3, u4} C _inst_2))) (AlgebraicGeometry.PresheafedSpace.colimit.{u1, u2, u3, u4} J _inst_1 C _inst_2 _inst_3 (AlgebraicGeometry.PresheafedSpace.ColimitCoconeIsColimit.desc._proof_1.{u4, u2, u3, u1} J _inst_1 C _inst_2 _inst_4) F) (CategoryTheory.Limits.Cocone.pt.{u1, u3, u2, max u4 (succ u3)} J _inst_1 (AlgebraicGeometry.PresheafedSpace.{u3, u3, u4} C _inst_2) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{u3, u4} C _inst_2) F s)
+but is expected to have type
+  forall {J : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} J] {C : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u3, u4} C] [_inst_3 : CategoryTheory.Limits.HasColimitsOfShape.{u1, u2, u3, succ u3} J _inst_1 TopCat.{u3} instTopCatLargeCategory.{u3}] [_inst_4 : forall (X : TopCat.{u3}), CategoryTheory.Limits.HasLimitsOfShape.{u1, u2, u3, max u4 u3} (Opposite.{succ u2} J) (CategoryTheory.Category.opposite.{u1, u2} J _inst_1) (TopCat.Presheaf.{u3, u3, u4} C _inst_2 X) (TopCat.instCategoryPresheaf.{u3, u3, u4} C _inst_2 X)] [_inst_5 : CategoryTheory.Limits.HasLimitsOfShape.{u1, u2, u3, u4} (Opposite.{succ u2} J) (CategoryTheory.Category.opposite.{u1, u2} J _inst_1) C _inst_2] (F : CategoryTheory.Functor.{u1, u3, u2, max (succ u3) u4} J _inst_1 (AlgebraicGeometry.PresheafedSpace.{u4, u3, u3} C _inst_2) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{u4, u3, u3} C _inst_2)) (s : CategoryTheory.Limits.Cocone.{u1, u3, u2, max u4 (succ u3)} J _inst_1 (AlgebraicGeometry.PresheafedSpace.{u4, u3, u3} C _inst_2) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{u4, u3, u3} C _inst_2) F), Quiver.Hom.{succ u3, max u4 (succ u3)} (AlgebraicGeometry.PresheafedSpace.{u4, u3, u3} C _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{u3, max u4 (succ u3)} (AlgebraicGeometry.PresheafedSpace.{u4, u3, u3} C _inst_2) (CategoryTheory.Category.toCategoryStruct.{u3, max u4 (succ u3)} (AlgebraicGeometry.PresheafedSpace.{u4, u3, u3} C _inst_2) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{u4, u3, u3} C _inst_2))) (AlgebraicGeometry.PresheafedSpace.colimit.{u1, u2, u3, u4} J _inst_1 C _inst_2 _inst_3 (fun (X : TopCat.{u3}) => _inst_4 X) F) (CategoryTheory.Limits.Cocone.pt.{u1, u3, u2, max u4 (succ u3)} J _inst_1 (AlgebraicGeometry.PresheafedSpace.{u4, u3, u3} C _inst_2) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{u4, u3, u3} C _inst_2) F s)
+Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.colimit_cocone_is_colimit.desc AlgebraicGeometry.PresheafedSpace.ColimitCoconeIsColimit.descₓ'. -/
 /-- Auxiliary definition for `PresheafedSpace.colimit_cocone_is_colimit`.
 -/
 def desc (F : J ⥤ PresheafedSpace.{v} C) (s : Cocone F) : colimit F ⟶ s.pt
@@ -308,6 +374,12 @@ def desc (F : J ⥤ PresheafedSpace.{v} C) (s : Cocone F) : colimit F ⟶ s.pt
       naturality' := fun U V i => desc_c_naturality F s i }
 #align algebraic_geometry.PresheafedSpace.colimit_cocone_is_colimit.desc AlgebraicGeometry.PresheafedSpace.ColimitCoconeIsColimit.desc
 
+/- warning: algebraic_geometry.PresheafedSpace.colimit_cocone_is_colimit.desc_fac -> AlgebraicGeometry.PresheafedSpace.ColimitCoconeIsColimit.desc_fac is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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(AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{u4, u3, u3} C _inst_2))) (CategoryTheory.Limits.Cocone.pt.{u1, u3, u2, max u4 (succ u3)} J _inst_1 (AlgebraicGeometry.PresheafedSpace.{u4, u3, u3} C _inst_2) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{u4, u3, u3} C _inst_2) F s)) (CategoryTheory.Limits.Cocone.ι.{u1, u3, u2, max u4 (succ u3)} J _inst_1 (AlgebraicGeometry.PresheafedSpace.{u4, u3, u3} C _inst_2) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{u4, u3, u3} C _inst_2) F s) j)
+Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.colimit_cocone_is_colimit.desc_fac AlgebraicGeometry.PresheafedSpace.ColimitCoconeIsColimit.desc_facₓ'. -/
 theorem desc_fac (F : J ⥤ PresheafedSpace.{v} C) (s : Cocone F) (j : J) :
     (colimitCocone F).ι.app j ≫ desc F s = s.ι.app j :=
   by
@@ -322,6 +394,12 @@ end ColimitCoconeIsColimit
 
 open ColimitCoconeIsColimit
 
+/- warning: algebraic_geometry.PresheafedSpace.colimit_cocone_is_colimit -> AlgebraicGeometry.PresheafedSpace.colimitCoconeIsColimit is a dubious translation:
+lean 3 declaration is
+  forall {J : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} J] {C : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u3, u4} C] [_inst_3 : CategoryTheory.Limits.HasColimitsOfShape.{u1, u2, u3, succ u3} J _inst_1 TopCat.{u3} TopCat.largeCategory.{u3}] [_inst_4 : forall (X : TopCat.{u3}), CategoryTheory.Limits.HasLimitsOfShape.{u1, u2, u3, max u4 u3} (Opposite.{succ u2} J) (CategoryTheory.Category.opposite.{u1, u2} J _inst_1) (TopCat.Presheaf.{u3, u3, u4} C _inst_2 X) (TopCat.Presheaf.category.{u3, u3, u4} C _inst_2 X)] [_inst_5 : CategoryTheory.Limits.HasLimitsOfShape.{u1, u2, u3, u4} (Opposite.{succ u2} J) (CategoryTheory.Category.opposite.{u1, u2} J _inst_1) C _inst_2] (F : CategoryTheory.Functor.{u1, u3, u2, max u4 (succ u3)} J _inst_1 (AlgebraicGeometry.PresheafedSpace.{u3, u3, u4} C _inst_2) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{u3, u4} C _inst_2)), CategoryTheory.Limits.IsColimit.{u1, u3, u2, max u4 (succ u3)} J _inst_1 (AlgebraicGeometry.PresheafedSpace.{u3, u3, u4} C _inst_2) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{u3, u4} C _inst_2) F (AlgebraicGeometry.PresheafedSpace.colimitCocone.{u1, u2, u3, u4} J _inst_1 C _inst_2 _inst_3 (AlgebraicGeometry.PresheafedSpace.colimitCoconeIsColimit._proof_1.{u4, u2, u3, u1} J _inst_1 C _inst_2 _inst_4) F)
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.colimit_cocone_is_colimit AlgebraicGeometry.PresheafedSpace.colimitCoconeIsColimitₓ'. -/
 /-- Auxiliary definition for `PresheafedSpace.has_colimits`.
 -/
 def colimitCoconeIsColimit (F : J ⥤ PresheafedSpace.{v} C) : IsColimit (colimitCocone F)
@@ -384,6 +462,12 @@ instance [HasLimits C] : HasColimits (PresheafedSpace.{v} C)
           { Cocone := colimit_cocone F
             IsColimit := colimit_cocone_is_colimit F } }
 
+/- warning: algebraic_geometry.PresheafedSpace.forget_preserves_colimits -> AlgebraicGeometry.PresheafedSpace.forgetPreservesColimits is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_2 : CategoryTheory.Category.{u1, u2} C] [_inst_6 : CategoryTheory.Limits.HasLimits.{u1, u2} C _inst_2], CategoryTheory.Limits.PreservesColimits.{u1, u1, max u2 (succ u1), succ u1} (AlgebraicGeometry.PresheafedSpace.{u1, u1, u2} C _inst_2) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{u1, u2} C _inst_2) TopCat.{u1} TopCat.largeCategory.{u1} (AlgebraicGeometry.PresheafedSpace.forget.{u1, u2} C _inst_2)
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_2 : CategoryTheory.Category.{u1, u2} C] [_inst_6 : CategoryTheory.Limits.HasLimits.{u1, u2} C _inst_2], CategoryTheory.Limits.PreservesColimits.{u1, u1, max (max u2 u1) (succ u1), succ u1} (AlgebraicGeometry.PresheafedSpace.{u2, u1, u1} C _inst_2) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{u2, u1, u1} C _inst_2) TopCat.{u1} instTopCatLargeCategory.{u1} (AlgebraicGeometry.PresheafedSpace.forget.{u2, u1, u1} C _inst_2)
+Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.forget_preserves_colimits AlgebraicGeometry.PresheafedSpace.forgetPreservesColimitsₓ'. -/
 /-- The underlying topological space of a colimit of presheaved spaces is
 the colimit of the underlying topological spaces.
 -/
@@ -401,6 +485,12 @@ instance forgetPreservesColimits [HasLimits C] : PreservesColimits (PresheafedSp
               simp) }
 #align algebraic_geometry.PresheafedSpace.forget_preserves_colimits AlgebraicGeometry.PresheafedSpace.forgetPreservesColimits
 
+/- warning: algebraic_geometry.PresheafedSpace.colimit_presheaf_obj_iso_componentwise_limit -> AlgebraicGeometry.PresheafedSpace.colimitPresheafObjIsoComponentwiseLimit is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.colimit_presheaf_obj_iso_componentwise_limit AlgebraicGeometry.PresheafedSpace.colimitPresheafObjIsoComponentwiseLimitₓ'. -/
 /-- The components of the colimit of a diagram of `PresheafedSpace C` is obtained
 via taking componentwise limits.
 -/
@@ -431,6 +521,12 @@ def colimitPresheafObjIsoComponentwiseLimit (F : J ⥤ PresheafedSpace.{v} C) [H
     congr
 #align algebraic_geometry.PresheafedSpace.colimit_presheaf_obj_iso_componentwise_limit AlgebraicGeometry.PresheafedSpace.colimitPresheafObjIsoComponentwiseLimit
 
+/- warning: algebraic_geometry.PresheafedSpace.colimit_presheaf_obj_iso_componentwise_limit_inv_ι_app -> AlgebraicGeometry.PresheafedSpace.colimitPresheafObjIsoComponentwiseLimit_inv_ι_app is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.colimit_presheaf_obj_iso_componentwise_limit_inv_ι_app AlgebraicGeometry.PresheafedSpace.colimitPresheafObjIsoComponentwiseLimit_inv_ι_appₓ'. -/
 @[simp]
 theorem colimitPresheafObjIsoComponentwiseLimit_inv_ι_app (F : J ⥤ PresheafedSpace.{v} C)
     (U : Opens (Limits.colimit F).carrier) (j : J) :
@@ -452,6 +548,12 @@ theorem colimitPresheafObjIsoComponentwiseLimit_inv_ι_app (F : J ⥤ Presheafed
   congr
 #align algebraic_geometry.PresheafedSpace.colimit_presheaf_obj_iso_componentwise_limit_inv_ι_app AlgebraicGeometry.PresheafedSpace.colimitPresheafObjIsoComponentwiseLimit_inv_ι_app
 
+/- warning: algebraic_geometry.PresheafedSpace.colimit_presheaf_obj_iso_componentwise_limit_hom_π -> AlgebraicGeometry.PresheafedSpace.colimitPresheafObjIsoComponentwiseLimit_hom_π is a dubious translation:
+lean 3 declaration is
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(AlgebraicGeometry.PresheafedSpace.instHasColimitsOfShapePresheafedSpaceCategoryOfPresheafedSpaces.{u1, u2, u3, u4} J _inst_1 C _inst_2 _inst_3 (fun (X : TopCat.{u3}) => _inst_4 X) _inst_5) F)) (CategoryTheory.Limits.colimit.ι.{u1, u2, u3, max u4 (succ u3)} J _inst_1 (AlgebraicGeometry.PresheafedSpace.{u4, u3, u3} C _inst_2) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{u4, u3, u3} C _inst_2) F (CategoryTheory.Limits.hasColimitOfHasColimitsOfShape.{u1, u2, u3, max u4 (succ u3)} (AlgebraicGeometry.PresheafedSpace.{u4, u3, u3} C _inst_2) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{u4, u3, u3} C _inst_2) J _inst_1 (AlgebraicGeometry.PresheafedSpace.instHasColimitsOfShapePresheafedSpaceCategoryOfPresheafedSpaces.{u1, u2, u3, u4} J _inst_1 C _inst_2 _inst_3 (fun (X : TopCat.{u3}) => _inst_4 X) _inst_5) F) j)) (Opposite.op.{succ u3} (TopologicalSpace.Opens.{u3} (CategoryTheory.Bundled.α.{u3, u3} TopologicalSpace.{u3} 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+Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.colimit_presheaf_obj_iso_componentwise_limit_hom_π AlgebraicGeometry.PresheafedSpace.colimitPresheafObjIsoComponentwiseLimit_hom_πₓ'. -/
 @[simp]
 theorem colimitPresheafObjIsoComponentwiseLimit_hom_π (F : J ⥤ PresheafedSpace.{v} C)
     (U : Opens (Limits.colimit F).carrier) (j : J) :

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

@@ -4,12 +4,12 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
 
 ! This file was ported from Lean 3 source module algebraic_geometry.presheafed_space.has_colimits
-! leanprover-community/mathlib commit d39590fc8728fbf6743249802486f8c91ffe07bc
+! leanprover-community/mathlib commit 178a32653e369dce2da68dc6b2694e385d484ef1
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.AlgebraicGeometry.PresheafedSpace
-import Mathbin.Topology.Category.Top.Limits
+import Mathbin.Topology.Category.Top.Limits.Basic
 import Mathbin.Topology.Sheaves.Limits
 
 /-!

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

@@ -153,7 +153,7 @@ def pushforwardDiagramToColimit (F : J ⥤ PresheafedSpace.{v} C) :
   map_id' j := by
     apply (op_equiv _ _).Injective
     ext U
-    induction U using Opposite.rec
+    induction U using Opposite.rec'
     cases U
     dsimp; simp; dsimp; simp
   map_comp' j₁ j₂ j₃ f g := by
@@ -220,7 +220,7 @@ def colimitCocone (F : J ⥤ PresheafedSpace.{v} C) : Cocone F
         · ext x
           exact colimit.w_apply (F ⋙ PresheafedSpace.forget C) f x
         · ext U
-          induction U using Opposite.rec
+          induction U using Opposite.rec'
           cases U
           dsimp
           simp only [PresheafedSpace.id_c_app, eq_to_hom_op, eq_to_hom_map, assoc,

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

@@ -210,7 +210,7 @@ theorem colimit_presheaf (F : J ⥤ PresheafedSpace.{v} C) :
 @[simps]
 def colimitCocone (F : J ⥤ PresheafedSpace.{v} C) : Cocone F
     where
-  x := colimit F
+  pt := colimit F
   ι :=
     { app := fun j =>
         { base := colimit.ι (F ⋙ PresheafedSpace.forget C) j
@@ -240,15 +240,15 @@ namespace ColimitCoconeIsColimit
 
 /-- Auxiliary definition for `PresheafedSpace.colimit_cocone_is_colimit`.
 -/
-def descCApp (F : J ⥤ PresheafedSpace.{v} C) (s : Cocone F) (U : (Opens ↥s.x.carrier)ᵒᵖ) :
-    s.x.Presheaf.obj U ⟶
+def descCApp (F : J ⥤ PresheafedSpace.{v} C) (s : Cocone F) (U : (Opens ↥s.pt.carrier)ᵒᵖ) :
+    s.pt.Presheaf.obj U ⟶
       (colimit.desc (F ⋙ PresheafedSpace.forget C) ((PresheafedSpace.forget C).mapCocone s) _*
             limit (pushforwardDiagramToColimit F).leftOp).obj
         U :=
   by
   refine'
     limit.lift _
-        { x := s.X.presheaf.obj U
+        { pt := s.X.presheaf.obj U
           π :=
             { app := fun j => _
               naturality' := fun j j' f => _ } } ≫
@@ -275,10 +275,10 @@ def descCApp (F : J ⥤ PresheafedSpace.{v} C) (s : Cocone F) (U : (Opens ↥s.x
 #align algebraic_geometry.PresheafedSpace.colimit_cocone_is_colimit.desc_c_app AlgebraicGeometry.PresheafedSpace.ColimitCoconeIsColimit.descCApp
 
 theorem desc_c_naturality (F : J ⥤ PresheafedSpace.{v} C) (s : Cocone F)
-    {U V : (Opens ↥s.x.carrier)ᵒᵖ} (i : U ⟶ V) :
-    s.x.Presheaf.map i ≫ descCApp F s V =
+    {U V : (Opens ↥s.pt.carrier)ᵒᵖ} (i : U ⟶ V) :
+    s.pt.Presheaf.map i ≫ descCApp F s V =
       descCApp F s U ≫
-        (colimit.desc (F ⋙ forget C) ((forget C).mapCocone s) _* (colimitCocone F).x.Presheaf).map
+        (colimit.desc (F ⋙ forget C) ((forget C).mapCocone s) _* (colimitCocone F).pt.Presheaf).map
           i :=
   by
   dsimp [desc_c_app]
@@ -300,7 +300,7 @@ theorem desc_c_naturality (F : J ⥤ PresheafedSpace.{v} C) (s : Cocone F)
 
 /-- Auxiliary definition for `PresheafedSpace.colimit_cocone_is_colimit`.
 -/
-def desc (F : J ⥤ PresheafedSpace.{v} C) (s : Cocone F) : colimit F ⟶ s.x
+def desc (F : J ⥤ PresheafedSpace.{v} C) (s : Cocone F) : colimit F ⟶ s.pt
     where
   base := colimit.desc (F ⋙ PresheafedSpace.forget C) ((PresheafedSpace.forget C).mapCocone s)
   c :=

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

@@ -327,8 +327,8 @@ open ColimitCoconeIsColimit
 def colimitCoconeIsColimit (F : J ⥤ PresheafedSpace.{v} C) : IsColimit (colimitCocone F)
     where
   desc s := desc F s
-  fac' s := desc_fac F s
-  uniq' s m w :=
+  fac s := desc_fac F s
+  uniq s m w :=
     by
     -- We need to use the identity on the continuous maps twice, so we prepare that first:
     have t :

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

These are changes from #11997, the latest adaptation PR for nightly-2024-04-07, which can be made directly on master.

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

@@ -220,7 +220,7 @@ def colimitCocone (F : J ⥤ PresheafedSpace.{_, _, v} C) : Cocone F where
             ← congr_arg NatTrans.app (limit.w (pushforwardDiagramToColimit F).leftOp f.op),
             NatTrans.comp_app, Functor.leftOp_map, pushforwardDiagramToColimit_map]
           dsimp [-Presheaf.comp_app]
-          rw [NatTrans.comp_app, NatTrans.comp_app, pushforwardEq_hom_app, id.def, eqToHom_op,
+          rw [NatTrans.comp_app, NatTrans.comp_app, pushforwardEq_hom_app, _root_.id, eqToHom_op,
             Pushforward.comp_inv_app, id_comp, pushforwardMap_app, ← assoc]
           congr 1 }
 set_option linter.uppercaseLean3 false in

A simple replacement . --> ·.

See #12143 for the source of these replacements.

@@ -394,7 +394,7 @@ def colimitPresheafObjIsoComponentwiseLimit (F : J ⥤ PresheafedSpace.{_, _, v}
     refine' (F.obj (unop X)).presheaf.mapIso (eqToIso _)
     simp only [Functor.op_obj, unop_op, op_inj_iff, Opens.map_coe, SetLike.ext'_iff,
       Set.preimage_preimage]
-    refine congr_arg (Set.preimage . U.1) (funext fun x => ?_)
+    refine congr_arg (Set.preimage · U.1) (funext fun x => ?_)
     erw [← TopCat.comp_app]
     congr
     exact ι_preservesColimitsIso_inv (forget C) F (unop X)

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

@@ -52,7 +52,7 @@ attribute [local simp] eqToHom_map
 -- Porting note: we used to have:
 -- local attribute [tidy] tactic.auto_cases_opens
 -- We would replace this by:
--- attribute [local aesop safe cases (rule_sets [CategoryTheory])] Opens
+-- attribute [local aesop safe cases (rule_sets := [CategoryTheory])] Opens
 -- although it doesn't appear to help in this file, in any case.
 
 @[simp]

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.

@@ -134,7 +134,7 @@ def pushforwardDiagramToColimit (F : J ⥤ PresheafedSpace.{_, _, v} C) :
       dsimp [comp_obj, forget_obj, Functor.comp_map, forget_map, op_comp, unop_op,
         pushforwardObj_obj, op_obj, Opens.map_obj, opEquiv, Equiv.coe_fn_mk, unop_comp,
         Quiver.Hom.unop_op, unop_id]
-      -- Porting note : some `simp` lemmas are not picked up
+      -- Porting note: some `simp` lemmas are not picked up
       rw [NatTrans.id_app]
       simp only [op_obj, unop_op, Opens.map_obj, map_id_c_app, Opens.map_id_obj',
         map_id, pushforwardEq_hom_app, eqToHom_op, id_eq, eqToHom_map, id_comp,
@@ -147,7 +147,7 @@ def pushforwardDiagramToColimit (F : J ⥤ PresheafedSpace.{_, _, v} C) :
     refine NatTrans.ext _ _ (funext fun U => ?_)
     dsimp only [comp_obj, forget_obj, Functor.comp_map, forget_map, op_comp, unop_op,
       pushforwardObj_obj, op_obj, opEquiv, Equiv.coe_fn_mk, unop_comp, Quiver.Hom.unop_op]
-    -- Porting note : some `simp` lemmas are not picked up
+    -- Porting note: some `simp` lemmas are not picked up
     rw [NatTrans.comp_app, pushforwardMap_app, NatTrans.comp_app, Pushforward.comp_inv_app,
       id_comp, pushforwardEq_hom_app, NatTrans.comp_app, NatTrans.comp_app, NatTrans.comp_app,
       pushforwardMap_app, Pushforward.comp_inv_app, id_comp, pushforwardEq_hom_app,
@@ -301,7 +301,7 @@ theorem desc_fac (F : J ⥤ PresheafedSpace.{_, _, v} C) (s : Cocone F) (j : J)
     (colimitCocone F).ι.app j ≫ desc F s = s.ι.app j := by
   ext U
   · simp [desc]
-  · -- Porting note : the original proof is just `ext; dsimp [desc, descCApp]; simpa`,
+  · -- Porting note: the original proof is just `ext; dsimp [desc, descCApp]; simpa`,
     -- but this has to be expanded a bit
     rw [NatTrans.comp_app, PresheafedSpace.comp_c_app, whiskerRight_app]
     dsimp [desc, descCApp]
@@ -422,7 +422,7 @@ theorem colimitPresheafObjIsoComponentwiseLimit_inv_ι_app (F : J ⥤ Presheafed
   erw [← comp_c_app_assoc]
   rw [congr_app (colimit.isoColimitCocone_ι_hom _ _), assoc]
   erw [limitObjIsoLimitCompEvaluation_inv_π_app_assoc, limMap_π_assoc]
-  -- Porting note : `convert` doesn't work due to meta variable, so change to a `suffices` block
+  -- Porting note: `convert` doesn't work due to meta variable, so change to a `suffices` block
   set f := _
   change _ ≫ f = _
   suffices f_eq : f = 𝟙 _ by rw [f_eq, comp_id]

This uses the improved shake script from #9772 to reduce imports across mathlib. The corresponding noshake.json file has been added to #9772.

Co-authored-by: Mario Carneiro <di.gama@gmail.com>

@@ -6,6 +6,7 @@ Authors: Scott Morrison
 import Mathlib.Geometry.RingedSpace.PresheafedSpace
 import Mathlib.Topology.Category.TopCat.Limits.Basic
 import Mathlib.Topology.Sheaves.Limits
+import Mathlib.CategoryTheory.ConcreteCategory.Elementwise
 
 #align_import algebraic_geometry.presheafed_space.has_colimits from "leanprover-community/mathlib"@"178a32653e369dce2da68dc6b2694e385d484ef1"
 

Various things break in the simpset for Presheaf when the simp algorithm changes in leanprover/lean4#3124. These backwards compatible fixes are, I think, improvements anyway.

One could further add a Presheaf.id_app lemma, and do further cleanup in the proofs which now use dsimp [-Presheaf.comp_app], but I'd prefer if these are done in a followup PR in order to not hold up #9500.

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

@@ -134,11 +134,11 @@ def pushforwardDiagramToColimit (F : J ⥤ PresheafedSpace.{_, _, v} C) :
         pushforwardObj_obj, op_obj, Opens.map_obj, opEquiv, Equiv.coe_fn_mk, unop_comp,
         Quiver.Hom.unop_op, unop_id]
       -- Porting note : some `simp` lemmas are not picked up
-      rw [NatTrans.comp_app, pushforwardMap_app, NatTrans.id_app]
+      rw [NatTrans.id_app]
       simp only [op_obj, unop_op, Opens.map_obj, map_id_c_app, Opens.map_id_obj',
         map_id, pushforwardEq_hom_app, eqToHom_op, id_eq, eqToHom_map, id_comp,
         TopCat.Presheaf.Pushforward.id_inv_app']
-      rw [NatTrans.comp_app, Pushforward.comp_inv_app, id_comp]
+      rw [Pushforward.comp_inv_app]
       dsimp
       simp
   map_comp {j₁ j₂ j₃} f g := by
@@ -212,13 +212,13 @@ def colimitCocone (F : J ⥤ PresheafedSpace.{_, _, v} C) : Cocone F where
         · ext x
           exact colimit.w_apply (F ⋙ PresheafedSpace.forget C) f x
         · ext ⟨U, hU⟩
-          dsimp
+          dsimp [-Presheaf.comp_app]
           rw [PresheafedSpace.id_c_app, map_id]
           erw [id_comp]
           rw [NatTrans.comp_app, PresheafedSpace.comp_c_app, whiskerRight_app, eqToHom_app,
             ← congr_arg NatTrans.app (limit.w (pushforwardDiagramToColimit F).leftOp f.op),
             NatTrans.comp_app, Functor.leftOp_map, pushforwardDiagramToColimit_map]
-          dsimp
+          dsimp [-Presheaf.comp_app]
           rw [NatTrans.comp_app, NatTrans.comp_app, pushforwardEq_hom_app, id.def, eqToHom_op,
             Pushforward.comp_inv_app, id_comp, pushforwardMap_app, ← assoc]
           congr 1 }
@@ -394,7 +394,7 @@ def colimitPresheafObjIsoComponentwiseLimit (F : J ⥤ PresheafedSpace.{_, _, v}
     simp only [Functor.op_obj, unop_op, op_inj_iff, Opens.map_coe, SetLike.ext'_iff,
       Set.preimage_preimage]
     refine congr_arg (Set.preimage . U.1) (funext fun x => ?_)
-    erw [← comp_app]
+    erw [← TopCat.comp_app]
     congr
     exact ι_preservesColimitsIso_inv (forget C) F (unop X)
   · intro X Y f

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

@@ -220,7 +220,7 @@ def colimitCocone (F : J ⥤ PresheafedSpace.{_, _, v} C) : Cocone F where
             NatTrans.comp_app, Functor.leftOp_map, pushforwardDiagramToColimit_map]
           dsimp
           rw [NatTrans.comp_app, NatTrans.comp_app, pushforwardEq_hom_app, id.def, eqToHom_op,
-            Pushforward.comp_inv_app, id_comp, pushforwardMap_app, ←assoc]
+            Pushforward.comp_inv_app, id_comp, pushforwardMap_app, ← assoc]
           congr 1 }
 set_option linter.uppercaseLean3 false in
 #align algebraic_geometry.PresheafedSpace.colimit_cocone AlgebraicGeometry.PresheafedSpace.colimitCocone
@@ -394,7 +394,7 @@ def colimitPresheafObjIsoComponentwiseLimit (F : J ⥤ PresheafedSpace.{_, _, v}
     simp only [Functor.op_obj, unop_op, op_inj_iff, Opens.map_coe, SetLike.ext'_iff,
       Set.preimage_preimage]
     refine congr_arg (Set.preimage . U.1) (funext fun x => ?_)
-    erw [←comp_app]
+    erw [← comp_app]
     congr
     exact ι_preservesColimitsIso_inv (forget C) F (unop X)
   · intro X Y f
@@ -403,7 +403,7 @@ def colimitPresheafObjIsoComponentwiseLimit (F : J ⥤ PresheafedSpace.{_, _, v}
     erw [Category.id_comp]
     rw [Category.assoc]
     erw [← (F.obj (unop Y)).presheaf.map_comp, (F.map f.unop).c.naturality_assoc,
-      ←(F.obj (unop Y)).presheaf.map_comp]
+      ← (F.obj (unop Y)).presheaf.map_comp]
     rfl
 set_option linter.uppercaseLean3 false in
 #align algebraic_geometry.PresheafedSpace.colimit_presheaf_obj_iso_componentwise_limit AlgebraicGeometry.PresheafedSpace.colimitPresheafObjIsoComponentwiseLimit

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.

@@ -3,7 +3,7 @@ Copyright (c) 2020 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
 -/
-import Mathlib.AlgebraicGeometry.PresheafedSpace
+import Mathlib.Geometry.RingedSpace.PresheafedSpace
 import Mathlib.Topology.Category.TopCat.Limits.Basic
 import Mathlib.Topology.Sheaves.Limits
 

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

@@ -156,7 +156,6 @@ def pushforwardDiagramToColimit (F : J ⥤ PresheafedSpace.{_, _, v} C) :
       Opens.map_comp_obj, Pushforward.comp_inv_app, pushforwardEq_hom_app, eqToHom_op, id_eq,
       eqToHom_map, id_comp, assoc, eqToHom_trans]
     dsimp
-    simp only [eqToHom_trans, id_comp]
     congr 1
     -- The key fact is `(F.map f).c.congr`,
     -- which allows us in rewrite in the argument of `(F.map f).c.app`.

@@ -113,7 +113,7 @@ variable [HasColimitsOfShape J TopCat.{v}]
 
 /-- Given a diagram of presheafed spaces,
 we can push all the presheaves forward to the colimit `X` of the underlying topological spaces,
-obtaining a diagram in `(presheaf C X)ᵒᵖ`.
+obtaining a diagram in `(Presheaf C X)ᵒᵖ`.
 -/
 @[simps]
 def pushforwardDiagramToColimit (F : J ⥤ PresheafedSpace.{_, _, v} C) :
@@ -177,7 +177,7 @@ set_option linter.uppercaseLean3 false in
 
 variable [∀ X : TopCat.{v}, HasLimitsOfShape Jᵒᵖ (X.Presheaf C)]
 
-/-- Auxiliary definition for `PresheafedSpace.has_colimits`.
+/-- Auxiliary definition for `AlgebraicGeometry.PresheafedSpace.instHasColimits`.
 -/
 def colimit (F : J ⥤ PresheafedSpace.{_, _, v} C) : PresheafedSpace C where
   carrier := Limits.colimit (F ⋙ PresheafedSpace.forget C)
@@ -199,7 +199,7 @@ theorem colimit_presheaf (F : J ⥤ PresheafedSpace.{_, _, v} C) :
 set_option linter.uppercaseLean3 false in
 #align algebraic_geometry.PresheafedSpace.colimit_presheaf AlgebraicGeometry.PresheafedSpace.colimit_presheaf
 
-/-- Auxiliary definition for `PresheafedSpace.has_colimits`.
+/-- Auxiliary definition for `AlgebraicGeometry.PresheafedSpace.instHasColimits`.
 -/
 @[simps]
 def colimitCocone (F : J ⥤ PresheafedSpace.{_, _, v} C) : Cocone F where
@@ -230,7 +230,7 @@ variable [HasLimitsOfShape Jᵒᵖ C]
 
 namespace ColimitCoconeIsColimit
 
-/-- Auxiliary definition for `PresheafedSpace.colimit_cocone_is_colimit`.
+/-- Auxiliary definition for `AlgebraicGeometry.PresheafedSpace.colimitCoconeIsColimit`.
 -/
 def descCApp (F : J ⥤ PresheafedSpace.{_, _, v} C) (s : Cocone F) (U : (Opens s.pt.carrier)ᵒᵖ) :
     s.pt.presheaf.obj U ⟶
@@ -287,7 +287,7 @@ theorem desc_c_naturality (F : J ⥤ PresheafedSpace.{_, _, v} C) (s : Cocone F)
 set_option linter.uppercaseLean3 false in
 #align algebraic_geometry.PresheafedSpace.colimit_cocone_is_colimit.desc_c_naturality AlgebraicGeometry.PresheafedSpace.ColimitCoconeIsColimit.desc_c_naturality
 
-/-- Auxiliary definition for `PresheafedSpace.colimit_cocone_is_colimit`.
+/-- Auxiliary definition for `AlgebraicGeometry.PresheafedSpace.colimitCoconeIsColimit`.
 -/
 def desc (F : J ⥤ PresheafedSpace.{_, _, v} C) (s : Cocone F) : colimit F ⟶ s.pt where
   base := colimit.desc (F ⋙ PresheafedSpace.forget C) ((PresheafedSpace.forget C).mapCocone s)
@@ -315,7 +315,7 @@ end ColimitCoconeIsColimit
 
 open ColimitCoconeIsColimit
 
-/-- Auxiliary definition for `PresheafedSpace.has_colimits`.
+/-- Auxiliary definition for `AlgebraicGeometry.PresheafedSpace.instHasColimits`.
 -/
 def colimitCoconeIsColimit (F : J ⥤ PresheafedSpace.{_, _, v} C) :
     IsColimit (colimitCocone F) where
@@ -347,8 +347,8 @@ def colimitCoconeIsColimit (F : J ⥤ PresheafedSpace.{_, _, v} C) :
 set_option linter.uppercaseLean3 false in
 #align algebraic_geometry.PresheafedSpace.colimit_cocone_is_colimit AlgebraicGeometry.PresheafedSpace.colimitCoconeIsColimit
 
-instance : HasColimitsOfShape J (PresheafedSpace.{_, _, v} C)
-  where has_colimit F := ⟨colimitCocone F, colimitCoconeIsColimit F⟩
+instance : HasColimitsOfShape J (PresheafedSpace.{_, _, v} C) where
+  has_colimit F := ⟨colimitCocone F, colimitCoconeIsColimit F⟩
 
 instance : PreservesColimitsOfShape J (PresheafedSpace.forget.{u, v, v} C) :=
   ⟨fun {F} => preservesColimitOfPreservesColimitCocone (colimitCoconeIsColimit F) <| by
@@ -360,14 +360,14 @@ instance : PreservesColimitsOfShape J (PresheafedSpace.forget.{u, v, v} C) :=
 
 /-- When `C` has limits, the category of presheaved spaces with values in `C` itself has colimits.
 -/
-instance [HasLimits C] : HasColimits (PresheafedSpace.{_, _, v} C) :=
+instance instHasColimits [HasLimits C] : HasColimits (PresheafedSpace.{_, _, v} C) :=
   ⟨fun {_ _} => ⟨fun {F} => ⟨colimitCocone F, colimitCoconeIsColimit F⟩⟩⟩
 
 /-- The underlying topological space of a colimit of presheaved spaces is
 the colimit of the underlying topological spaces.
 -/
-instance forgetPreservesColimits [HasLimits C] : PreservesColimits (PresheafedSpace.forget C)
-    where preservesColimitsOfShape {J 𝒥} :=
+instance forgetPreservesColimits [HasLimits C] : PreservesColimits (PresheafedSpace.forget C) where
+  preservesColimitsOfShape {J 𝒥} :=
     { preservesColimit := fun {F} =>
         preservesColimitOfPreservesColimitCocone (colimitCoconeIsColimit F)
           (by apply IsColimit.ofIsoColimit (colimit.isColimit _)

• depends on: #5966

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

@@ -2,16 +2,13 @@
 Copyright (c) 2020 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
-
-! This file was ported from Lean 3 source module algebraic_geometry.presheafed_space.has_colimits
-! leanprover-community/mathlib commit 178a32653e369dce2da68dc6b2694e385d484ef1
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.AlgebraicGeometry.PresheafedSpace
 import Mathlib.Topology.Category.TopCat.Limits.Basic
 import Mathlib.Topology.Sheaves.Limits
 
+#align_import algebraic_geometry.presheafed_space.has_colimits from "leanprover-community/mathlib"@"178a32653e369dce2da68dc6b2694e385d484ef1"
+
 /-!
 # `PresheafedSpace C` has colimits.
 

• depends on: https://github.com/leanprover/std4/pull/163
• depends on: #5584
• depends on: #5715
• depends on: #5729
• depends on: https://github.com/leanprover/std4/pull/173

Co-authored-by: Komyyy <pol_tta@outlook.jp> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: Mario Carneiro <di.gama@gmail.com>

@@ -213,8 +213,6 @@ def colimitCocone (F : J ⥤ PresheafedSpace.{_, _, v} C) : Cocone F where
           c := limit.π _ (op j) }
       naturality := fun {j j'} f => by
         ext1
-        -- See https://github.com/leanprover/std4/pull/158
-        swap
         · ext x
           exact colimit.w_apply (F ⋙ PresheafedSpace.forget C) f x
         · ext ⟨U, hU⟩
@@ -305,8 +303,6 @@ set_option linter.uppercaseLean3 false in
 theorem desc_fac (F : J ⥤ PresheafedSpace.{_, _, v} C) (s : Cocone F) (j : J) :
     (colimitCocone F).ι.app j ≫ desc F s = s.ι.app j := by
   ext U
-  -- See https://github.com/leanprover/std4/pull/158
-  swap
   · simp [desc]
   · -- Porting note : the original proof is just `ext; dsimp [desc, descCApp]; simpa`,
     -- but this has to be expanded a bit
@@ -338,9 +334,6 @@ def colimitCoconeIsColimit (F : J ⥤ PresheafedSpace.{_, _, v} C) :
       rw [colimit.ι_desc, mapCocone_ι_app, ← w j]
       simp
     ext : 1
-    swap
-    -- could `ext` please not reorder goals?
-    -- See https://github.com/leanprover/std4/pull/158
     · exact t
     · refine NatTrans.ext _ _ (funext fun U => limit_obj_ext fun j => ?_)
       dsimp only [colimitCocone_pt, colimit_carrier, leftOp_obj, pushforwardDiagramToColimit_obj,

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au>

@@ -167,8 +167,8 @@ def pushforwardDiagramToColimit (F : J ⥤ PresheafedSpace.{_, _, v} C) :
       (op ((Opens.map (F.map g).base).obj ((Opens.map (colimit.ι (F ⋙ forget C) j₃)).obj U.unop)))
       (op ((Opens.map (colimit.ι (F ⋙ PresheafedSpace.forget C) j₂)).obj (unop U)))
       _]
-    -- Now we show the open sets are equal.
     swap
+    -- Now we show the open sets are equal.
     · apply unop_injective
       rw [← Opens.map_comp_obj]
       congr
@@ -212,11 +212,12 @@ def colimitCocone (F : J ⥤ PresheafedSpace.{_, _, v} C) : Cocone F where
         { base := colimit.ι (F ⋙ PresheafedSpace.forget C) j
           c := limit.π _ (op j) }
       naturality := fun {j j'} f => by
-        fapply PresheafedSpace.ext
+        ext1
+        -- See https://github.com/leanprover/std4/pull/158
+        swap
         · ext x
           exact colimit.w_apply (F ⋙ PresheafedSpace.forget C) f x
-        · ext U
-          rcases U with ⟨U, hU⟩
+        · ext ⟨U, hU⟩
           dsimp
           rw [PresheafedSpace.id_c_app, map_id]
           erw [id_comp]
@@ -303,11 +304,12 @@ set_option linter.uppercaseLean3 false in
 
 theorem desc_fac (F : J ⥤ PresheafedSpace.{_, _, v} C) (s : Cocone F) (j : J) :
     (colimitCocone F).ι.app j ≫ desc F s = s.ι.app j := by
-  fapply PresheafedSpace.ext
+  ext U
+  -- See https://github.com/leanprover/std4/pull/158
+  swap
   · simp [desc]
   · -- Porting note : the original proof is just `ext; dsimp [desc, descCApp]; simpa`,
     -- but this has to be expanded a bit
-    ext U
     rw [NatTrans.comp_app, PresheafedSpace.comp_c_app, whiskerRight_app]
     dsimp [desc, descCApp]
     simp only [eqToHom_app, op_obj, Opens.map_comp_obj, eqToHom_map, Functor.leftOp, assoc]
@@ -331,14 +333,14 @@ def colimitCoconeIsColimit (F : J ⥤ PresheafedSpace.{_, _, v} C) :
     have t :
       m.base =
         colimit.desc (F ⋙ PresheafedSpace.forget C) ((PresheafedSpace.forget C).mapCocone s) := by
-      apply CategoryTheory.Limits.colimit.hom_ext
-      intro j
-      apply ContinuousMap.ext
-      intro x
+      dsimp
+      ext j
       rw [colimit.ι_desc, mapCocone_ι_app, ← w j]
       simp
-    fapply PresheafedSpace.ext
+    ext : 1
+    swap
     -- could `ext` please not reorder goals?
+    -- See https://github.com/leanprover/std4/pull/158
     · exact t
     · refine NatTrans.ext _ _ (funext fun U => limit_obj_ext fun j => ?_)
       dsimp only [colimitCocone_pt, colimit_carrier, leftOp_obj, pushforwardDiagramToColimit_obj,

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au>

@@ -215,20 +215,18 @@ def colimitCocone (F : J ⥤ PresheafedSpace.{_, _, v} C) : Cocone F where
         fapply PresheafedSpace.ext
         · ext x
           exact colimit.w_apply (F ⋙ PresheafedSpace.forget C) f x
-        · refine NatTrans.ext _ _ (funext fun U => ?_)
-          induction U with
-          | h U =>
-            rcases U with ⟨U, hU⟩
-            dsimp
-            rw [PresheafedSpace.id_c_app, map_id]
-            erw [id_comp]
-            rw [NatTrans.comp_app, PresheafedSpace.comp_c_app, whiskerRight_app, eqToHom_app,
-              ← congr_arg NatTrans.app (limit.w (pushforwardDiagramToColimit F).leftOp f.op),
-              NatTrans.comp_app, Functor.leftOp_map, pushforwardDiagramToColimit_map]
-            dsimp
-            rw [NatTrans.comp_app, NatTrans.comp_app, pushforwardEq_hom_app, id.def, eqToHom_op,
-              Pushforward.comp_inv_app, id_comp, pushforwardMap_app, ←assoc]
-            congr 1 }
+        · ext U
+          rcases U with ⟨U, hU⟩
+          dsimp
+          rw [PresheafedSpace.id_c_app, map_id]
+          erw [id_comp]
+          rw [NatTrans.comp_app, PresheafedSpace.comp_c_app, whiskerRight_app, eqToHom_app,
+            ← congr_arg NatTrans.app (limit.w (pushforwardDiagramToColimit F).leftOp f.op),
+            NatTrans.comp_app, Functor.leftOp_map, pushforwardDiagramToColimit_map]
+          dsimp
+          rw [NatTrans.comp_app, NatTrans.comp_app, pushforwardEq_hom_app, id.def, eqToHom_op,
+            Pushforward.comp_inv_app, id_comp, pushforwardMap_app, ←assoc]
+          congr 1 }
 set_option linter.uppercaseLean3 false in
 #align algebraic_geometry.PresheafedSpace.colimit_cocone AlgebraicGeometry.PresheafedSpace.colimitCocone
 
@@ -309,7 +307,7 @@ theorem desc_fac (F : J ⥤ PresheafedSpace.{_, _, v} C) (s : Cocone F) (j : J)
   · simp [desc]
   · -- Porting note : the original proof is just `ext; dsimp [desc, descCApp]; simpa`,
     -- but this has to be expanded a bit
-    refine NatTrans.ext _ _ (funext fun U => ?_)
+    ext U
     rw [NatTrans.comp_app, PresheafedSpace.comp_c_app, whiskerRight_app]
     dsimp [desc, descCApp]
     simp only [eqToHom_app, op_obj, Opens.map_comp_obj, eqToHom_map, Functor.leftOp, assoc]

@@ -404,8 +404,8 @@ def colimitPresheafObjIsoComponentwiseLimit (F : J ⥤ PresheafedSpace.{_, _, v}
     refine' (F.obj (unop X)).presheaf.mapIso (eqToIso _)
     simp only [Functor.op_obj, unop_op, op_inj_iff, Opens.map_coe, SetLike.ext'_iff,
       Set.preimage_preimage]
-    simp_rw [← comp_app]
-    refine congr_arg (Set.preimage . U.1) (funext fun x => congr_fun ?_ x)
+    refine congr_arg (Set.preimage . U.1) (funext fun x => ?_)
+    erw [←comp_app]
     congr
     exact ι_preservesColimitsIso_inv (forget C) F (unop X)
   · intro X Y f

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

@@ -361,17 +361,17 @@ instance : HasColimitsOfShape J (PresheafedSpace.{_, _, v} C)
   where has_colimit F := ⟨colimitCocone F, colimitCoconeIsColimit F⟩
 
 instance : PreservesColimitsOfShape J (PresheafedSpace.forget.{u, v, v} C) :=
-⟨fun {F} => preservesColimitOfPreservesColimitCocone (colimitCoconeIsColimit F) <| by
-  apply IsColimit.ofIsoColimit (colimit.isColimit _)
-  fapply Cocones.ext
-  · rfl
-  · intro j
-    simp⟩
+  ⟨fun {F} => preservesColimitOfPreservesColimitCocone (colimitCoconeIsColimit F) <| by
+    apply IsColimit.ofIsoColimit (colimit.isColimit _)
+    fapply Cocones.ext
+    · rfl
+    · intro j
+      simp⟩
 
 /-- When `C` has limits, the category of presheaved spaces with values in `C` itself has colimits.
 -/
 instance [HasLimits C] : HasColimits (PresheafedSpace.{_, _, v} C) :=
-⟨fun {_ _} => ⟨fun {F} => ⟨colimitCocone F, colimitCoconeIsColimit F⟩⟩⟩
+  ⟨fun {_ _} => ⟨fun {F} => ⟨colimitCocone F, colimitCoconeIsColimit F⟩⟩⟩
 
 /-- The underlying topological space of a colimit of presheaved spaces is
 the colimit of the underlying topological spaces.

Mostly this is installing the Opposite.rec' induction principle as the default @[eliminator], but also many other fixes and removing unnecessary steps from proofs.

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

@@ -40,25 +40,10 @@ noncomputable section
 
 universe v' u' v u
 
-open CategoryTheory
+open CategoryTheory Opposite CategoryTheory.Category CategoryTheory.Functor CategoryTheory.Limits
+  TopCat TopCat.Presheaf TopologicalSpace
 
-open TopCat
-
-open TopCat.Presheaf
-
-open TopologicalSpace
-
-open Opposite
-
-open CategoryTheory.Category
-
-open CategoryTheory.Limits
-
-open CategoryTheory.Functor
-
-variable {J : Type u'} [Category.{v'} J]
-
-variable {C : Type u} [Category.{v} C]
+variable {J : Type u'} [Category.{v'} J] {C : Type u} [Category.{v} C]
 
 namespace AlgebraicGeometry
 
@@ -66,8 +51,11 @@ namespace PresheafedSpace
 
 attribute [local simp] eqToHom_map
 
--- Porting note : `tidy` no longer exist
--- attribute [local tidy] tactic.auto_cases_opens
+-- Porting note: we used to have:
+-- local attribute [tidy] tactic.auto_cases_opens
+-- We would replace this by:
+-- attribute [local aesop safe cases (rule_sets [CategoryTheory])] Opens
+-- although it doesn't appear to help in this file, in any case.
 
 @[simp]
 theorem map_id_c_app (F : J ⥤ PresheafedSpace.{_, _, v} C) (j) (U) :
@@ -76,7 +64,6 @@ theorem map_id_c_app (F : J ⥤ PresheafedSpace.{_, _, v} C) (j) (U) :
         (pushforwardEq (by simp) (F.obj j).presheaf).hom.app
           (op U) := by
   cases U
-  dsimp
   simp [PresheafedSpace.congr_app (F.map_id j)]
 set_option linter.uppercaseLean3 false in
 #align algebraic_geometry.PresheafedSpace.map_id_c_app AlgebraicGeometry.PresheafedSpace.map_id_c_app
@@ -91,9 +78,7 @@ theorem map_comp_c_app (F : J ⥤ PresheafedSpace.{_, _, v} C) {j₁ j₂ j₃}
             (pushforwardEq (by rw [F.map_comp]; rfl) _).hom.app
               _ := by
   cases U
-  dsimp
-  simp only [PresheafedSpace.congr_app (F.map_comp f g)]
-  dsimp; simp
+  simp [PresheafedSpace.congr_app (F.map_comp f g)]
 set_option linter.uppercaseLean3 false in
 #align algebraic_geometry.PresheafedSpace.map_comp_c_app AlgebraicGeometry.PresheafedSpace.map_comp_c_app
 
@@ -106,10 +91,8 @@ This is the componentwise diagram for an open set `U` of the colimit of the unde
 def componentwiseDiagram (F : J ⥤ PresheafedSpace.{_, _, v} C) [HasColimit F]
     (U : Opens (Limits.colimit F).carrier) : Jᵒᵖ ⥤ C where
   obj j := (F.obj (unop j)).presheaf.obj (op ((Opens.map (colimit.ι F (unop j)).base).obj U))
-  map {j k} f :=
-    (F.map f.unop).c.app _ ≫
-      (F.obj (unop k)).presheaf.map
-        (eqToHom (by rw [← colimit.w F f.unop, comp_base]; rfl))
+  map {j k} f := (F.map f.unop).c.app _ ≫
+    (F.obj (unop k)).presheaf.map (eqToHom (by rw [← colimit.w F f.unop, comp_base]; rfl))
   map_comp {i j k} f g := by
     dsimp
     simp_rw [map_comp_c_app]
@@ -147,7 +130,7 @@ def pushforwardDiagramToColimit (F : J ⥤ PresheafedSpace.{_, _, v} C) :
   map_id j := by
     apply (opEquiv _ _).injective
     refine NatTrans.ext _ _ (funext fun U => ?_)
-    induction U using Opposite.rec' with
+    induction U with
     | h U =>
       rcases U with ⟨U, hU⟩
       dsimp [comp_obj, forget_obj, Functor.comp_map, forget_map, op_comp, unop_op,
@@ -233,7 +216,7 @@ def colimitCocone (F : J ⥤ PresheafedSpace.{_, _, v} C) : Cocone F where
         · ext x
           exact colimit.w_apply (F ⋙ PresheafedSpace.forget C) f x
         · refine NatTrans.ext _ _ (funext fun U => ?_)
-          induction U using Opposite.rec' with
+          induction U with
           | h U =>
             rcases U with ⟨U, hU⟩
             dsimp
@@ -274,7 +257,6 @@ def descCApp (F : J ⥤ PresheafedSpace.{_, _, v} C) (s : Cocone F) (U : (Opens
     simp
   · dsimp
     rw [PresheafedSpace.congr_app (s.w f.unop).symm U]
-    dsimp
     have w :=
       Functor.congr_obj
         (congr_arg Opens.map (colimit.ι_desc ((PresheafedSpace.forget C).mapCocone s) (unop j)))
@@ -283,7 +265,6 @@ def descCApp (F : J ⥤ PresheafedSpace.{_, _, v} C) (s : Cocone F) (U : (Opens
     replace w := congr_arg op w
     have w' := NatTrans.congr (F.map f.unop).c w
     rw [w']
-    dsimp
     simp
 set_option linter.uppercaseLean3 false in
 #align algebraic_geometry.PresheafedSpace.colimit_cocone_is_colimit.desc_c_app AlgebraicGeometry.PresheafedSpace.ColimitCoconeIsColimit.descCApp
@@ -308,7 +289,7 @@ theorem desc_c_naturality (F : J ⥤ PresheafedSpace.{_, _, v} C) (s : Cocone F)
   simp only [Opens.map_comp_map] at w
   replace w := congr_arg Quiver.Hom.op w
   rw [w]
-  dsimp; simp
+  simp
 set_option linter.uppercaseLean3 false in
 #align algebraic_geometry.PresheafedSpace.colimit_cocone_is_colimit.desc_c_naturality AlgebraicGeometry.PresheafedSpace.ColimitCoconeIsColimit.desc_c_naturality
 
@@ -385,7 +366,6 @@ instance : PreservesColimitsOfShape J (PresheafedSpace.forget.{u, v, v} C) :=
   fapply Cocones.ext
   · rfl
   · intro j
-    dsimp
     simp⟩
 
 /-- When `C` has limits, the category of presheaved spaces with values in `C` itself has colimits.
@@ -404,7 +384,6 @@ instance forgetPreservesColimits [HasLimits C] : PreservesColimits (PresheafedSp
               fapply Cocones.ext
               · rfl
               · intro j
-                dsimp
                 simp) }
 set_option linter.uppercaseLean3 false in
 #align algebraic_geometry.PresheafedSpace.forget_preserves_colimits AlgebraicGeometry.PresheafedSpace.forgetPreservesColimits

• Run a non-interactive version of fix-comments.py on all files.
• Go through the diff and manually add/discard/edit chunks.

@@ -16,7 +16,7 @@ import Mathlib.Topology.Sheaves.Limits
 # `PresheafedSpace C` has colimits.
 
 If `C` has limits, then the category `PresheafedSpace C` has colimits,
-and the forgetful functor to `Top` preserves these colimits.
+and the forgetful functor to `TopCat` preserves these colimits.
 
 When restricted to a diagram where the underlying continuous maps are open embeddings,
 this says that we can glue presheaved spaces.