topology.category.Top.limits.products ⟷ Mathlib.Topology.Category.TopCat.Limits.Products

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

@@ -3,8 +3,8 @@ Copyright (c) 2017 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Patrick Massot, Scott Morrison, Mario Carneiro, Andrew Yang
 -/
-import Topology.Category.Top.EpiMono
-import Topology.Category.Top.Limits.Basic
+import Topology.Category.TopCat.EpiMono
+import Topology.Category.TopCat.Limits.Basic
 
 #align_import topology.category.Top.limits.products from "leanprover-community/mathlib"@"781cb2eed038c4caf53bdbd8d20a95e5822d77df"
 

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

@@ -86,7 +86,7 @@ theorem piIsoPi_hom_apply {ι : Type v} (α : ι → TopCat.{max v u}) (i : ι)
     (piIsoPi α).Hom x i = (Pi.π α i : _) x :=
   by
   have := pi_iso_pi_inv_π α i
-  rw [iso.inv_comp_eq] at this 
+  rw [iso.inv_comp_eq] at this
   exact concrete_category.congr_hom this x
 #align Top.pi_iso_pi_hom_apply TopCat.piIsoPi_hom_apply
 -/
@@ -202,10 +202,10 @@ def prodBinaryFanIsLimit (X Y : TopCat.{u}) : IsLimit (prodBinaryFan X Y)
     intro S m h
     ext x
     · specialize h ⟨walking_pair.left⟩
-      apply_fun fun e => e x at h 
+      apply_fun fun e => e x at h
       exact h
     · specialize h ⟨walking_pair.right⟩
-      apply_fun fun e => e x at h 
+      apply_fun fun e => e x at h
       exact h
 #align Top.prod_binary_fan_is_limit TopCat.prodBinaryFanIsLimit
 -/
@@ -404,7 +404,7 @@ theorem binaryCofan_isColimit_iff {X Y : TopCat} (c : BinaryCofan X Y) :
       · rw [Equiv.ofInjective_symm_apply]
     · intro T f g; ext x; refine' (dif_neg _).trans _
       · rintro ⟨y, e⟩; have : c.inr x ∈ Set.range c.inl ⊓ Set.range c.inr := ⟨⟨_, e⟩, ⟨_, rfl⟩⟩
-        rwa [disjoint_iff.mp h₃.1] at this 
+        rwa [disjoint_iff.mp h₃.1] at this
       · exact congr_arg g (Equiv.ofInjective_symm_apply _ _)
     · rintro T _ _ m rfl rfl; ext x; change m x = dite _ _ _
       split_ifs <;> exact congr_arg _ (Equiv.apply_ofInjective_symm _ ⟨_, _⟩).symm

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

@@ -340,7 +340,74 @@ def binaryCofanIsColimit (X Y : TopCat.{u}) : IsColimit (TopCat.binaryCofan X Y)
 theorem binaryCofan_isColimit_iff {X Y : TopCat} (c : BinaryCofan X Y) :
     Nonempty (IsColimit c) ↔
       OpenEmbedding c.inl ∧ OpenEmbedding c.inr ∧ IsCompl (Set.range c.inl) (Set.range c.inr) :=
-  by classical
+  by
+  classical
+  constructor
+  · rintro ⟨h⟩
+    rw [←
+      show _ = c.inl from
+        h.comp_cocone_point_unique_up_to_iso_inv (binary_cofan_is_colimit X Y) ⟨walking_pair.left⟩,
+      ←
+      show _ = c.inr from
+        h.comp_cocone_point_unique_up_to_iso_inv (binary_cofan_is_colimit X Y) ⟨walking_pair.right⟩]
+    dsimp
+    refine'
+      ⟨(homeo_of_iso <|
+                  h.cocone_point_unique_up_to_iso
+                    (binary_cofan_is_colimit X Y)).symm.OpenEmbedding.comp
+          openEmbedding_inl,
+        (homeo_of_iso <|
+                  h.cocone_point_unique_up_to_iso
+                    (binary_cofan_is_colimit X Y)).symm.OpenEmbedding.comp
+          openEmbedding_inr,
+        _⟩
+    erw [Set.range_comp, ← eq_compl_iff_isCompl, Set.range_comp _ Sum.inr, ←
+      Set.image_compl_eq
+        (homeo_of_iso <|
+              h.cocone_point_unique_up_to_iso (binary_cofan_is_colimit X Y)).symm.Bijective]
+    congr 1
+    exact set.compl_range_inr.symm
+  · rintro ⟨h₁, h₂, h₃⟩
+    have : ∀ x, x ∈ Set.range c.inl ∨ x ∈ Set.range c.inr := by
+      rw [eq_compl_iff_is_compl.mpr h₃.symm]; exact fun _ => or_not
+    refine' ⟨binary_cofan.is_colimit.mk _ _ _ _ _⟩
+    · intro T f g
+      refine' ContinuousMap.mk _ _
+      ·
+        exact fun x =>
+          if h : x ∈ Set.range c.inl then f ((Equiv.ofInjective _ h₁.inj).symm ⟨x, h⟩)
+          else g ((Equiv.ofInjective _ h₂.inj).symm ⟨x, (this x).resolve_left h⟩)
+      rw [continuous_iff_continuousAt]
+      intro x
+      by_cases x ∈ Set.range c.inl
+      · revert h x
+        apply (IsOpen.continuousOn_iff _).mp
+        · rw [continuousOn_iff_continuous_restrict]
+          convert_to Continuous (f ∘ (Homeomorph.ofEmbedding _ h₁.to_embedding).symm)
+          · ext ⟨x, hx⟩; exact dif_pos hx
+          continuity
+        · exact h₁.open_range
+      · revert h x
+        apply (IsOpen.continuousOn_iff _).mp
+        · rw [continuousOn_iff_continuous_restrict]
+          have : ∀ a, a ∉ Set.range c.inl → a ∈ Set.range c.inr := by
+            rintro a (h : a ∈ Set.range c.inlᶜ); rwa [eq_compl_iff_is_compl.mpr h₃.symm]
+          convert_to
+            Continuous (g ∘ (Homeomorph.ofEmbedding _ h₂.to_embedding).symm ∘ Subtype.map _ this)
+          · ext ⟨x, hx⟩; exact dif_neg hx
+          continuity
+          rw [embedding_subtype_coe.to_inducing.continuous_iff]
+          exact continuous_subtype_val
+        · change IsOpen (Set.range c.inlᶜ); rw [← eq_compl_iff_is_compl.mpr h₃.symm]
+          exact h₂.open_range
+    · intro T f g; ext x; refine' (dif_pos _).trans _; · exact ⟨x, rfl⟩
+      · rw [Equiv.ofInjective_symm_apply]
+    · intro T f g; ext x; refine' (dif_neg _).trans _
+      · rintro ⟨y, e⟩; have : c.inr x ∈ Set.range c.inl ⊓ Set.range c.inr := ⟨⟨_, e⟩, ⟨_, rfl⟩⟩
+        rwa [disjoint_iff.mp h₃.1] at this 
+      · exact congr_arg g (Equiv.ofInjective_symm_apply _ _)
+    · rintro T _ _ m rfl rfl; ext x; change m x = dite _ _ _
+      split_ifs <;> exact congr_arg _ (Equiv.apply_ofInjective_symm _ ⟨_, _⟩).symm
 #align Top.binary_cofan_is_colimit_iff TopCat.binaryCofan_isColimit_iff
 -/
 

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

@@ -340,74 +340,7 @@ def binaryCofanIsColimit (X Y : TopCat.{u}) : IsColimit (TopCat.binaryCofan X Y)
 theorem binaryCofan_isColimit_iff {X Y : TopCat} (c : BinaryCofan X Y) :
     Nonempty (IsColimit c) ↔
       OpenEmbedding c.inl ∧ OpenEmbedding c.inr ∧ IsCompl (Set.range c.inl) (Set.range c.inr) :=
-  by
-  classical
-  constructor
-  · rintro ⟨h⟩
-    rw [←
-      show _ = c.inl from
-        h.comp_cocone_point_unique_up_to_iso_inv (binary_cofan_is_colimit X Y) ⟨walking_pair.left⟩,
-      ←
-      show _ = c.inr from
-        h.comp_cocone_point_unique_up_to_iso_inv (binary_cofan_is_colimit X Y) ⟨walking_pair.right⟩]
-    dsimp
-    refine'
-      ⟨(homeo_of_iso <|
-                  h.cocone_point_unique_up_to_iso
-                    (binary_cofan_is_colimit X Y)).symm.OpenEmbedding.comp
-          openEmbedding_inl,
-        (homeo_of_iso <|
-                  h.cocone_point_unique_up_to_iso
-                    (binary_cofan_is_colimit X Y)).symm.OpenEmbedding.comp
-          openEmbedding_inr,
-        _⟩
-    erw [Set.range_comp, ← eq_compl_iff_isCompl, Set.range_comp _ Sum.inr, ←
-      Set.image_compl_eq
-        (homeo_of_iso <|
-              h.cocone_point_unique_up_to_iso (binary_cofan_is_colimit X Y)).symm.Bijective]
-    congr 1
-    exact set.compl_range_inr.symm
-  · rintro ⟨h₁, h₂, h₃⟩
-    have : ∀ x, x ∈ Set.range c.inl ∨ x ∈ Set.range c.inr := by
-      rw [eq_compl_iff_is_compl.mpr h₃.symm]; exact fun _ => or_not
-    refine' ⟨binary_cofan.is_colimit.mk _ _ _ _ _⟩
-    · intro T f g
-      refine' ContinuousMap.mk _ _
-      ·
-        exact fun x =>
-          if h : x ∈ Set.range c.inl then f ((Equiv.ofInjective _ h₁.inj).symm ⟨x, h⟩)
-          else g ((Equiv.ofInjective _ h₂.inj).symm ⟨x, (this x).resolve_left h⟩)
-      rw [continuous_iff_continuousAt]
-      intro x
-      by_cases x ∈ Set.range c.inl
-      · revert h x
-        apply (IsOpen.continuousOn_iff _).mp
-        · rw [continuousOn_iff_continuous_restrict]
-          convert_to Continuous (f ∘ (Homeomorph.ofEmbedding _ h₁.to_embedding).symm)
-          · ext ⟨x, hx⟩; exact dif_pos hx
-          continuity
-        · exact h₁.open_range
-      · revert h x
-        apply (IsOpen.continuousOn_iff _).mp
-        · rw [continuousOn_iff_continuous_restrict]
-          have : ∀ a, a ∉ Set.range c.inl → a ∈ Set.range c.inr := by
-            rintro a (h : a ∈ Set.range c.inlᶜ); rwa [eq_compl_iff_is_compl.mpr h₃.symm]
-          convert_to
-            Continuous (g ∘ (Homeomorph.ofEmbedding _ h₂.to_embedding).symm ∘ Subtype.map _ this)
-          · ext ⟨x, hx⟩; exact dif_neg hx
-          continuity
-          rw [embedding_subtype_coe.to_inducing.continuous_iff]
-          exact continuous_subtype_val
-        · change IsOpen (Set.range c.inlᶜ); rw [← eq_compl_iff_is_compl.mpr h₃.symm]
-          exact h₂.open_range
-    · intro T f g; ext x; refine' (dif_pos _).trans _; · exact ⟨x, rfl⟩
-      · rw [Equiv.ofInjective_symm_apply]
-    · intro T f g; ext x; refine' (dif_neg _).trans _
-      · rintro ⟨y, e⟩; have : c.inr x ∈ Set.range c.inl ⊓ Set.range c.inr := ⟨⟨_, e⟩, ⟨_, rfl⟩⟩
-        rwa [disjoint_iff.mp h₃.1] at this 
-      · exact congr_arg g (Equiv.ofInjective_symm_apply _ _)
-    · rintro T _ _ m rfl rfl; ext x; change m x = dite _ _ _
-      split_ifs <;> exact congr_arg _ (Equiv.apply_ofInjective_symm _ ⟨_, _⟩).symm
+  by classical
 #align Top.binary_cofan_is_colimit_iff TopCat.binaryCofan_isColimit_iff
 -/
 

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

@@ -3,8 +3,8 @@ Copyright (c) 2017 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Patrick Massot, Scott Morrison, Mario Carneiro, Andrew Yang
 -/
-import Mathbin.Topology.Category.Top.EpiMono
-import Mathbin.Topology.Category.Top.Limits.Basic
+import Topology.Category.Top.EpiMono
+import Topology.Category.Top.Limits.Basic
 
 #align_import topology.category.Top.limits.products from "leanprover-community/mathlib"@"781cb2eed038c4caf53bdbd8d20a95e5822d77df"
 

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

@@ -284,7 +284,7 @@ theorem range_prod_map {W X Y Z : TopCat.{u}} (f : W ⟶ Y) (g : X ⟶ Z) :
     simp only [limits.prod.map_fst, limits.prod.map_snd, exists_apply_eq_apply, comp_apply,
       and_self_iff]
   · rintro ⟨⟨x₁, hx₁⟩, ⟨x₂, hx₂⟩⟩
-    use (prod_iso_prod W X).inv (x₁, x₂)
+    use(prod_iso_prod W X).inv (x₁, x₂)
     apply concrete.limit_ext
     rintro ⟨⟨⟩⟩
     · simp only [← comp_apply, category.assoc]; erw [limits.prod.map_fst]; simp [hx₁]

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

@@ -2,15 +2,12 @@
 Copyright (c) 2017 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Patrick Massot, Scott Morrison, Mario Carneiro, Andrew Yang
-
-! This file was ported from Lean 3 source module topology.category.Top.limits.products
-! leanprover-community/mathlib commit 781cb2eed038c4caf53bdbd8d20a95e5822d77df
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Topology.Category.Top.EpiMono
 import Mathbin.Topology.Category.Top.Limits.Basic
 
+#align_import topology.category.Top.limits.products from "leanprover-community/mathlib"@"781cb2eed038c4caf53bdbd8d20a95e5822d77df"
+
 /-!
 # Products and coproducts in the category of topological spaces
 

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

@@ -54,7 +54,7 @@ def piFan {ι : Type v} (α : ι → TopCat.{max v u}) : Fan α :=
 def piFanIsLimit {ι : Type v} (α : ι → TopCat.{max v u}) : IsLimit (piFan α)
     where
   lift S := { toFun := fun s i => S.π.app ⟨i⟩ s }
-  uniq := by intro S m h; ext (x i); simp [← h ⟨i⟩]
+  uniq := by intro S m h; ext x i; simp [← h ⟨i⟩]
   fac s j := by cases j; tidy
 #align Top.pi_fan_is_limit TopCat.piFanIsLimit
 -/

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

@@ -34,17 +34,22 @@ namespace TopCat
 
 variable {J : Type v} [SmallCategory J]
 
+#print TopCat.piπ /-
 /-- The projection from the product as a bundled continous map. -/
 abbrev piπ {ι : Type v} (α : ι → TopCat.{max v u}) (i : ι) : TopCat.of (∀ i, α i) ⟶ α i :=
   ⟨fun f => f i, continuous_apply i⟩
 #align Top.pi_π TopCat.piπ
+-/
 
+#print TopCat.piFan /-
 /-- The explicit fan of a family of topological spaces given by the pi type. -/
 @[simps pt π_app]
 def piFan {ι : Type v} (α : ι → TopCat.{max v u}) : Fan α :=
   Fan.mk (TopCat.of (∀ i, α i)) (piπ α)
 #align Top.pi_fan TopCat.piFan
+-/
 
+#print TopCat.piFanIsLimit /-
 /-- The constructed fan is indeed a limit -/
 def piFanIsLimit {ι : Type v} (α : ι → TopCat.{max v u}) : IsLimit (piFan α)
     where
@@ -52,25 +57,33 @@ def piFanIsLimit {ι : Type v} (α : ι → TopCat.{max v u}) : IsLimit (piFan 
   uniq := by intro S m h; ext (x i); simp [← h ⟨i⟩]
   fac s j := by cases j; tidy
 #align Top.pi_fan_is_limit TopCat.piFanIsLimit
+-/
 
+#print TopCat.piIsoPi /-
 /-- The product is homeomorphic to the product of the underlying spaces,
 equipped with the product topology.
 -/
 def piIsoPi {ι : Type v} (α : ι → TopCat.{max v u}) : ∏ α ≅ TopCat.of (∀ i, α i) :=
   (limit.isLimit _).conePointUniqueUpToIso (piFanIsLimit α)
 #align Top.pi_iso_pi TopCat.piIsoPi
+-/
 
+#print TopCat.piIsoPi_inv_π /-
 @[simp, reassoc]
 theorem piIsoPi_inv_π {ι : Type v} (α : ι → TopCat.{max v u}) (i : ι) :
     (piIsoPi α).inv ≫ Pi.π α i = piπ α i := by simp [pi_iso_pi]
 #align Top.pi_iso_pi_inv_π TopCat.piIsoPi_inv_π
+-/
 
+#print TopCat.piIsoPi_inv_π_apply /-
 @[simp]
 theorem piIsoPi_inv_π_apply {ι : Type v} (α : ι → TopCat.{max v u}) (i : ι) (x : ∀ i, α i) :
     (Pi.π α i : _) ((piIsoPi α).inv x) = x i :=
   ConcreteCategory.congr_hom (piIsoPi_inv_π α i) x
 #align Top.pi_iso_pi_inv_π_apply TopCat.piIsoPi_inv_π_apply
+-/
 
+#print TopCat.piIsoPi_hom_apply /-
 @[simp]
 theorem piIsoPi_hom_apply {ι : Type v} (α : ι → TopCat.{max v u}) (i : ι) (x : ∏ α) :
     (piIsoPi α).Hom x i = (Pi.π α i : _) x :=
@@ -79,18 +92,24 @@ theorem piIsoPi_hom_apply {ι : Type v} (α : ι → TopCat.{max v u}) (i : ι)
   rw [iso.inv_comp_eq] at this 
   exact concrete_category.congr_hom this x
 #align Top.pi_iso_pi_hom_apply TopCat.piIsoPi_hom_apply
+-/
 
+#print TopCat.sigmaι /-
 /-- The inclusion to the coproduct as a bundled continous map. -/
 abbrev sigmaι {ι : Type v} (α : ι → TopCat.{max v u}) (i : ι) : α i ⟶ TopCat.of (Σ i, α i) :=
   ⟨Sigma.mk i⟩
 #align Top.sigma_ι TopCat.sigmaι
+-/
 
+#print TopCat.sigmaCofan /-
 /-- The explicit cofan of a family of topological spaces given by the sigma type. -/
 @[simps pt ι_app]
 def sigmaCofan {ι : Type v} (α : ι → TopCat.{max v u}) : Cofan α :=
   Cofan.mk (TopCat.of (Σ i, α i)) (sigmaι α)
 #align Top.sigma_cofan TopCat.sigmaCofan
+-/
 
+#print TopCat.sigmaCofanIsColimit /-
 /-- The constructed cofan is indeed a colimit -/
 def sigmaCofanIsColimit {ι : Type v} (α : ι → TopCat.{max v u}) : IsColimit (sigmaCofan α)
     where
@@ -100,30 +119,40 @@ def sigmaCofanIsColimit {ι : Type v} (α : ι → TopCat.{max v u}) : IsColimit
   uniq := by intro S m h; ext ⟨i, x⟩; simp [← h ⟨i⟩]
   fac s j := by cases j; tidy
 #align Top.sigma_cofan_is_colimit TopCat.sigmaCofanIsColimit
+-/
 
+#print TopCat.sigmaIsoSigma /-
 /-- The coproduct is homeomorphic to the disjoint union of the topological spaces.
 -/
 def sigmaIsoSigma {ι : Type v} (α : ι → TopCat.{max v u}) : ∐ α ≅ TopCat.of (Σ i, α i) :=
   (colimit.isColimit _).coconePointUniqueUpToIso (sigmaCofanIsColimit α)
 #align Top.sigma_iso_sigma TopCat.sigmaIsoSigma
+-/
 
+#print TopCat.sigmaIsoSigma_hom_ι /-
 @[simp, reassoc]
 theorem sigmaIsoSigma_hom_ι {ι : Type v} (α : ι → TopCat.{max v u}) (i : ι) :
     Sigma.ι α i ≫ (sigmaIsoSigma α).Hom = sigmaι α i := by simp [sigma_iso_sigma]
 #align Top.sigma_iso_sigma_hom_ι TopCat.sigmaIsoSigma_hom_ι
+-/
 
+#print TopCat.sigmaIsoSigma_hom_ι_apply /-
 @[simp]
 theorem sigmaIsoSigma_hom_ι_apply {ι : Type v} (α : ι → TopCat.{max v u}) (i : ι) (x : α i) :
     (sigmaIsoSigma α).Hom ((Sigma.ι α i : _) x) = Sigma.mk i x :=
   ConcreteCategory.congr_hom (sigmaIsoSigma_hom_ι α i) x
 #align Top.sigma_iso_sigma_hom_ι_apply TopCat.sigmaIsoSigma_hom_ι_apply
+-/
 
+#print TopCat.sigmaIsoSigma_inv_apply /-
 @[simp]
 theorem sigmaIsoSigma_inv_apply {ι : Type v} (α : ι → TopCat.{max v u}) (i : ι) (x : α i) :
     (sigmaIsoSigma α).inv ⟨i, x⟩ = (Sigma.ι α i : _) x := by
   rw [← sigma_iso_sigma_hom_ι_apply, ← comp_app]; simp
 #align Top.sigma_iso_sigma_inv_apply TopCat.sigmaIsoSigma_inv_apply
+-/
 
+#print TopCat.induced_of_isLimit /-
 theorem induced_of_isLimit {F : J ⥤ TopCat.{max v u}} (C : Cone F) (hC : IsLimit C) :
     C.pt.TopologicalSpace = ⨅ j, (F.obj j).TopologicalSpace.induced (C.π.app j) :=
   by
@@ -132,23 +161,30 @@ theorem induced_of_isLimit {F : J ⥤ TopCat.{max v u}} (C : Cone F) (hC : IsLim
   change induced homeo (⨅ j : J, _) = _
   simpa [induced_iInf, induced_compose]
 #align Top.induced_of_is_limit TopCat.induced_of_isLimit
+-/
 
+#print TopCat.limit_topology /-
 theorem limit_topology (F : J ⥤ TopCat.{max v u}) :
     (limit F).TopologicalSpace = ⨅ j, (F.obj j).TopologicalSpace.induced (limit.π F j) :=
   induced_of_isLimit _ (limit.isLimit F)
 #align Top.limit_topology TopCat.limit_topology
+-/
 
 section Prod
 
+#print TopCat.prodFst /-
 /-- The first projection from the product. -/
 abbrev prodFst {X Y : TopCat.{u}} : TopCat.of (X × Y) ⟶ X :=
   ⟨Prod.fst⟩
 #align Top.prod_fst TopCat.prodFst
+-/
 
+#print TopCat.prodSnd /-
 /-- The second projection from the product. -/
 abbrev prodSnd {X Y : TopCat.{u}} : TopCat.of (X × Y) ⟶ Y :=
   ⟨Prod.snd⟩
 #align Top.prod_snd TopCat.prodSnd
+-/
 
 #print TopCat.prodBinaryFan /-
 /-- The explicit binary cofan of `X, Y` given by `X × Y`. -/
@@ -177,12 +213,14 @@ def prodBinaryFanIsLimit (X Y : TopCat.{u}) : IsLimit (prodBinaryFan X Y)
 #align Top.prod_binary_fan_is_limit TopCat.prodBinaryFanIsLimit
 -/
 
+#print TopCat.prodIsoProd /-
 /-- The homeomorphism between `X ⨯ Y` and the set-theoretic product of `X` and `Y`,
 equipped with the product topology.
 -/
 def prodIsoProd (X Y : TopCat.{u}) : X ⨯ Y ≅ TopCat.of (X × Y) :=
   (limit.isLimit _).conePointUniqueUpToIso (prodBinaryFanIsLimit X Y)
 #align Top.prod_iso_prod TopCat.prodIsoProd
+-/
 
 #print TopCat.prodIsoProd_hom_fst /-
 @[simp, reassoc]
@@ -198,6 +236,7 @@ theorem prodIsoProd_hom_snd (X Y : TopCat.{u}) :
 #align Top.prod_iso_prod_hom_snd TopCat.prodIsoProd_hom_snd
 -/
 
+#print TopCat.prodIsoProd_hom_apply /-
 @[simp]
 theorem prodIsoProd_hom_apply {X Y : TopCat.{u}} (x : X ⨯ Y) :
     (prodIsoProd X Y).Hom x = ((Limits.prod.fst : X ⨯ Y ⟶ _) x, (Limits.prod.snd : X ⨯ Y ⟶ _) x) :=
@@ -206,17 +245,23 @@ theorem prodIsoProd_hom_apply {X Y : TopCat.{u}} (x : X ⨯ Y) :
   · exact concrete_category.congr_hom (prod_iso_prod_hom_fst X Y) x
   · exact concrete_category.congr_hom (prod_iso_prod_hom_snd X Y) x
 #align Top.prod_iso_prod_hom_apply TopCat.prodIsoProd_hom_apply
+-/
 
+#print TopCat.prodIsoProd_inv_fst /-
 @[simp, reassoc, elementwise]
 theorem prodIsoProd_inv_fst (X Y : TopCat.{u}) :
     (prodIsoProd X Y).inv ≫ Limits.prod.fst = prodFst := by simp [iso.inv_comp_eq]
 #align Top.prod_iso_prod_inv_fst TopCat.prodIsoProd_inv_fst
+-/
 
+#print TopCat.prodIsoProd_inv_snd /-
 @[simp, reassoc, elementwise]
 theorem prodIsoProd_inv_snd (X Y : TopCat.{u}) :
     (prodIsoProd X Y).inv ≫ Limits.prod.snd = prodSnd := by simp [iso.inv_comp_eq]
 #align Top.prod_iso_prod_inv_snd TopCat.prodIsoProd_inv_snd
+-/
 
+#print TopCat.prod_topology /-
 theorem prod_topology {X Y : TopCat} :
     (X ⨯ Y).TopologicalSpace =
       induced (Limits.prod.fst : X ⨯ Y ⟶ _) X.TopologicalSpace ⊓
@@ -227,7 +272,9 @@ theorem prod_topology {X Y : TopCat} :
   change induced homeo (_ ⊓ _) = _
   simpa [induced_compose]
 #align Top.prod_topology TopCat.prod_topology
+-/
 
+#print TopCat.range_prod_map /-
 theorem range_prod_map {W X Y Z : TopCat.{u}} (f : W ⟶ Y) (g : X ⟶ Z) :
     Set.range (Limits.prod.map f g) =
       (Limits.prod.fst : Y ⨯ Z ⟶ _) ⁻¹' Set.range f ∩
@@ -246,7 +293,9 @@ theorem range_prod_map {W X Y Z : TopCat.{u}} (f : W ⟶ Y) (g : X ⟶ Z) :
     · simp only [← comp_apply, category.assoc]; erw [limits.prod.map_fst]; simp [hx₁]
     · simp only [← comp_apply, category.assoc]; erw [limits.prod.map_snd]; simp [hx₂]
 #align Top.range_prod_map TopCat.range_prod_map
+-/
 
+#print TopCat.inducing_prod_map /-
 theorem inducing_prod_map {W X Y Z : TopCat} {f : W ⟶ X} {g : Y ⟶ Z} (hf : Inducing f)
     (hg : Inducing g) : Inducing (Limits.prod.map f g) :=
   by
@@ -256,7 +305,9 @@ theorem inducing_prod_map {W X Y Z : TopCat} {f : W ⟶ X} {g : Y ⟶ Z} (hf : I
   simp only [coe_comp]
   rw [← @induced_compose _ _ _ _ _ f, ← @induced_compose _ _ _ _ _ g, ← hf.induced, ← hg.induced]
 #align Top.inducing_prod_map TopCat.inducing_prod_map
+-/
 
+#print TopCat.embedding_prod_map /-
 theorem embedding_prod_map {W X Y Z : TopCat} {f : W ⟶ X} {g : Y ⟶ Z} (hf : Embedding f)
     (hg : Embedding g) : Embedding (Limits.prod.map f g) :=
   ⟨inducing_prod_map hf.to_inducing hg.to_inducing,
@@ -265,6 +316,7 @@ theorem embedding_prod_map {W X Y Z : TopCat} {f : W ⟶ X} {g : Y ⟶ Z} (hf :
     haveI := (TopCat.mono_iff_injective _).mpr hg.inj
     exact (TopCat.mono_iff_injective _).mp inferInstance⟩
 #align Top.embedding_prod_map TopCat.embedding_prod_map
+-/
 
 end Prod
 
@@ -287,6 +339,7 @@ def binaryCofanIsColimit (X Y : TopCat.{u}) : IsColimit (TopCat.binaryCofan X Y)
 #align Top.binary_cofan_is_colimit TopCat.binaryCofanIsColimit
 -/
 
+#print TopCat.binaryCofan_isColimit_iff /-
 theorem binaryCofan_isColimit_iff {X Y : TopCat} (c : BinaryCofan X Y) :
     Nonempty (IsColimit c) ↔
       OpenEmbedding c.inl ∧ OpenEmbedding c.inr ∧ IsCompl (Set.range c.inl) (Set.range c.inr) :=
@@ -359,6 +412,7 @@ theorem binaryCofan_isColimit_iff {X Y : TopCat} (c : BinaryCofan X Y) :
     · rintro T _ _ m rfl rfl; ext x; change m x = dite _ _ _
       split_ifs <;> exact congr_arg _ (Equiv.apply_ofInjective_symm _ ⟨_, _⟩).symm
 #align Top.binary_cofan_is_colimit_iff TopCat.binaryCofan_isColimit_iff
+-/
 
 --TODO: Add analogous constructions for `pushout`.
 end TopCat

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

@@ -169,10 +169,10 @@ def prodBinaryFanIsLimit (X Y : TopCat.{u}) : IsLimit (prodBinaryFan X Y)
     intro S m h
     ext x
     · specialize h ⟨walking_pair.left⟩
-      apply_fun fun e => e x  at h 
+      apply_fun fun e => e x at h 
       exact h
     · specialize h ⟨walking_pair.right⟩
-      apply_fun fun e => e x  at h 
+      apply_fun fun e => e x at h 
       exact h
 #align Top.prod_binary_fan_is_limit TopCat.prodBinaryFanIsLimit
 -/
@@ -292,74 +292,72 @@ theorem binaryCofan_isColimit_iff {X Y : TopCat} (c : BinaryCofan X Y) :
       OpenEmbedding c.inl ∧ OpenEmbedding c.inr ∧ IsCompl (Set.range c.inl) (Set.range c.inr) :=
   by
   classical
-    constructor
-    · rintro ⟨h⟩
-      rw [←
-        show _ = c.inl from
-          h.comp_cocone_point_unique_up_to_iso_inv (binary_cofan_is_colimit X Y)
-            ⟨walking_pair.left⟩,
-        ←
-        show _ = c.inr from
-          h.comp_cocone_point_unique_up_to_iso_inv (binary_cofan_is_colimit X Y)
-            ⟨walking_pair.right⟩]
-      dsimp
-      refine'
-        ⟨(homeo_of_iso <|
-                    h.cocone_point_unique_up_to_iso
-                      (binary_cofan_is_colimit X Y)).symm.OpenEmbedding.comp
-            openEmbedding_inl,
-          (homeo_of_iso <|
-                    h.cocone_point_unique_up_to_iso
-                      (binary_cofan_is_colimit X Y)).symm.OpenEmbedding.comp
-            openEmbedding_inr,
-          _⟩
-      erw [Set.range_comp, ← eq_compl_iff_isCompl, Set.range_comp _ Sum.inr, ←
-        Set.image_compl_eq
-          (homeo_of_iso <|
-                h.cocone_point_unique_up_to_iso (binary_cofan_is_colimit X Y)).symm.Bijective]
-      congr 1
-      exact set.compl_range_inr.symm
-    · rintro ⟨h₁, h₂, h₃⟩
-      have : ∀ x, x ∈ Set.range c.inl ∨ x ∈ Set.range c.inr := by
-        rw [eq_compl_iff_is_compl.mpr h₃.symm]; exact fun _ => or_not
-      refine' ⟨binary_cofan.is_colimit.mk _ _ _ _ _⟩
-      · intro T f g
-        refine' ContinuousMap.mk _ _
-        ·
-          exact fun x =>
-            if h : x ∈ Set.range c.inl then f ((Equiv.ofInjective _ h₁.inj).symm ⟨x, h⟩)
-            else g ((Equiv.ofInjective _ h₂.inj).symm ⟨x, (this x).resolve_left h⟩)
-        rw [continuous_iff_continuousAt]
-        intro x
-        by_cases x ∈ Set.range c.inl
-        · revert h x
-          apply (IsOpen.continuousOn_iff _).mp
-          · rw [continuousOn_iff_continuous_restrict]
-            convert_to Continuous (f ∘ (Homeomorph.ofEmbedding _ h₁.to_embedding).symm)
-            · ext ⟨x, hx⟩; exact dif_pos hx
-            continuity
-          · exact h₁.open_range
-        · revert h x
-          apply (IsOpen.continuousOn_iff _).mp
-          · rw [continuousOn_iff_continuous_restrict]
-            have : ∀ a, a ∉ Set.range c.inl → a ∈ Set.range c.inr := by
-              rintro a (h : a ∈ Set.range c.inlᶜ); rwa [eq_compl_iff_is_compl.mpr h₃.symm]
-            convert_to Continuous
-                (g ∘ (Homeomorph.ofEmbedding _ h₂.to_embedding).symm ∘ Subtype.map _ this)
-            · ext ⟨x, hx⟩; exact dif_neg hx
-            continuity
-            rw [embedding_subtype_coe.to_inducing.continuous_iff]
-            exact continuous_subtype_val
-          · change IsOpen (Set.range c.inlᶜ); rw [← eq_compl_iff_is_compl.mpr h₃.symm]
-            exact h₂.open_range
-      · intro T f g; ext x; refine' (dif_pos _).trans _; · exact ⟨x, rfl⟩
-        · rw [Equiv.ofInjective_symm_apply]
-      · intro T f g; ext x; refine' (dif_neg _).trans _
-        · rintro ⟨y, e⟩; have : c.inr x ∈ Set.range c.inl ⊓ Set.range c.inr := ⟨⟨_, e⟩, ⟨_, rfl⟩⟩
-          rwa [disjoint_iff.mp h₃.1] at this 
-        · exact congr_arg g (Equiv.ofInjective_symm_apply _ _)
-      · rintro T _ _ m rfl rfl; ext x; change m x = dite _ _ _
-        split_ifs <;> exact congr_arg _ (Equiv.apply_ofInjective_symm _ ⟨_, _⟩).symm
+  constructor
+  · rintro ⟨h⟩
+    rw [←
+      show _ = c.inl from
+        h.comp_cocone_point_unique_up_to_iso_inv (binary_cofan_is_colimit X Y) ⟨walking_pair.left⟩,
+      ←
+      show _ = c.inr from
+        h.comp_cocone_point_unique_up_to_iso_inv (binary_cofan_is_colimit X Y) ⟨walking_pair.right⟩]
+    dsimp
+    refine'
+      ⟨(homeo_of_iso <|
+                  h.cocone_point_unique_up_to_iso
+                    (binary_cofan_is_colimit X Y)).symm.OpenEmbedding.comp
+          openEmbedding_inl,
+        (homeo_of_iso <|
+                  h.cocone_point_unique_up_to_iso
+                    (binary_cofan_is_colimit X Y)).symm.OpenEmbedding.comp
+          openEmbedding_inr,
+        _⟩
+    erw [Set.range_comp, ← eq_compl_iff_isCompl, Set.range_comp _ Sum.inr, ←
+      Set.image_compl_eq
+        (homeo_of_iso <|
+              h.cocone_point_unique_up_to_iso (binary_cofan_is_colimit X Y)).symm.Bijective]
+    congr 1
+    exact set.compl_range_inr.symm
+  · rintro ⟨h₁, h₂, h₃⟩
+    have : ∀ x, x ∈ Set.range c.inl ∨ x ∈ Set.range c.inr := by
+      rw [eq_compl_iff_is_compl.mpr h₃.symm]; exact fun _ => or_not
+    refine' ⟨binary_cofan.is_colimit.mk _ _ _ _ _⟩
+    · intro T f g
+      refine' ContinuousMap.mk _ _
+      ·
+        exact fun x =>
+          if h : x ∈ Set.range c.inl then f ((Equiv.ofInjective _ h₁.inj).symm ⟨x, h⟩)
+          else g ((Equiv.ofInjective _ h₂.inj).symm ⟨x, (this x).resolve_left h⟩)
+      rw [continuous_iff_continuousAt]
+      intro x
+      by_cases x ∈ Set.range c.inl
+      · revert h x
+        apply (IsOpen.continuousOn_iff _).mp
+        · rw [continuousOn_iff_continuous_restrict]
+          convert_to Continuous (f ∘ (Homeomorph.ofEmbedding _ h₁.to_embedding).symm)
+          · ext ⟨x, hx⟩; exact dif_pos hx
+          continuity
+        · exact h₁.open_range
+      · revert h x
+        apply (IsOpen.continuousOn_iff _).mp
+        · rw [continuousOn_iff_continuous_restrict]
+          have : ∀ a, a ∉ Set.range c.inl → a ∈ Set.range c.inr := by
+            rintro a (h : a ∈ Set.range c.inlᶜ); rwa [eq_compl_iff_is_compl.mpr h₃.symm]
+          convert_to
+            Continuous (g ∘ (Homeomorph.ofEmbedding _ h₂.to_embedding).symm ∘ Subtype.map _ this)
+          · ext ⟨x, hx⟩; exact dif_neg hx
+          continuity
+          rw [embedding_subtype_coe.to_inducing.continuous_iff]
+          exact continuous_subtype_val
+        · change IsOpen (Set.range c.inlᶜ); rw [← eq_compl_iff_is_compl.mpr h₃.symm]
+          exact h₂.open_range
+    · intro T f g; ext x; refine' (dif_pos _).trans _; · exact ⟨x, rfl⟩
+      · rw [Equiv.ofInjective_symm_apply]
+    · intro T f g; ext x; refine' (dif_neg _).trans _
+      · rintro ⟨y, e⟩; have : c.inr x ∈ Set.range c.inl ⊓ Set.range c.inr := ⟨⟨_, e⟩, ⟨_, rfl⟩⟩
+        rwa [disjoint_iff.mp h₃.1] at this 
+      · exact congr_arg g (Equiv.ofInjective_symm_apply _ _)
+    · rintro T _ _ m rfl rfl; ext x; change m x = dite _ _ _
+      split_ifs <;> exact congr_arg _ (Equiv.apply_ofInjective_symm _ ⟨_, _⟩).symm
 #align Top.binary_cofan_is_colimit_iff TopCat.binaryCofan_isColimit_iff
 
 --TODO: Add analogous constructions for `pushout`.

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

@@ -76,19 +76,19 @@ theorem piIsoPi_hom_apply {ι : Type v} (α : ι → TopCat.{max v u}) (i : ι)
     (piIsoPi α).Hom x i = (Pi.π α i : _) x :=
   by
   have := pi_iso_pi_inv_π α i
-  rw [iso.inv_comp_eq] at this
+  rw [iso.inv_comp_eq] at this 
   exact concrete_category.congr_hom this x
 #align Top.pi_iso_pi_hom_apply TopCat.piIsoPi_hom_apply
 
 /-- The inclusion to the coproduct as a bundled continous map. -/
-abbrev sigmaι {ι : Type v} (α : ι → TopCat.{max v u}) (i : ι) : α i ⟶ TopCat.of (Σi, α i) :=
+abbrev sigmaι {ι : Type v} (α : ι → TopCat.{max v u}) (i : ι) : α i ⟶ TopCat.of (Σ i, α i) :=
   ⟨Sigma.mk i⟩
 #align Top.sigma_ι TopCat.sigmaι
 
 /-- The explicit cofan of a family of topological spaces given by the sigma type. -/
 @[simps pt ι_app]
 def sigmaCofan {ι : Type v} (α : ι → TopCat.{max v u}) : Cofan α :=
-  Cofan.mk (TopCat.of (Σi, α i)) (sigmaι α)
+  Cofan.mk (TopCat.of (Σ i, α i)) (sigmaι α)
 #align Top.sigma_cofan TopCat.sigmaCofan
 
 /-- The constructed cofan is indeed a colimit -/
@@ -103,7 +103,7 @@ def sigmaCofanIsColimit {ι : Type v} (α : ι → TopCat.{max v u}) : IsColimit
 
 /-- The coproduct is homeomorphic to the disjoint union of the topological spaces.
 -/
-def sigmaIsoSigma {ι : Type v} (α : ι → TopCat.{max v u}) : ∐ α ≅ TopCat.of (Σi, α i) :=
+def sigmaIsoSigma {ι : Type v} (α : ι → TopCat.{max v u}) : ∐ α ≅ TopCat.of (Σ i, α i) :=
   (colimit.isColimit _).coconePointUniqueUpToIso (sigmaCofanIsColimit α)
 #align Top.sigma_iso_sigma TopCat.sigmaIsoSigma
 
@@ -169,10 +169,10 @@ def prodBinaryFanIsLimit (X Y : TopCat.{u}) : IsLimit (prodBinaryFan X Y)
     intro S m h
     ext x
     · specialize h ⟨walking_pair.left⟩
-      apply_fun fun e => e x  at h
+      apply_fun fun e => e x  at h 
       exact h
     · specialize h ⟨walking_pair.right⟩
-      apply_fun fun e => e x  at h
+      apply_fun fun e => e x  at h 
       exact h
 #align Top.prod_binary_fan_is_limit TopCat.prodBinaryFanIsLimit
 -/
@@ -283,7 +283,7 @@ def binaryCofanIsColimit (X Y : TopCat.{u}) : IsColimit (TopCat.binaryCofan X Y)
   · intro s; ext; rfl
   · intro s; ext; rfl
   · intro s m h₁ h₂; ext (x | x)
-    exacts[(concrete_category.congr_hom h₁ x : _), (concrete_category.congr_hom h₂ x : _)]
+    exacts [(concrete_category.congr_hom h₁ x : _), (concrete_category.congr_hom h₂ x : _)]
 #align Top.binary_cofan_is_colimit TopCat.binaryCofanIsColimit
 -/
 
@@ -356,7 +356,7 @@ theorem binaryCofan_isColimit_iff {X Y : TopCat} (c : BinaryCofan X Y) :
         · rw [Equiv.ofInjective_symm_apply]
       · intro T f g; ext x; refine' (dif_neg _).trans _
         · rintro ⟨y, e⟩; have : c.inr x ∈ Set.range c.inl ⊓ Set.range c.inr := ⟨⟨_, e⟩, ⟨_, rfl⟩⟩
-          rwa [disjoint_iff.mp h₃.1] at this
+          rwa [disjoint_iff.mp h₃.1] at this 
         · exact congr_arg g (Equiv.ofInjective_symm_apply _ _)
       · rintro T _ _ m rfl rfl; ext x; change m x = dite _ _ _
         split_ifs <;> exact congr_arg _ (Equiv.apply_ofInjective_symm _ ⟨_, _⟩).symm

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

@@ -34,35 +34,17 @@ namespace TopCat
 
 variable {J : Type v} [SmallCategory J]
 
-/- warning: Top.pi_π -> TopCat.piπ is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u2}} (α : ι -> TopCat.{max u2 u1}) (i : ι), Quiver.Hom.{succ (max u2 u1), succ (max u2 u1)} TopCat.{max u2 u1} (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, succ (max u2 u1)} TopCat.{max u2 u1} (CategoryTheory.Category.toCategoryStruct.{max u2 u1, succ (max u2 u1)} TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1})) (TopCat.of.{max u2 u1} (forall (i : ι), coeSort.{succ (succ (max u2 u1)), succ (succ (max u2 u1))} TopCat.{max u2 u1} Type.{max u2 u1} TopCat.hasCoeToSort.{max u2 u1} (α i)) (Pi.topologicalSpace.{u2, max u2 u1} ι (fun (i : ι) => coeSort.{succ (succ (max u2 u1)), succ (succ (max u2 u1))} TopCat.{max u2 u1} Type.{max u2 u1} TopCat.hasCoeToSort.{max u2 u1} (α i)) (fun (a : ι) => TopCat.topologicalSpace.{max u2 u1} (α a)))) (α i)
-but is expected to have type
-  forall {ι : Type.{u1}} (α : ι -> TopCatMax.{u1, u2}) (i : ι), Quiver.Hom.{max (succ u2) (succ u1), succ (max u2 u1)} TopCat.{max u2 u1} (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max (succ u2) (succ u1)} TopCat.{max u2 u1} (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max (succ u2) (succ u1)} TopCat.{max u2 u1} instTopCatLargeCategory.{max u2 u1})) (TopCat.of.{max u2 u1} (forall (i : ι), CategoryTheory.Bundled.α.{max u2 u1, max u2 u1} TopologicalSpace.{max u2 u1} (α i)) (Pi.topologicalSpace.{u1, max u2 u1} ι (fun (i : ι) => CategoryTheory.Bundled.α.{max u2 u1, max u2 u1} TopologicalSpace.{max u2 u1} (α i)) (fun (a : ι) => TopCat.topologicalSpace_coe.{max u2 u1} (α a)))) (α i)
-Case conversion may be inaccurate. Consider using '#align Top.pi_π TopCat.piπₓ'. -/
 /-- The projection from the product as a bundled continous map. -/
 abbrev piπ {ι : Type v} (α : ι → TopCat.{max v u}) (i : ι) : TopCat.of (∀ i, α i) ⟶ α i :=
   ⟨fun f => f i, continuous_apply i⟩
 #align Top.pi_π TopCat.piπ
 
-/- warning: Top.pi_fan -> TopCat.piFan is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u2}} (α : ι -> TopCat.{max u2 u1}), CategoryTheory.Limits.Fan.{u2, max u2 u1, succ (max u2 u1)} ι TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} α
-but is expected to have type
-  forall {ι : Type.{u1}} (α : ι -> TopCatMax.{u1, u2}), CategoryTheory.Limits.Fan.{u1, max u2 u1, max (succ u2) (succ u1)} ι TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} α
-Case conversion may be inaccurate. Consider using '#align Top.pi_fan TopCat.piFanₓ'. -/
 /-- The explicit fan of a family of topological spaces given by the pi type. -/
 @[simps pt π_app]
 def piFan {ι : Type v} (α : ι → TopCat.{max v u}) : Fan α :=
   Fan.mk (TopCat.of (∀ i, α i)) (piπ α)
 #align Top.pi_fan TopCat.piFan
 
-/- warning: Top.pi_fan_is_limit -> TopCat.piFanIsLimit is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u2}} (α : ι -> TopCat.{max u2 u1}), CategoryTheory.Limits.IsLimit.{u2, max u2 u1, u2, succ (max u2 u1)} (CategoryTheory.Discrete.{u2} ι) (CategoryTheory.discreteCategory.{u2} ι) TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} (CategoryTheory.Discrete.functor.{max u2 u1, u2, succ (max u2 u1)} TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} ι α) (TopCat.piFan.{u1, u2} ι α)
-but is expected to have type
-  forall {ι : Type.{u1}} (α : ι -> TopCatMax.{u1, u2}), CategoryTheory.Limits.IsLimit.{u1, max u2 u1, u1, max (succ u2) (succ u1)} (CategoryTheory.Discrete.{u1} ι) (CategoryTheory.discreteCategory.{u1} ι) TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} (CategoryTheory.Discrete.functor.{max u2 u1, u1, max (succ u2) (succ u1)} TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} ι α) (TopCat.piFan.{u1, u2} ι α)
-Case conversion may be inaccurate. Consider using '#align Top.pi_fan_is_limit TopCat.piFanIsLimitₓ'. -/
 /-- The constructed fan is indeed a limit -/
 def piFanIsLimit {ι : Type v} (α : ι → TopCat.{max v u}) : IsLimit (piFan α)
     where
@@ -71,12 +53,6 @@ def piFanIsLimit {ι : Type v} (α : ι → TopCat.{max v u}) : IsLimit (piFan 
   fac s j := by cases j; tidy
 #align Top.pi_fan_is_limit TopCat.piFanIsLimit
 
-/- warning: Top.pi_iso_pi -> TopCat.piIsoPi is a dubious translation:
-lean 3 declaration is
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 /-- The product is homeomorphic to the product of the underlying spaces,
 equipped with the product topology.
 -/
@@ -84,29 +60,17 @@ def piIsoPi {ι : Type v} (α : ι → TopCat.{max v u}) : ∏ α ≅ TopCat.of
   (limit.isLimit _).conePointUniqueUpToIso (piFanIsLimit α)
 #align Top.pi_iso_pi TopCat.piIsoPi
 
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 @[simp, reassoc]
 theorem piIsoPi_inv_π {ι : Type v} (α : ι → TopCat.{max v u}) (i : ι) :
     (piIsoPi α).inv ≫ Pi.π α i = piπ α i := by simp [pi_iso_pi]
 #align Top.pi_iso_pi_inv_π TopCat.piIsoPi_inv_π
 
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 @[simp]
 theorem piIsoPi_inv_π_apply {ι : Type v} (α : ι → TopCat.{max v u}) (i : ι) (x : ∀ i, α i) :
     (Pi.π α i : _) ((piIsoPi α).inv x) = x i :=
   ConcreteCategory.congr_hom (piIsoPi_inv_π α i) x
 #align Top.pi_iso_pi_inv_π_apply TopCat.piIsoPi_inv_π_apply
 
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 @[simp]
 theorem piIsoPi_hom_apply {ι : Type v} (α : ι → TopCat.{max v u}) (i : ι) (x : ∏ α) :
     (piIsoPi α).Hom x i = (Pi.π α i : _) x :=
@@ -116,35 +80,17 @@ theorem piIsoPi_hom_apply {ι : Type v} (α : ι → TopCat.{max v u}) (i : ι)
   exact concrete_category.congr_hom this x
 #align Top.pi_iso_pi_hom_apply TopCat.piIsoPi_hom_apply
 
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 /-- The inclusion to the coproduct as a bundled continous map. -/
 abbrev sigmaι {ι : Type v} (α : ι → TopCat.{max v u}) (i : ι) : α i ⟶ TopCat.of (Σi, α i) :=
   ⟨Sigma.mk i⟩
 #align Top.sigma_ι TopCat.sigmaι
 
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 /-- The explicit cofan of a family of topological spaces given by the sigma type. -/
 @[simps pt ι_app]
 def sigmaCofan {ι : Type v} (α : ι → TopCat.{max v u}) : Cofan α :=
   Cofan.mk (TopCat.of (Σi, α i)) (sigmaι α)
 #align Top.sigma_cofan TopCat.sigmaCofan
 
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 /-- The constructed cofan is indeed a colimit -/
 def sigmaCofanIsColimit {ι : Type v} (α : ι → TopCat.{max v u}) : IsColimit (sigmaCofan α)
     where
@@ -155,50 +101,29 @@ def sigmaCofanIsColimit {ι : Type v} (α : ι → TopCat.{max v u}) : IsColimit
   fac s j := by cases j; tidy
 #align Top.sigma_cofan_is_colimit TopCat.sigmaCofanIsColimit
 
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 /-- The coproduct is homeomorphic to the disjoint union of the topological spaces.
 -/
 def sigmaIsoSigma {ι : Type v} (α : ι → TopCat.{max v u}) : ∐ α ≅ TopCat.of (Σi, α i) :=
   (colimit.isColimit _).coconePointUniqueUpToIso (sigmaCofanIsColimit α)
 #align Top.sigma_iso_sigma TopCat.sigmaIsoSigma
 
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 @[simp, reassoc]
 theorem sigmaIsoSigma_hom_ι {ι : Type v} (α : ι → TopCat.{max v u}) (i : ι) :
     Sigma.ι α i ≫ (sigmaIsoSigma α).Hom = sigmaι α i := by simp [sigma_iso_sigma]
 #align Top.sigma_iso_sigma_hom_ι TopCat.sigmaIsoSigma_hom_ι
 
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 @[simp]
 theorem sigmaIsoSigma_hom_ι_apply {ι : Type v} (α : ι → TopCat.{max v u}) (i : ι) (x : α i) :
     (sigmaIsoSigma α).Hom ((Sigma.ι α i : _) x) = Sigma.mk i x :=
   ConcreteCategory.congr_hom (sigmaIsoSigma_hom_ι α i) x
 #align Top.sigma_iso_sigma_hom_ι_apply TopCat.sigmaIsoSigma_hom_ι_apply
 
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 @[simp]
 theorem sigmaIsoSigma_inv_apply {ι : Type v} (α : ι → TopCat.{max v u}) (i : ι) (x : α i) :
     (sigmaIsoSigma α).inv ⟨i, x⟩ = (Sigma.ι α i : _) x := by
   rw [← sigma_iso_sigma_hom_ι_apply, ← comp_app]; simp
 #align Top.sigma_iso_sigma_inv_apply TopCat.sigmaIsoSigma_inv_apply
 
-/- warning: Top.induced_of_is_limit -> TopCat.induced_of_isLimit is a dubious translation:
-<too large>
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 theorem induced_of_isLimit {F : J ⥤ TopCat.{max v u}} (C : Cone F) (hC : IsLimit C) :
     C.pt.TopologicalSpace = ⨅ j, (F.obj j).TopologicalSpace.induced (C.π.app j) :=
   by
@@ -208,9 +133,6 @@ theorem induced_of_isLimit {F : J ⥤ TopCat.{max v u}} (C : Cone F) (hC : IsLim
   simpa [induced_iInf, induced_compose]
 #align Top.induced_of_is_limit TopCat.induced_of_isLimit
 
-/- warning: Top.limit_topology -> TopCat.limit_topology is a dubious translation:
-<too large>
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 theorem limit_topology (F : J ⥤ TopCat.{max v u}) :
     (limit F).TopologicalSpace = ⨅ j, (F.obj j).TopologicalSpace.induced (limit.π F j) :=
   induced_of_isLimit _ (limit.isLimit F)
@@ -218,23 +140,11 @@ theorem limit_topology (F : J ⥤ TopCat.{max v u}) :
 
 section Prod
 
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 /-- The first projection from the product. -/
 abbrev prodFst {X Y : TopCat.{u}} : TopCat.of (X × Y) ⟶ X :=
   ⟨Prod.fst⟩
 #align Top.prod_fst TopCat.prodFst
 
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 /-- The second projection from the product. -/
 abbrev prodSnd {X Y : TopCat.{u}} : TopCat.of (X × Y) ⟶ Y :=
   ⟨Prod.snd⟩
@@ -267,12 +177,6 @@ def prodBinaryFanIsLimit (X Y : TopCat.{u}) : IsLimit (prodBinaryFan X Y)
 #align Top.prod_binary_fan_is_limit TopCat.prodBinaryFanIsLimit
 -/
 
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 /-- The homeomorphism between `X ⨯ Y` and the set-theoretic product of `X` and `Y`,
 equipped with the product topology.
 -/
@@ -294,9 +198,6 @@ theorem prodIsoProd_hom_snd (X Y : TopCat.{u}) :
 #align Top.prod_iso_prod_hom_snd TopCat.prodIsoProd_hom_snd
 -/
 
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 @[simp]
 theorem prodIsoProd_hom_apply {X Y : TopCat.{u}} (x : X ⨯ Y) :
     (prodIsoProd X Y).Hom x = ((Limits.prod.fst : X ⨯ Y ⟶ _) x, (Limits.prod.snd : X ⨯ Y ⟶ _) x) :=
@@ -306,31 +207,16 @@ theorem prodIsoProd_hom_apply {X Y : TopCat.{u}} (x : X ⨯ Y) :
   · exact concrete_category.congr_hom (prod_iso_prod_hom_snd X Y) x
 #align Top.prod_iso_prod_hom_apply TopCat.prodIsoProd_hom_apply
 
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-Case conversion may be inaccurate. Consider using '#align Top.prod_iso_prod_inv_fst TopCat.prodIsoProd_inv_fstₓ'. -/
 @[simp, reassoc, elementwise]
 theorem prodIsoProd_inv_fst (X Y : TopCat.{u}) :
     (prodIsoProd X Y).inv ≫ Limits.prod.fst = prodFst := by simp [iso.inv_comp_eq]
 #align Top.prod_iso_prod_inv_fst TopCat.prodIsoProd_inv_fst
 
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-Case conversion may be inaccurate. Consider using '#align Top.prod_iso_prod_inv_snd TopCat.prodIsoProd_inv_sndₓ'. -/
 @[simp, reassoc, elementwise]
 theorem prodIsoProd_inv_snd (X Y : TopCat.{u}) :
     (prodIsoProd X Y).inv ≫ Limits.prod.snd = prodSnd := by simp [iso.inv_comp_eq]
 #align Top.prod_iso_prod_inv_snd TopCat.prodIsoProd_inv_snd
 
-/- warning: Top.prod_topology -> TopCat.prod_topology is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align Top.prod_topology TopCat.prod_topologyₓ'. -/
 theorem prod_topology {X Y : TopCat} :
     (X ⨯ Y).TopologicalSpace =
       induced (Limits.prod.fst : X ⨯ Y ⟶ _) X.TopologicalSpace ⊓
@@ -342,9 +228,6 @@ theorem prod_topology {X Y : TopCat} :
   simpa [induced_compose]
 #align Top.prod_topology TopCat.prod_topology
 
-/- warning: Top.range_prod_map -> TopCat.range_prod_map is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align Top.range_prod_map TopCat.range_prod_mapₓ'. -/
 theorem range_prod_map {W X Y Z : TopCat.{u}} (f : W ⟶ Y) (g : X ⟶ Z) :
     Set.range (Limits.prod.map f g) =
       (Limits.prod.fst : Y ⨯ Z ⟶ _) ⁻¹' Set.range f ∩
@@ -364,9 +247,6 @@ theorem range_prod_map {W X Y Z : TopCat.{u}} (f : W ⟶ Y) (g : X ⟶ Z) :
     · simp only [← comp_apply, category.assoc]; erw [limits.prod.map_snd]; simp [hx₂]
 #align Top.range_prod_map TopCat.range_prod_map
 
-/- warning: Top.inducing_prod_map -> TopCat.inducing_prod_map is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align Top.inducing_prod_map TopCat.inducing_prod_mapₓ'. -/
 theorem inducing_prod_map {W X Y Z : TopCat} {f : W ⟶ X} {g : Y ⟶ Z} (hf : Inducing f)
     (hg : Inducing g) : Inducing (Limits.prod.map f g) :=
   by
@@ -377,9 +257,6 @@ theorem inducing_prod_map {W X Y Z : TopCat} {f : W ⟶ X} {g : Y ⟶ Z} (hf : I
   rw [← @induced_compose _ _ _ _ _ f, ← @induced_compose _ _ _ _ _ g, ← hf.induced, ← hg.induced]
 #align Top.inducing_prod_map TopCat.inducing_prod_map
 
-/- warning: Top.embedding_prod_map -> TopCat.embedding_prod_map is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align Top.embedding_prod_map TopCat.embedding_prod_mapₓ'. -/
 theorem embedding_prod_map {W X Y Z : TopCat} {f : W ⟶ X} {g : Y ⟶ Z} (hf : Embedding f)
     (hg : Embedding g) : Embedding (Limits.prod.map f g) :=
   ⟨inducing_prod_map hf.to_inducing hg.to_inducing,
@@ -410,9 +287,6 @@ def binaryCofanIsColimit (X Y : TopCat.{u}) : IsColimit (TopCat.binaryCofan X Y)
 #align Top.binary_cofan_is_colimit TopCat.binaryCofanIsColimit
 -/
 
-/- warning: Top.binary_cofan_is_colimit_iff -> TopCat.binaryCofan_isColimit_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align Top.binary_cofan_is_colimit_iff TopCat.binaryCofan_isColimit_iffₓ'. -/
 theorem binaryCofan_isColimit_iff {X Y : TopCat} (c : BinaryCofan X Y) :
     Nonempty (IsColimit c) ↔
       OpenEmbedding c.inl ∧ OpenEmbedding c.inr ∧ IsCompl (Set.range c.inl) (Set.range c.inr) :=

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

@@ -67,13 +67,8 @@ Case conversion may be inaccurate. Consider using '#align Top.pi_fan_is_limit To
 def piFanIsLimit {ι : Type v} (α : ι → TopCat.{max v u}) : IsLimit (piFan α)
     where
   lift S := { toFun := fun s i => S.π.app ⟨i⟩ s }
-  uniq := by
-    intro S m h
-    ext (x i)
-    simp [← h ⟨i⟩]
-  fac s j := by
-    cases j
-    tidy
+  uniq := by intro S m h; ext (x i); simp [← h ⟨i⟩]
+  fac s j := by cases j; tidy
 #align Top.pi_fan_is_limit TopCat.piFanIsLimit
 
 /- warning: Top.pi_iso_pi -> TopCat.piIsoPi is a dubious translation:
@@ -156,13 +151,8 @@ def sigmaCofanIsColimit {ι : Type v} (α : ι → TopCat.{max v u}) : IsColimit
   desc S :=
     { toFun := fun s => S.ι.app ⟨s.1⟩ s.2
       continuous_toFun := continuous_sigma fun i => map_continuous (S.ι.app ⟨i⟩) }
-  uniq := by
-    intro S m h
-    ext ⟨i, x⟩
-    simp [← h ⟨i⟩]
-  fac s j := by
-    cases j
-    tidy
+  uniq := by intro S m h; ext ⟨i, x⟩; simp [← h ⟨i⟩]
+  fac s j := by cases j; tidy
 #align Top.sigma_cofan_is_colimit TopCat.sigmaCofanIsColimit
 
 /- warning: Top.sigma_iso_sigma -> TopCat.sigmaIsoSigma is a dubious translation:
@@ -202,10 +192,8 @@ theorem sigmaIsoSigma_hom_ι_apply {ι : Type v} (α : ι → TopCat.{max v u})
 Case conversion may be inaccurate. Consider using '#align Top.sigma_iso_sigma_inv_apply TopCat.sigmaIsoSigma_inv_applyₓ'. -/
 @[simp]
 theorem sigmaIsoSigma_inv_apply {ι : Type v} (α : ι → TopCat.{max v u}) (i : ι) (x : α i) :
-    (sigmaIsoSigma α).inv ⟨i, x⟩ = (Sigma.ι α i : _) x :=
-  by
-  rw [← sigma_iso_sigma_hom_ι_apply, ← comp_app]
-  simp
+    (sigmaIsoSigma α).inv ⟨i, x⟩ = (Sigma.ι α i : _) x := by
+  rw [← sigma_iso_sigma_hom_ι_apply, ← comp_app]; simp
 #align Top.sigma_iso_sigma_inv_apply TopCat.sigmaIsoSigma_inv_apply
 
 /- warning: Top.induced_of_is_limit -> TopCat.induced_of_isLimit is a dubious translation:
@@ -372,12 +360,8 @@ theorem range_prod_map {W X Y Z : TopCat.{u}} (f : W ⟶ Y) (g : X ⟶ Z) :
     use (prod_iso_prod W X).inv (x₁, x₂)
     apply concrete.limit_ext
     rintro ⟨⟨⟩⟩
-    · simp only [← comp_apply, category.assoc]
-      erw [limits.prod.map_fst]
-      simp [hx₁]
-    · simp only [← comp_apply, category.assoc]
-      erw [limits.prod.map_snd]
-      simp [hx₂]
+    · simp only [← comp_apply, category.assoc]; erw [limits.prod.map_fst]; simp [hx₁]
+    · simp only [← comp_apply, category.assoc]; erw [limits.prod.map_snd]; simp [hx₂]
 #align Top.range_prod_map TopCat.range_prod_map
 
 /- warning: Top.inducing_prod_map -> TopCat.inducing_prod_map is a dubious translation:
@@ -419,14 +403,9 @@ protected def binaryCofan (X Y : TopCat.{u}) : BinaryCofan X Y :=
 def binaryCofanIsColimit (X Y : TopCat.{u}) : IsColimit (TopCat.binaryCofan X Y) :=
   by
   refine' limits.binary_cofan.is_colimit_mk (fun s => ⟨Sum.elim s.inl s.inr⟩) _ _ _
-  · intro s
-    ext
-    rfl
-  · intro s
-    ext
-    rfl
-  · intro s m h₁ h₂
-    ext (x | x)
+  · intro s; ext; rfl
+  · intro s; ext; rfl
+  · intro s m h₁ h₂; ext (x | x)
     exacts[(concrete_category.congr_hom h₁ x : _), (concrete_category.congr_hom h₂ x : _)]
 #align Top.binary_cofan_is_colimit TopCat.binaryCofanIsColimit
 -/
@@ -467,10 +446,8 @@ theorem binaryCofan_isColimit_iff {X Y : TopCat} (c : BinaryCofan X Y) :
       congr 1
       exact set.compl_range_inr.symm
     · rintro ⟨h₁, h₂, h₃⟩
-      have : ∀ x, x ∈ Set.range c.inl ∨ x ∈ Set.range c.inr :=
-        by
-        rw [eq_compl_iff_is_compl.mpr h₃.symm]
-        exact fun _ => or_not
+      have : ∀ x, x ∈ Set.range c.inl ∨ x ∈ Set.range c.inr := by
+        rw [eq_compl_iff_is_compl.mpr h₃.symm]; exact fun _ => or_not
       refine' ⟨binary_cofan.is_colimit.mk _ _ _ _ _⟩
       · intro T f g
         refine' ContinuousMap.mk _ _
@@ -485,42 +462,29 @@ theorem binaryCofan_isColimit_iff {X Y : TopCat} (c : BinaryCofan X Y) :
           apply (IsOpen.continuousOn_iff _).mp
           · rw [continuousOn_iff_continuous_restrict]
             convert_to Continuous (f ∘ (Homeomorph.ofEmbedding _ h₁.to_embedding).symm)
-            · ext ⟨x, hx⟩
-              exact dif_pos hx
+            · ext ⟨x, hx⟩; exact dif_pos hx
             continuity
           · exact h₁.open_range
         · revert h x
           apply (IsOpen.continuousOn_iff _).mp
           · rw [continuousOn_iff_continuous_restrict]
-            have : ∀ a, a ∉ Set.range c.inl → a ∈ Set.range c.inr :=
-              by
-              rintro a (h : a ∈ Set.range c.inlᶜ)
-              rwa [eq_compl_iff_is_compl.mpr h₃.symm]
+            have : ∀ a, a ∉ Set.range c.inl → a ∈ Set.range c.inr := by
+              rintro a (h : a ∈ Set.range c.inlᶜ); rwa [eq_compl_iff_is_compl.mpr h₃.symm]
             convert_to Continuous
                 (g ∘ (Homeomorph.ofEmbedding _ h₂.to_embedding).symm ∘ Subtype.map _ this)
-            · ext ⟨x, hx⟩
-              exact dif_neg hx
+            · ext ⟨x, hx⟩; exact dif_neg hx
             continuity
             rw [embedding_subtype_coe.to_inducing.continuous_iff]
             exact continuous_subtype_val
-          · change IsOpen (Set.range c.inlᶜ)
-            rw [← eq_compl_iff_is_compl.mpr h₃.symm]
+          · change IsOpen (Set.range c.inlᶜ); rw [← eq_compl_iff_is_compl.mpr h₃.symm]
             exact h₂.open_range
-      · intro T f g
-        ext x
-        refine' (dif_pos _).trans _
-        · exact ⟨x, rfl⟩
+      · intro T f g; ext x; refine' (dif_pos _).trans _; · exact ⟨x, rfl⟩
         · rw [Equiv.ofInjective_symm_apply]
-      · intro T f g
-        ext x
-        refine' (dif_neg _).trans _
-        · rintro ⟨y, e⟩
-          have : c.inr x ∈ Set.range c.inl ⊓ Set.range c.inr := ⟨⟨_, e⟩, ⟨_, rfl⟩⟩
+      · intro T f g; ext x; refine' (dif_neg _).trans _
+        · rintro ⟨y, e⟩; have : c.inr x ∈ Set.range c.inl ⊓ Set.range c.inr := ⟨⟨_, e⟩, ⟨_, rfl⟩⟩
           rwa [disjoint_iff.mp h₃.1] at this
         · exact congr_arg g (Equiv.ofInjective_symm_apply _ _)
-      · rintro T _ _ m rfl rfl
-        ext x
-        change m x = dite _ _ _
+      · rintro T _ _ m rfl rfl; ext x; change m x = dite _ _ _
         split_ifs <;> exact congr_arg _ (Equiv.apply_ofInjective_symm _ ⟨_, _⟩).symm
 #align Top.binary_cofan_is_colimit_iff TopCat.binaryCofan_isColimit_iff
 

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

@@ -101,10 +101,7 @@ theorem piIsoPi_inv_π {ι : Type v} (α : ι → TopCat.{max v u}) (i : ι) :
 #align Top.pi_iso_pi_inv_π TopCat.piIsoPi_inv_π
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align Top.pi_iso_pi_inv_π_apply TopCat.piIsoPi_inv_π_applyₓ'. -/
 @[simp]
 theorem piIsoPi_inv_π_apply {ι : Type v} (α : ι → TopCat.{max v u}) (i : ι) (x : ∀ i, α i) :
@@ -113,10 +110,7 @@ theorem piIsoPi_inv_π_apply {ι : Type v} (α : ι → TopCat.{max v u}) (i : 
 #align Top.pi_iso_pi_inv_π_apply TopCat.piIsoPi_inv_π_apply
 
 /- warning: Top.pi_iso_pi_hom_apply -> TopCat.piIsoPi_hom_apply is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align Top.pi_iso_pi_hom_apply TopCat.piIsoPi_hom_applyₓ'. -/
 @[simp]
 theorem piIsoPi_hom_apply {ι : Type v} (α : ι → TopCat.{max v u}) (i : ι) (x : ∏ α) :
@@ -195,10 +189,7 @@ theorem sigmaIsoSigma_hom_ι {ι : Type v} (α : ι → TopCat.{max v u}) (i : 
 #align Top.sigma_iso_sigma_hom_ι TopCat.sigmaIsoSigma_hom_ι
 
 /- warning: Top.sigma_iso_sigma_hom_ι_apply -> TopCat.sigmaIsoSigma_hom_ι_apply is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align Top.sigma_iso_sigma_hom_ι_apply TopCat.sigmaIsoSigma_hom_ι_applyₓ'. -/
 @[simp]
 theorem sigmaIsoSigma_hom_ι_apply {ι : Type v} (α : ι → TopCat.{max v u}) (i : ι) (x : α i) :
@@ -207,10 +198,7 @@ theorem sigmaIsoSigma_hom_ι_apply {ι : Type v} (α : ι → TopCat.{max v u})
 #align Top.sigma_iso_sigma_hom_ι_apply TopCat.sigmaIsoSigma_hom_ι_apply
 
 /- warning: Top.sigma_iso_sigma_inv_apply -> TopCat.sigmaIsoSigma_inv_apply is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align Top.sigma_iso_sigma_inv_apply TopCat.sigmaIsoSigma_inv_applyₓ'. -/
 @[simp]
 theorem sigmaIsoSigma_inv_apply {ι : Type v} (α : ι → TopCat.{max v u}) (i : ι) (x : α i) :
@@ -221,10 +209,7 @@ theorem sigmaIsoSigma_inv_apply {ι : Type v} (α : ι → TopCat.{max v u}) (i
 #align Top.sigma_iso_sigma_inv_apply TopCat.sigmaIsoSigma_inv_apply
 
 /- warning: Top.induced_of_is_limit -> TopCat.induced_of_isLimit is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align Top.induced_of_is_limit TopCat.induced_of_isLimitₓ'. -/
 theorem induced_of_isLimit {F : J ⥤ TopCat.{max v u}} (C : Cone F) (hC : IsLimit C) :
     C.pt.TopologicalSpace = ⨅ j, (F.obj j).TopologicalSpace.induced (C.π.app j) :=
@@ -236,10 +221,7 @@ theorem induced_of_isLimit {F : J ⥤ TopCat.{max v u}} (C : Cone F) (hC : IsLim
 #align Top.induced_of_is_limit TopCat.induced_of_isLimit
 
 /- warning: Top.limit_topology -> TopCat.limit_topology is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align Top.limit_topology TopCat.limit_topologyₓ'. -/
 theorem limit_topology (F : J ⥤ TopCat.{max v u}) :
     (limit F).TopologicalSpace = ⨅ j, (F.obj j).TopologicalSpace.induced (limit.π F j) :=
@@ -325,10 +307,7 @@ theorem prodIsoProd_hom_snd (X Y : TopCat.{u}) :
 -/
 
 /- warning: Top.prod_iso_prod_hom_apply -> TopCat.prodIsoProd_hom_apply is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align Top.prod_iso_prod_hom_apply TopCat.prodIsoProd_hom_applyₓ'. -/
 @[simp]
 theorem prodIsoProd_hom_apply {X Y : TopCat.{u}} (x : X ⨯ Y) :
@@ -362,10 +341,7 @@ theorem prodIsoProd_inv_snd (X Y : TopCat.{u}) :
 #align Top.prod_iso_prod_inv_snd TopCat.prodIsoProd_inv_snd
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align Top.prod_topology TopCat.prod_topologyₓ'. -/
 theorem prod_topology {X Y : TopCat} :
     (X ⨯ Y).TopologicalSpace =
@@ -379,10 +355,7 @@ theorem prod_topology {X Y : TopCat} :
 #align Top.prod_topology TopCat.prod_topology
 
 /- warning: Top.range_prod_map -> TopCat.range_prod_map is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align Top.range_prod_map TopCat.range_prod_mapₓ'. -/
 theorem range_prod_map {W X Y Z : TopCat.{u}} (f : W ⟶ Y) (g : X ⟶ Z) :
     Set.range (Limits.prod.map f g) =
@@ -408,10 +381,7 @@ theorem range_prod_map {W X Y Z : TopCat.{u}} (f : W ⟶ Y) (g : X ⟶ Z) :
 #align Top.range_prod_map TopCat.range_prod_map
 
 /- warning: Top.inducing_prod_map -> TopCat.inducing_prod_map is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align Top.inducing_prod_map TopCat.inducing_prod_mapₓ'. -/
 theorem inducing_prod_map {W X Y Z : TopCat} {f : W ⟶ X} {g : Y ⟶ Z} (hf : Inducing f)
     (hg : Inducing g) : Inducing (Limits.prod.map f g) :=
@@ -424,10 +394,7 @@ theorem inducing_prod_map {W X Y Z : TopCat} {f : W ⟶ X} {g : Y ⟶ Z} (hf : I
 #align Top.inducing_prod_map TopCat.inducing_prod_map
 
 /- warning: Top.embedding_prod_map -> TopCat.embedding_prod_map is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align Top.embedding_prod_map TopCat.embedding_prod_mapₓ'. -/
 theorem embedding_prod_map {W X Y Z : TopCat} {f : W ⟶ X} {g : Y ⟶ Z} (hf : Embedding f)
     (hg : Embedding g) : Embedding (Limits.prod.map f g) :=
@@ -465,10 +432,7 @@ def binaryCofanIsColimit (X Y : TopCat.{u}) : IsColimit (TopCat.binaryCofan X Y)
 -/
 
 /- warning: Top.binary_cofan_is_colimit_iff -> TopCat.binaryCofan_isColimit_iff is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align Top.binary_cofan_is_colimit_iff TopCat.binaryCofan_isColimit_iffₓ'. -/
 theorem binaryCofan_isColimit_iff {X Y : TopCat} (c : BinaryCofan X Y) :
     Nonempty (IsColimit c) ↔

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

@@ -95,7 +95,7 @@ lean 3 declaration is
 but is expected to have type
   forall {ι : Type.{u1}} (α : ι -> TopCatMax.{u1, u2}) (i : ι), Eq.{max (succ u2) (succ u1)} (Quiver.Hom.{succ (max u2 u1), max (succ u2) (succ u1)} TopCatMax.{u1, u2} (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max (succ u2) (succ u1)} TopCatMax.{u1, u2} (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max (succ u2) (succ u1)} TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1})) (TopCat.of.{max u2 u1} (forall (i : ι), CategoryTheory.Bundled.α.{max u2 u1, max u2 u1} TopologicalSpace.{max u2 u1} (α i)) (Pi.topologicalSpace.{u1, max u2 u1} ι (fun (i : ι) => CategoryTheory.Bundled.α.{max u2 u1, max u2 u1} TopologicalSpace.{max u2 u1} (α i)) (fun (a : ι) => TopCat.topologicalSpace_coe.{max u2 u1} (α a)))) (α i)) (CategoryTheory.CategoryStruct.comp.{max u2 u1, max (succ u2) (succ u1)} TopCatMax.{u1, u2} (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max (succ u2) (succ u1)} TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1}) (TopCat.of.{max u2 u1} (forall (i : ι), CategoryTheory.Bundled.α.{max u2 u1, max u2 u1} TopologicalSpace.{max u2 u1} (α i)) (Pi.topologicalSpace.{u1, max u2 u1} ι (fun (i : ι) => CategoryTheory.Bundled.α.{max u2 u1, max u2 u1} TopologicalSpace.{max u2 u1} (α i)) (fun (a : ι) => TopCat.topologicalSpace_coe.{max u2 u1} (α a)))) (CategoryTheory.Limits.piObj.{u1, max u2 u1, max (succ u2) (succ u1)} ι TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} α (CategoryTheory.Limits.hasLimitOfHasLimitsOfShape.{u1, u1, max u2 u1, max (succ u2) (succ u1)} TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} (CategoryTheory.Discrete.{u1} ι) (CategoryTheory.discreteCategory.{u1} ι) (CategoryTheory.Limits.hasLimitsOfShapeOfHasLimits.{u1, u1, max u2 u1, max (succ u2) (succ u1)} TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} (CategoryTheory.Discrete.{u1} ι) (CategoryTheory.discreteCategory.{u1} ι) TopCat.topCat_hasLimitsOfSize.{u1, u2}) (CategoryTheory.Discrete.functor.{max u2 u1, u1, max (succ u2) (succ u1)} TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} ι α))) (α i) (CategoryTheory.Iso.inv.{max u2 u1, max (succ u2) (succ u1)} TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} (CategoryTheory.Limits.piObj.{u1, max u2 u1, max (succ u2) (succ u1)} ι TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} α (CategoryTheory.Limits.hasLimitOfHasLimitsOfShape.{u1, u1, max u2 u1, max (succ u2) (succ u1)} TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} (CategoryTheory.Discrete.{u1} ι) (CategoryTheory.discreteCategory.{u1} ι) (CategoryTheory.Limits.hasLimitsOfShapeOfHasLimits.{u1, u1, max u2 u1, max (succ u2) (succ u1)} TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} (CategoryTheory.Discrete.{u1} ι) (CategoryTheory.discreteCategory.{u1} ι) TopCat.topCat_hasLimitsOfSize.{u1, u2}) (CategoryTheory.Discrete.functor.{max u2 u1, u1, max (succ u2) (succ u1)} TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} ι α))) (TopCat.of.{max u2 u1} (forall (i : ι), CategoryTheory.Bundled.α.{max u2 u1, max u2 u1} TopologicalSpace.{max u2 u1} (α i)) (Pi.topologicalSpace.{u1, max u2 u1} ι (fun (i : ι) => CategoryTheory.Bundled.α.{max u2 u1, max u2 u1} TopologicalSpace.{max u2 u1} (α i)) (fun (a : ι) => TopCat.topologicalSpace_coe.{max u2 u1} (α a)))) (TopCat.piIsoPi.{u1, u2} ι α)) (CategoryTheory.Limits.Pi.π.{u1, max u2 u1, max (succ u2) (succ u1)} ι TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} α (CategoryTheory.Limits.hasLimitOfHasLimitsOfShape.{u1, u1, max u2 u1, max (succ u2) (succ u1)} TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} (CategoryTheory.Discrete.{u1} ι) (CategoryTheory.discreteCategory.{u1} ι) (CategoryTheory.Limits.hasLimitsOfShapeOfHasLimits.{u1, u1, max u2 u1, max (succ u2) (succ u1)} TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} (CategoryTheory.Discrete.{u1} ι) (CategoryTheory.discreteCategory.{u1} ι) TopCat.topCat_hasLimitsOfSize.{u1, u2}) (CategoryTheory.Discrete.functor.{max u2 u1, u1, max (succ u2) (succ u1)} TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} ι α)) i)) (TopCat.piπ.{u1, u2} ι α i)
 Case conversion may be inaccurate. Consider using '#align Top.pi_iso_pi_inv_π TopCat.piIsoPi_inv_πₓ'. -/
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem piIsoPi_inv_π {ι : Type v} (α : ι → TopCat.{max v u}) (i : ι) :
     (piIsoPi α).inv ≫ Pi.π α i = piπ α i := by simp [pi_iso_pi]
 #align Top.pi_iso_pi_inv_π TopCat.piIsoPi_inv_π
@@ -189,7 +189,7 @@ lean 3 declaration is
 but is expected to have type
   forall {ι : Type.{u1}} (α : ι -> TopCatMax.{u1, u2}) (i : ι), Eq.{max (succ u2) (succ u1)} (Quiver.Hom.{succ (max u2 u1), max (succ u2) (succ u1)} TopCatMax.{u1, u2} (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max (succ u2) (succ u1)} TopCatMax.{u1, u2} (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max (succ u2) (succ u1)} TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1})) (α i) (TopCat.of.{max u2 u1} (Sigma.{u1, max u2 u1} ι (fun (i : ι) => CategoryTheory.Bundled.α.{max u2 u1, max u2 u1} TopologicalSpace.{max u2 u1} (α i))) (instTopologicalSpaceSigma.{u1, max u2 u1} ι (fun (i : ι) => CategoryTheory.Bundled.α.{max u2 u1, max u2 u1} TopologicalSpace.{max u2 u1} (α i)) (fun (a : ι) => TopCat.topologicalSpace_coe.{max u2 u1} (α a))))) (CategoryTheory.CategoryStruct.comp.{max u2 u1, max (succ u2) (succ u1)} TopCatMax.{u1, u2} (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max (succ u2) (succ u1)} TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1}) (α i) (CategoryTheory.Limits.sigmaObj.{u1, max u2 u1, max (succ u2) (succ u1)} ι TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} α (CategoryTheory.Limits.hasColimitOfHasColimitsOfShape.{u1, u1, max u2 u1, max (succ u2) (succ u1)} TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} (CategoryTheory.Discrete.{u1} ι) (CategoryTheory.discreteCategory.{u1} ι) (CategoryTheory.Limits.hasColimitsOfShapeOfHasColimitsOfSize.{u1, u1, max u2 u1, max (succ u2) (succ u1)} TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} (CategoryTheory.Discrete.{u1} ι) (CategoryTheory.discreteCategory.{u1} ι) TopCat.topCat_hasColimitsOfSize.{u1, u2}) (CategoryTheory.Discrete.functor.{max u2 u1, u1, max (succ u2) (succ u1)} TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} ι α))) (TopCat.of.{max u2 u1} (Sigma.{u1, max u2 u1} ι (fun (i : ι) => CategoryTheory.Bundled.α.{max u2 u1, max u2 u1} TopologicalSpace.{max u2 u1} (α i))) (instTopologicalSpaceSigma.{u1, max u2 u1} ι (fun (i : ι) => CategoryTheory.Bundled.α.{max u2 u1, max u2 u1} TopologicalSpace.{max u2 u1} (α i)) (fun (a : ι) => TopCat.topologicalSpace_coe.{max u2 u1} (α a)))) (CategoryTheory.Limits.Sigma.ι.{u1, max u2 u1, max (succ u2) (succ u1)} ι TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} α (CategoryTheory.Limits.hasColimitOfHasColimitsOfShape.{u1, u1, max u2 u1, max (succ u2) (succ u1)} TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} (CategoryTheory.Discrete.{u1} ι) (CategoryTheory.discreteCategory.{u1} ι) (CategoryTheory.Limits.hasColimitsOfShapeOfHasColimitsOfSize.{u1, u1, max u2 u1, max (succ u2) (succ u1)} TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} (CategoryTheory.Discrete.{u1} ι) (CategoryTheory.discreteCategory.{u1} ι) TopCat.topCat_hasColimitsOfSize.{u1, u2}) (CategoryTheory.Discrete.functor.{max u2 u1, u1, max (succ u2) (succ u1)} TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} ι α)) i) (CategoryTheory.Iso.hom.{max u2 u1, max (succ u2) (succ u1)} TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} (CategoryTheory.Limits.sigmaObj.{u1, max u2 u1, max (succ u2) (succ u1)} ι TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} α (CategoryTheory.Limits.hasColimitOfHasColimitsOfShape.{u1, u1, max u2 u1, max (succ u2) (succ u1)} TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} (CategoryTheory.Discrete.{u1} ι) (CategoryTheory.discreteCategory.{u1} ι) (CategoryTheory.Limits.hasColimitsOfShapeOfHasColimitsOfSize.{u1, u1, max u2 u1, max (succ u2) (succ u1)} TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} (CategoryTheory.Discrete.{u1} ι) (CategoryTheory.discreteCategory.{u1} ι) TopCat.topCat_hasColimitsOfSize.{u1, u2}) (CategoryTheory.Discrete.functor.{max u2 u1, u1, max (succ u2) (succ u1)} TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} ι α))) (TopCat.of.{max u2 u1} (Sigma.{u1, max u2 u1} ι (fun (i : ι) => CategoryTheory.Bundled.α.{max u2 u1, max u2 u1} TopologicalSpace.{max u2 u1} (α i))) (instTopologicalSpaceSigma.{u1, max u2 u1} ι (fun (i : ι) => CategoryTheory.Bundled.α.{max u2 u1, max u2 u1} TopologicalSpace.{max u2 u1} (α i)) (fun (a : ι) => TopCat.topologicalSpace_coe.{max u2 u1} (α a)))) (TopCat.sigmaIsoSigma.{u1, u2} ι α))) (TopCat.sigmaι.{u1, u2} ι α i)
 Case conversion may be inaccurate. Consider using '#align Top.sigma_iso_sigma_hom_ι TopCat.sigmaIsoSigma_hom_ιₓ'. -/
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem sigmaIsoSigma_hom_ι {ι : Type v} (α : ι → TopCat.{max v u}) (i : ι) :
     Sigma.ι α i ≫ (sigmaIsoSigma α).Hom = sigmaι α i := by simp [sigma_iso_sigma]
 #align Top.sigma_iso_sigma_hom_ι TopCat.sigmaIsoSigma_hom_ι
@@ -311,14 +311,14 @@ def prodIsoProd (X Y : TopCat.{u}) : X ⨯ Y ≅ TopCat.of (X × Y) :=
 #align Top.prod_iso_prod TopCat.prodIsoProd
 
 #print TopCat.prodIsoProd_hom_fst /-
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem prodIsoProd_hom_fst (X Y : TopCat.{u}) :
     (prodIsoProd X Y).Hom ≫ prodFst = Limits.prod.fst := by simpa [← iso.eq_inv_comp, prod_iso_prod]
 #align Top.prod_iso_prod_hom_fst TopCat.prodIsoProd_hom_fst
 -/
 
 #print TopCat.prodIsoProd_hom_snd /-
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem prodIsoProd_hom_snd (X Y : TopCat.{u}) :
     (prodIsoProd X Y).Hom ≫ prodSnd = Limits.prod.snd := by simpa [← iso.eq_inv_comp, prod_iso_prod]
 #align Top.prod_iso_prod_hom_snd TopCat.prodIsoProd_hom_snd
@@ -345,7 +345,7 @@ lean 3 declaration is
 but is expected to have type
   forall (X : TopCat.{u1}) (Y : TopCat.{u1}), Eq.{succ u1} (Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) (TopCat.of.{u1} (Prod.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y)) (instTopologicalSpaceProd.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} X) (TopCat.topologicalSpace_coe.{u1} Y))) X) (CategoryTheory.CategoryStruct.comp.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) (TopCat.of.{u1} (Prod.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y)) (instTopologicalSpaceProd.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} X) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Limits.prod.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y (CategoryTheory.Limits.hasLimitOfHasLimitsOfShape.{0, 0, u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} (CategoryTheory.Discrete.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.discreteCategory.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.Limits.hasLimitsOfShapeOfHasLimits.{0, 0, u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} (CategoryTheory.Discrete.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.discreteCategory.{0} CategoryTheory.Limits.WalkingPair) TopCat.topCat_hasLimitsOfSize.{0, u1}) (CategoryTheory.Limits.pair.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y))) X (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} (CategoryTheory.Limits.prod.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y (CategoryTheory.Limits.hasLimitOfHasLimitsOfShape.{0, 0, u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} (CategoryTheory.Discrete.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.discreteCategory.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.Limits.hasLimitsOfShapeOfHasLimits.{0, 0, u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} (CategoryTheory.Discrete.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.discreteCategory.{0} CategoryTheory.Limits.WalkingPair) TopCat.topCat_hasLimitsOfSize.{0, u1}) (CategoryTheory.Limits.pair.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y))) (TopCat.of.{u1} (Prod.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y)) (instTopologicalSpaceProd.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} X) (TopCat.topologicalSpace_coe.{u1} Y))) (TopCat.prodIsoProd.{u1} X Y)) (CategoryTheory.Limits.prod.fst.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y (CategoryTheory.Limits.hasLimitOfHasLimitsOfShape.{0, 0, u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} (CategoryTheory.Discrete.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.discreteCategory.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.Limits.hasLimitsOfShapeOfHasLimits.{0, 0, u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} (CategoryTheory.Discrete.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.discreteCategory.{0} CategoryTheory.Limits.WalkingPair) TopCat.topCat_hasLimitsOfSize.{0, u1}) (CategoryTheory.Limits.pair.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y)))) (TopCat.prodFst.{u1} X Y)
 Case conversion may be inaccurate. Consider using '#align Top.prod_iso_prod_inv_fst TopCat.prodIsoProd_inv_fstₓ'. -/
-@[simp, reassoc.1, elementwise]
+@[simp, reassoc, elementwise]
 theorem prodIsoProd_inv_fst (X Y : TopCat.{u}) :
     (prodIsoProd X Y).inv ≫ Limits.prod.fst = prodFst := by simp [iso.inv_comp_eq]
 #align Top.prod_iso_prod_inv_fst TopCat.prodIsoProd_inv_fst
@@ -356,7 +356,7 @@ lean 3 declaration is
 but is expected to have type
   forall (X : TopCat.{u1}) (Y : TopCat.{u1}), Eq.{succ u1} (Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) (TopCat.of.{u1} (Prod.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y)) (instTopologicalSpaceProd.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} X) (TopCat.topologicalSpace_coe.{u1} Y))) Y) (CategoryTheory.CategoryStruct.comp.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1}) (TopCat.of.{u1} (Prod.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y)) (instTopologicalSpaceProd.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} X) (TopCat.topologicalSpace_coe.{u1} Y))) (CategoryTheory.Limits.prod.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y (CategoryTheory.Limits.hasLimitOfHasLimitsOfShape.{0, 0, u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} (CategoryTheory.Discrete.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.discreteCategory.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.Limits.hasLimitsOfShapeOfHasLimits.{0, 0, u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} (CategoryTheory.Discrete.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.discreteCategory.{0} CategoryTheory.Limits.WalkingPair) TopCat.topCat_hasLimitsOfSize.{0, u1}) (CategoryTheory.Limits.pair.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y))) Y (CategoryTheory.Iso.inv.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} (CategoryTheory.Limits.prod.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y (CategoryTheory.Limits.hasLimitOfHasLimitsOfShape.{0, 0, u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} (CategoryTheory.Discrete.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.discreteCategory.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.Limits.hasLimitsOfShapeOfHasLimits.{0, 0, u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} (CategoryTheory.Discrete.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.discreteCategory.{0} CategoryTheory.Limits.WalkingPair) TopCat.topCat_hasLimitsOfSize.{0, u1}) (CategoryTheory.Limits.pair.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y))) (TopCat.of.{u1} (Prod.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y)) (instTopologicalSpaceProd.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} Y) (TopCat.topologicalSpace_coe.{u1} X) (TopCat.topologicalSpace_coe.{u1} Y))) (TopCat.prodIsoProd.{u1} X Y)) (CategoryTheory.Limits.prod.snd.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y (CategoryTheory.Limits.hasLimitOfHasLimitsOfShape.{0, 0, u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} (CategoryTheory.Discrete.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.discreteCategory.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.Limits.hasLimitsOfShapeOfHasLimits.{0, 0, u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} (CategoryTheory.Discrete.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.discreteCategory.{0} CategoryTheory.Limits.WalkingPair) TopCat.topCat_hasLimitsOfSize.{0, u1}) (CategoryTheory.Limits.pair.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y)))) (TopCat.prodSnd.{u1} X Y)
 Case conversion may be inaccurate. Consider using '#align Top.prod_iso_prod_inv_snd TopCat.prodIsoProd_inv_sndₓ'. -/
-@[simp, reassoc.1, elementwise]
+@[simp, reassoc, elementwise]
 theorem prodIsoProd_inv_snd (X Y : TopCat.{u}) :
     (prodIsoProd X Y).inv ≫ Limits.prod.snd = prodSnd := by simp [iso.inv_comp_eq]
 #align Top.prod_iso_prod_inv_snd TopCat.prodIsoProd_inv_snd

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

@@ -222,9 +222,9 @@ theorem sigmaIsoSigma_inv_apply {ι : Type v} (α : ι → TopCat.{max v u}) (i
 
 /- warning: Top.induced_of_is_limit -> TopCat.induced_of_isLimit is a dubious translation:
 lean 3 declaration is
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(TopologicalSpace.completeLattice.{max u2 u1} (coeSort.{succ (succ (max u2 u1)), succ (succ (max u2 u1))} TopCat.{max u2 u1} Type.{max u2 u1} TopCat.hasCoeToSort.{max u2 u1} (CategoryTheory.Limits.Cone.pt.{u2, max u2 u1, u2, succ (max u2 u1)} J _inst_1 TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} F C))))) J (fun (j : J) => TopologicalSpace.induced.{max u2 u1, max u2 u1} (coeSort.{succ (succ (max u2 u1)), succ (succ (max u2 u1))} TopCat.{max u2 u1} Type.{max u2 u1} TopCat.hasCoeToSort.{max u2 u1} (CategoryTheory.Limits.Cone.pt.{u2, max u2 u1, u2, succ (max u2 u1)} J _inst_1 TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} F C)) (coeSort.{succ (succ (max u2 u1)), succ (succ (max u2 u1))} TopCat.{max u2 u1} Type.{max u2 u1} TopCat.hasCoeToSort.{max u2 u1} (CategoryTheory.Functor.obj.{u2, max u2 u1, u2, succ (max u2 u1)} J _inst_1 TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} F j)) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (Quiver.Hom.{succ (max u2 u1), succ (max u2 u1)} 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TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} F C)) j) (CategoryTheory.Functor.obj.{u2, max u2 u1, u2, succ (max u2 u1)} J _inst_1 TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} F j)) (fun (_x : ContinuousMap.{max u2 u1, max u2 u1} (coeSort.{succ (succ (max u2 u1)), succ (succ (max u2 u1))} (CategoryTheory.Bundled.{max u2 u1, max u2 u1} TopologicalSpace.{max u2 u1}) Type.{max u2 u1} (CategoryTheory.Bundled.hasCoeToSort.{max u2 u1, max u2 u1} TopologicalSpace.{max u2 u1}) (CategoryTheory.Functor.obj.{u2, max u2 u1, u2, succ (max u2 u1)} J _inst_1 TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} (CategoryTheory.Functor.obj.{max u2 u1, max u2 u1, succ (max u2 u1), max u2 (max u2 u1) u2 (succ (max u2 u1))} TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} (CategoryTheory.Functor.{u2, max u2 u1, u2, succ (max u2 u1)} J _inst_1 TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1}) (CategoryTheory.Functor.category.{u2, max u2 u1, u2, succ (max u2 u1)} J _inst_1 TopCat.{max u2 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TopCat.largeCategory.{max u2 u1} (CategoryTheory.Functor.obj.{max u2 u1, max u2 u1, succ (max u2 u1), max u2 (max u2 u1) u2 (succ (max u2 u1))} TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} (CategoryTheory.Functor.{u2, max u2 u1, u2, succ (max u2 u1)} J _inst_1 TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1}) (CategoryTheory.Functor.category.{u2, max u2 u1, u2, succ (max u2 u1)} J _inst_1 TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1}) (CategoryTheory.Functor.const.{u2, max u2 u1, u2, succ (max u2 u1)} J _inst_1 TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1}) (CategoryTheory.Limits.Cone.pt.{u2, max u2 u1, u2, succ (max u2 u1)} J _inst_1 TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} F C)) j)) (CategoryTheory.Bundled.str.{max u2 u1, max u2 u1} TopologicalSpace.{max u2 u1} (CategoryTheory.Functor.obj.{u2, max u2 u1, u2, succ (max u2 u1)} J _inst_1 TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} F j))) (CategoryTheory.NatTrans.app.{u2, max u2 u1, u2, succ (max u2 u1)} J _inst_1 TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} (CategoryTheory.Functor.obj.{max u2 u1, max u2 u1, succ (max u2 u1), max u2 (max u2 u1) u2 (succ (max u2 u1))} TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} (CategoryTheory.Functor.{u2, max u2 u1, u2, succ (max u2 u1)} J _inst_1 TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1}) (CategoryTheory.Functor.category.{u2, max u2 u1, u2, succ (max u2 u1)} J _inst_1 TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1}) (CategoryTheory.Functor.const.{u2, max u2 u1, u2, succ (max u2 u1)} J _inst_1 TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1}) (CategoryTheory.Limits.Cone.pt.{u2, max u2 u1, u2, succ (max u2 u1)} J _inst_1 TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} F C)) F (CategoryTheory.Limits.Cone.π.{u2, max u2 u1, u2, succ (max u2 u1)} J _inst_1 TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} F C) j)) (TopCat.topologicalSpace.{max u2 u1} (CategoryTheory.Functor.obj.{u2, max u2 u1, u2, succ (max u2 u1)} J _inst_1 TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} F j)))))
+  forall {J : Type.{u2}} [_inst_1 : CategoryTheory.SmallCategory.{u2} J] {F : CategoryTheory.Functor.{u2, max u2 u1, u2, succ (max u2 u1)} J _inst_1 TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1}} (C : CategoryTheory.Limits.Cone.{u2, max u2 u1, u2, succ (max u2 u1)} J _inst_1 TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} F), (CategoryTheory.Limits.IsLimit.{u2, max u2 u1, u2, succ (max u2 u1)} J _inst_1 TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} F C) -> (Eq.{succ (max u2 u1)} (TopologicalSpace.{max u2 u1} (coeSort.{succ (succ (max u2 u1)), succ (succ (max u2 u1))} TopCat.{max u2 u1} Type.{max u2 u1} TopCat.hasCoeToSort.{max u2 u1} (CategoryTheory.Limits.Cone.pt.{u2, max u2 u1, u2, succ (max u2 u1)} J _inst_1 TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} F C))) (TopCat.topologicalSpace.{max u2 u1} (CategoryTheory.Limits.Cone.pt.{u2, max u2 u1, u2, succ (max u2 u1)} J _inst_1 TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} F C)) (iInf.{max u2 u1, succ u2} (TopologicalSpace.{max u2 u1} (coeSort.{succ (succ (max u2 u1)), succ (succ (max u2 u1))} TopCat.{max u2 u1} Type.{max u2 u1} TopCat.hasCoeToSort.{max u2 u1} (CategoryTheory.Limits.Cone.pt.{u2, max u2 u1, u2, succ (max u2 u1)} J _inst_1 TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} F C))) (ConditionallyCompleteLattice.toHasInf.{max u2 u1} (TopologicalSpace.{max u2 u1} (coeSort.{succ (succ (max u2 u1)), succ (succ (max u2 u1))} TopCat.{max u2 u1} Type.{max u2 u1} TopCat.hasCoeToSort.{max u2 u1} (CategoryTheory.Limits.Cone.pt.{u2, max u2 u1, u2, succ (max u2 u1)} J _inst_1 TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} F C))) (CompleteLattice.toConditionallyCompleteLattice.{max u2 u1} (TopologicalSpace.{max u2 u1} (coeSort.{succ (succ (max u2 u1)), succ (succ (max u2 u1))} TopCat.{max u2 u1} Type.{max u2 u1} TopCat.hasCoeToSort.{max u2 u1} (CategoryTheory.Limits.Cone.pt.{u2, max u2 u1, u2, succ (max u2 u1)} J _inst_1 TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} F C))) (TopologicalSpace.completeLattice.{max u2 u1} (coeSort.{succ (succ (max u2 u1)), succ (succ (max u2 u1))} TopCat.{max u2 u1} Type.{max u2 u1} TopCat.hasCoeToSort.{max u2 u1} (CategoryTheory.Limits.Cone.pt.{u2, max u2 u1, u2, succ (max u2 u1)} J _inst_1 TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} F C))))) J (fun (j : J) => TopologicalSpace.induced.{max u2 u1, max u2 u1} (coeSort.{succ (succ (max u2 u1)), succ (succ (max u2 u1))} TopCat.{max u2 u1} Type.{max u2 u1} TopCat.hasCoeToSort.{max u2 u1} (CategoryTheory.Limits.Cone.pt.{u2, max u2 u1, u2, succ (max u2 u1)} J _inst_1 TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} F C)) (coeSort.{succ (succ (max u2 u1)), succ (succ (max u2 u1))} TopCat.{max u2 u1} Type.{max u2 u1} TopCat.hasCoeToSort.{max u2 u1} (CategoryTheory.Functor.obj.{u2, max u2 u1, u2, succ (max u2 u1)} J _inst_1 TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} F j)) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (Quiver.Hom.{succ (max u2 u1), succ (max u2 u1)} 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 but is expected to have type
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+  forall {J : Type.{u1}} [_inst_1 : CategoryTheory.SmallCategory.{u1} J] {F : CategoryTheory.Functor.{u1, max u2 u1, u1, max (succ u2) (succ u1)} J _inst_1 TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1}} (C : CategoryTheory.Limits.Cone.{u1, max u2 u1, u1, max (succ u2) (succ u1)} J _inst_1 TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} F), (CategoryTheory.Limits.IsLimit.{u1, max u2 u1, u1, max (succ u2) (succ u1)} J _inst_1 TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} F C) -> (Eq.{max (succ u2) (succ u1)} (TopologicalSpace.{max u1 u2} (CategoryTheory.Bundled.α.{max u2 u1, max u2 u1} TopologicalSpace.{max u1 u2} (CategoryTheory.Limits.Cone.pt.{u1, max u2 u1, u1, max (succ u2) (succ u1)} J _inst_1 TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} F C))) (CategoryTheory.Bundled.str.{max u2 u1, max u2 u1} TopologicalSpace.{max u1 u2} (CategoryTheory.Limits.Cone.pt.{u1, max u2 u1, u1, max (succ u2) (succ u1)} J _inst_1 TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} F C)) (iInf.{max u2 u1, succ u1} (TopologicalSpace.{max u2 u1} (CategoryTheory.Bundled.α.{max u2 u1, max u2 u1} TopologicalSpace.{max u1 u2} (CategoryTheory.Limits.Cone.pt.{u1, max u2 u1, u1, max (succ u2) (succ u1)} J _inst_1 TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} F C))) (ConditionallyCompleteLattice.toInfSet.{max u2 u1} (TopologicalSpace.{max u2 u1} (CategoryTheory.Bundled.α.{max u2 u1, max u2 u1} TopologicalSpace.{max u1 u2} (CategoryTheory.Limits.Cone.pt.{u1, max u2 u1, u1, max (succ u2) (succ u1)} J _inst_1 TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} F C))) (CompleteLattice.toConditionallyCompleteLattice.{max u2 u1} (TopologicalSpace.{max u2 u1} (CategoryTheory.Bundled.α.{max u2 u1, max u2 u1} TopologicalSpace.{max u1 u2} (CategoryTheory.Limits.Cone.pt.{u1, max u2 u1, u1, max (succ u2) (succ u1)} J _inst_1 TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} F C))) (TopologicalSpace.instCompleteLatticeTopologicalSpace.{max u2 u1} (CategoryTheory.Bundled.α.{max u2 u1, max u2 u1} TopologicalSpace.{max u1 u2} (CategoryTheory.Limits.Cone.pt.{u1, max u2 u1, u1, max (succ u2) (succ u1)} J _inst_1 TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} F C))))) J (fun (j : J) => TopologicalSpace.induced.{max u2 u1, max u2 u1} (CategoryTheory.Bundled.α.{max u2 u1, max u2 u1} TopologicalSpace.{max u1 u2} (CategoryTheory.Limits.Cone.pt.{u1, max u2 u1, u1, max (succ u2) (succ u1)} J _inst_1 TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} F C)) (CategoryTheory.Bundled.α.{max u2 u1, max u2 u1} TopologicalSpace.{max u1 u2} (Prefunctor.obj.{succ u1, max (succ u2) (succ u1), u1, max (succ u2) (succ u1)} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_1)) TopCatMax.{u1, u2} (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max (succ u2) (succ u1)} TopCatMax.{u1, u2} 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(CategoryTheory.Functor.toPrefunctor.{u1, max u2 u1, u1, max (succ u2) (succ u1)} J _inst_1 TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} F) j)))))
 Case conversion may be inaccurate. Consider using '#align Top.induced_of_is_limit TopCat.induced_of_isLimitₓ'. -/
 theorem induced_of_isLimit {F : J ⥤ TopCat.{max v u}} (C : Cone F) (hC : IsLimit C) :
     C.pt.TopologicalSpace = ⨅ j, (F.obj j).TopologicalSpace.induced (C.π.app j) :=
@@ -232,14 +232,14 @@ theorem induced_of_isLimit {F : J ⥤ TopCat.{max v u}} (C : Cone F) (hC : IsLim
   let homeo := homeo_of_iso (hC.cone_point_unique_up_to_iso (limit_cone_infi_is_limit F))
   refine' homeo.inducing.induced.trans _
   change induced homeo (⨅ j : J, _) = _
-  simpa [induced_infᵢ, induced_compose]
+  simpa [induced_iInf, induced_compose]
 #align Top.induced_of_is_limit TopCat.induced_of_isLimit
 
 /- warning: Top.limit_topology -> TopCat.limit_topology is a dubious translation:
 lean 3 declaration is
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TopCat.largeCategory.{max u2 u1} J _inst_1 TopCat.topCat_hasLimitsOfSize.{u1, u2}) F)))))) J (fun (j : J) => TopologicalSpace.induced.{max u2 u1, max u2 u1} (coeSort.{succ (succ (max u2 u1)), succ (succ (max u2 u1))} TopCat.{max u2 u1} Type.{max u2 u1} TopCat.hasCoeToSort.{max u2 u1} (CategoryTheory.Limits.limit.{u2, u2, max u2 u1, succ (max u2 u1)} J _inst_1 TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} F (CategoryTheory.Limits.hasLimitOfHasLimitsOfShape.{u2, u2, max u2 u1, succ (max u2 u1)} TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} J _inst_1 (CategoryTheory.Limits.hasLimitsOfShapeOfHasLimits.{u2, u2, max u2 u1, succ (max u2 u1)} TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} J _inst_1 TopCat.topCat_hasLimitsOfSize.{u1, u2}) F))) (coeSort.{succ (succ (max u2 u1)), succ (succ (max u2 u1))} TopCat.{max u2 u1} Type.{max u2 u1} TopCat.hasCoeToSort.{max u2 u1} (CategoryTheory.Functor.obj.{u2, max u2 u1, u2, succ (max u2 u1)} J _inst_1 TopCat.{max u2 u1} 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(CategoryTheory.Bundled.hasCoeToSort.{max u2 u1, max u2 u1} TopologicalSpace.{max u2 u1}) (CategoryTheory.Functor.obj.{u2, max u2 u1, u2, succ (max u2 u1)} J _inst_1 TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} F j)) (CategoryTheory.Bundled.str.{max u2 u1, max u2 u1} TopologicalSpace.{max u2 u1} (CategoryTheory.Limits.limit.{u2, u2, max u2 u1, succ (max u2 u1)} J _inst_1 TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} F (CategoryTheory.Limits.hasLimitOfHasLimitsOfShape.{u2, u2, max u2 u1, succ (max u2 u1)} TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} J _inst_1 (CategoryTheory.Limits.hasLimitsOfShapeOfHasLimits.{u2, u2, max u2 u1, succ (max u2 u1)} TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} J _inst_1 TopCat.topCat_hasLimitsOfSize.{u1, u2}) F))) (CategoryTheory.Bundled.str.{max u2 u1, max u2 u1} TopologicalSpace.{max u2 u1} (CategoryTheory.Functor.obj.{u2, max u2 u1, u2, succ (max u2 u1)} J _inst_1 TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} F j))) (CategoryTheory.Limits.limit.π.{u2, u2, max u2 u1, succ (max u2 u1)} J _inst_1 TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} F (CategoryTheory.Limits.hasLimitOfHasLimitsOfShape.{u2, u2, max u2 u1, succ (max u2 u1)} TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} J _inst_1 (CategoryTheory.Limits.hasLimitsOfShapeOfHasLimits.{u2, u2, max u2 u1, succ (max u2 u1)} TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} J _inst_1 TopCat.topCat_hasLimitsOfSize.{u1, u2}) F) j)) (TopCat.topologicalSpace.{max u2 u1} (CategoryTheory.Functor.obj.{u2, max u2 u1, u2, succ (max u2 u1)} J _inst_1 TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} F j))))
+  forall {J : Type.{u2}} [_inst_1 : CategoryTheory.SmallCategory.{u2} J] (F : CategoryTheory.Functor.{u2, max u2 u1, u2, succ (max u2 u1)} J _inst_1 TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1}), Eq.{succ (max u2 u1)} (TopologicalSpace.{max u2 u1} (coeSort.{succ (succ (max u2 u1)), succ (succ (max u2 u1))} TopCat.{max u2 u1} Type.{max u2 u1} TopCat.hasCoeToSort.{max u2 u1} (CategoryTheory.Limits.limit.{u2, u2, max u2 u1, succ (max u2 u1)} J _inst_1 TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} F (CategoryTheory.Limits.hasLimitOfHasLimitsOfShape.{u2, u2, max u2 u1, succ (max u2 u1)} TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} J _inst_1 (CategoryTheory.Limits.hasLimitsOfShapeOfHasLimits.{u2, u2, max u2 u1, succ (max u2 u1)} TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} J _inst_1 TopCat.topCat_hasLimitsOfSize.{u1, u2}) F)))) (TopCat.topologicalSpace.{max u2 u1} (CategoryTheory.Limits.limit.{u2, u2, max u2 u1, succ (max u2 u1)} J _inst_1 TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} F (CategoryTheory.Limits.hasLimitOfHasLimitsOfShape.{u2, u2, max u2 u1, succ (max u2 u1)} TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} J _inst_1 (CategoryTheory.Limits.hasLimitsOfShapeOfHasLimits.{u2, u2, max u2 u1, succ (max u2 u1)} TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} J _inst_1 TopCat.topCat_hasLimitsOfSize.{u1, u2}) F))) (iInf.{max u2 u1, succ u2} (TopologicalSpace.{max u2 u1} (coeSort.{succ (succ (max u2 u1)), succ (succ (max u2 u1))} TopCat.{max u2 u1} Type.{max u2 u1} TopCat.hasCoeToSort.{max u2 u1} (CategoryTheory.Limits.limit.{u2, u2, max u2 u1, succ (max u2 u1)} J _inst_1 TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} F (CategoryTheory.Limits.hasLimitOfHasLimitsOfShape.{u2, u2, max u2 u1, succ (max u2 u1)} TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} J _inst_1 (CategoryTheory.Limits.hasLimitsOfShapeOfHasLimits.{u2, u2, max u2 u1, succ (max u2 u1)} TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} J _inst_1 TopCat.topCat_hasLimitsOfSize.{u1, u2}) F)))) (ConditionallyCompleteLattice.toHasInf.{max u2 u1} (TopologicalSpace.{max u2 u1} (coeSort.{succ (succ (max u2 u1)), succ (succ (max u2 u1))} TopCat.{max u2 u1} Type.{max u2 u1} TopCat.hasCoeToSort.{max u2 u1} (CategoryTheory.Limits.limit.{u2, u2, max u2 u1, succ (max u2 u1)} J _inst_1 TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} F (CategoryTheory.Limits.hasLimitOfHasLimitsOfShape.{u2, u2, max u2 u1, succ (max u2 u1)} TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} J _inst_1 (CategoryTheory.Limits.hasLimitsOfShapeOfHasLimits.{u2, u2, max u2 u1, succ (max u2 u1)} TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} J _inst_1 TopCat.topCat_hasLimitsOfSize.{u1, u2}) F)))) (CompleteLattice.toConditionallyCompleteLattice.{max u2 u1} (TopologicalSpace.{max u2 u1} (coeSort.{succ (succ (max u2 u1)), succ (succ (max u2 u1))} TopCat.{max u2 u1} Type.{max u2 u1} TopCat.hasCoeToSort.{max u2 u1} (CategoryTheory.Limits.limit.{u2, u2, max u2 u1, succ (max u2 u1)} J _inst_1 TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} F (CategoryTheory.Limits.hasLimitOfHasLimitsOfShape.{u2, u2, max u2 u1, succ (max u2 u1)} TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} J _inst_1 (CategoryTheory.Limits.hasLimitsOfShapeOfHasLimits.{u2, u2, max u2 u1, succ (max u2 u1)} TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} J _inst_1 TopCat.topCat_hasLimitsOfSize.{u1, u2}) F)))) (TopologicalSpace.completeLattice.{max u2 u1} (coeSort.{succ (succ (max u2 u1)), succ (succ (max u2 u1))} TopCat.{max u2 u1} Type.{max u2 u1} TopCat.hasCoeToSort.{max u2 u1} (CategoryTheory.Limits.limit.{u2, u2, max u2 u1, succ (max u2 u1)} J _inst_1 TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} F (CategoryTheory.Limits.hasLimitOfHasLimitsOfShape.{u2, u2, max u2 u1, succ (max u2 u1)} TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} J _inst_1 (CategoryTheory.Limits.hasLimitsOfShapeOfHasLimits.{u2, u2, max u2 u1, succ (max u2 u1)} TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} J _inst_1 TopCat.topCat_hasLimitsOfSize.{u1, u2}) F)))))) J (fun (j : J) => TopologicalSpace.induced.{max u2 u1, max u2 u1} (coeSort.{succ (succ (max u2 u1)), succ (succ (max u2 u1))} TopCat.{max u2 u1} Type.{max u2 u1} TopCat.hasCoeToSort.{max u2 u1} (CategoryTheory.Limits.limit.{u2, u2, max u2 u1, succ (max u2 u1)} J _inst_1 TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} F (CategoryTheory.Limits.hasLimitOfHasLimitsOfShape.{u2, u2, max u2 u1, succ (max u2 u1)} TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} J _inst_1 (CategoryTheory.Limits.hasLimitsOfShapeOfHasLimits.{u2, u2, max u2 u1, succ (max u2 u1)} TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} J _inst_1 TopCat.topCat_hasLimitsOfSize.{u1, u2}) F))) (coeSort.{succ (succ (max u2 u1)), succ (succ (max u2 u1))} TopCat.{max u2 u1} Type.{max u2 u1} TopCat.hasCoeToSort.{max u2 u1} (CategoryTheory.Functor.obj.{u2, max u2 u1, u2, succ (max u2 u1)} J _inst_1 TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} F j)) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (Quiver.Hom.{succ (max u2 u1), succ (max u2 u1)} TopCat.{max u2 u1} (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, succ (max u2 u1)} TopCat.{max u2 u1} (CategoryTheory.Category.toCategoryStruct.{max u2 u1, succ (max u2 u1)} TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1})) (CategoryTheory.Limits.limit.{u2, u2, max u2 u1, succ (max u2 u1)} J _inst_1 TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} F (CategoryTheory.Limits.hasLimitOfHasLimitsOfShape.{u2, u2, max u2 u1, succ (max u2 u1)} TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} J _inst_1 (CategoryTheory.Limits.hasLimitsOfShapeOfHasLimits.{u2, u2, max u2 u1, succ (max u2 u1)} TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} J _inst_1 TopCat.topCat_hasLimitsOfSize.{u1, u2}) F)) (CategoryTheory.Functor.obj.{u2, max u2 u1, u2, succ (max u2 u1)} J _inst_1 TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} F j)) (fun (_x : 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 but is expected to have type
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+  forall {J : Type.{u1}} [_inst_1 : CategoryTheory.SmallCategory.{u1} J] (F : CategoryTheory.Functor.{u1, max u2 u1, u1, max (succ u2) (succ u1)} J _inst_1 TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1}), Eq.{max (succ u2) (succ u1)} (TopologicalSpace.{max u1 u2} (CategoryTheory.Bundled.α.{max u2 u1, max u2 u1} TopologicalSpace.{max u1 u2} (CategoryTheory.Limits.limit.{u1, u1, max u2 u1, max (succ u2) (succ u1)} J _inst_1 TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} F (CategoryTheory.Limits.hasLimitOfHasLimitsOfShape.{u1, u1, max u2 u1, max (succ u2) (succ u1)} TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} J _inst_1 (CategoryTheory.Limits.hasLimitsOfShapeOfHasLimits.{u1, u1, max u2 u1, max (succ u2) (succ u1)} TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} J _inst_1 TopCat.topCat_hasLimitsOfSize.{u1, u2}) F)))) (CategoryTheory.Bundled.str.{max u2 u1, max u2 u1} TopologicalSpace.{max u1 u2} (CategoryTheory.Limits.limit.{u1, u1, max u2 u1, max (succ 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_inst_1 TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} F (CategoryTheory.Limits.hasLimitOfHasLimitsOfShape.{u1, u1, max u2 u1, max (succ u2) (succ u1)} TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} J _inst_1 (CategoryTheory.Limits.hasLimitsOfShapeOfHasLimits.{u1, u1, max u2 u1, max (succ u2) (succ u1)} TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} J _inst_1 TopCat.topCat_hasLimitsOfSize.{u1, u2}) F)))) (CompleteLattice.toConditionallyCompleteLattice.{max u2 u1} (TopologicalSpace.{max u2 u1} (Prefunctor.obj.{succ (max u2 u1), succ (max u2 u1), succ (max u2 u1), succ (max u2 u1)} TopCat.{max u2 u1} (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, succ (max u2 u1)} TopCat.{max u2 u1} (CategoryTheory.Category.toCategoryStruct.{max u2 u1, succ (max u2 u1)} TopCat.{max u2 u1} instTopCatLargeCategory.{max u2 u1})) Type.{max u2 u1} (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, succ (max u2 u1)} Type.{max u2 u1} (CategoryTheory.Category.toCategoryStruct.{max u2 u1, succ (max u2 u1)} Type.{max u2 u1} CategoryTheory.types.{max u2 u1})) (CategoryTheory.Functor.toPrefunctor.{max u2 u1, max u2 u1, succ (max u2 u1), succ (max u2 u1)} TopCat.{max u2 u1} instTopCatLargeCategory.{max u2 u1} Type.{max u2 u1} CategoryTheory.types.{max u2 u1} (CategoryTheory.forget.{succ (max u2 u1), max u2 u1, max u2 u1} TopCat.{max u2 u1} instTopCatLargeCategory.{max u2 u1} TopCat.concreteCategory.{max u2 u1})) (CategoryTheory.Limits.limit.{u1, u1, max u2 u1, max (succ u2) (succ u1)} J _inst_1 TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} F (CategoryTheory.Limits.hasLimitOfHasLimitsOfShape.{u1, u1, max u2 u1, max (succ u2) (succ u1)} TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} J _inst_1 (CategoryTheory.Limits.hasLimitsOfShapeOfHasLimits.{u1, u1, max u2 u1, max (succ u2) (succ u1)} TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} J _inst_1 TopCat.topCat_hasLimitsOfSize.{u1, u2}) F)))) (TopologicalSpace.instCompleteLatticeTopologicalSpace.{max u2 u1} (Prefunctor.obj.{succ (max u2 u1), succ (max u2 u1), succ (max u2 u1), succ (max u2 u1)} TopCat.{max u2 u1} (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, succ (max u2 u1)} TopCat.{max u2 u1} (CategoryTheory.Category.toCategoryStruct.{max u2 u1, succ (max u2 u1)} TopCat.{max u2 u1} instTopCatLargeCategory.{max u2 u1})) Type.{max u2 u1} (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, succ (max u2 u1)} Type.{max u2 u1} (CategoryTheory.Category.toCategoryStruct.{max u2 u1, succ (max u2 u1)} Type.{max u2 u1} CategoryTheory.types.{max u2 u1})) (CategoryTheory.Functor.toPrefunctor.{max u2 u1, max u2 u1, succ (max u2 u1), succ (max u2 u1)} TopCat.{max u2 u1} instTopCatLargeCategory.{max u2 u1} Type.{max u2 u1} CategoryTheory.types.{max u2 u1} (CategoryTheory.forget.{succ (max u2 u1), max u2 u1, max u2 u1} TopCat.{max u2 u1} instTopCatLargeCategory.{max u2 u1} TopCat.concreteCategory.{max u2 u1})) (CategoryTheory.Limits.limit.{u1, u1, max u2 u1, max (succ u2) (succ u1)} J _inst_1 TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} F (CategoryTheory.Limits.hasLimitOfHasLimitsOfShape.{u1, u1, max u2 u1, max (succ u2) (succ u1)} TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} J _inst_1 (CategoryTheory.Limits.hasLimitsOfShapeOfHasLimits.{u1, u1, max u2 u1, max (succ u2) (succ u1)} TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} J _inst_1 TopCat.topCat_hasLimitsOfSize.{u1, u2}) F)))))) J (fun (j : J) => TopologicalSpace.induced.{max u2 u1, max u2 u1} (Prefunctor.obj.{succ (max u2 u1), succ (max u2 u1), succ (max u2 u1), succ (max u2 u1)} TopCat.{max u2 u1} (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, succ (max u2 u1)} TopCat.{max u2 u1} (CategoryTheory.Category.toCategoryStruct.{max u2 u1, succ (max u2 u1)} TopCat.{max u2 u1} instTopCatLargeCategory.{max u2 u1})) Type.{max u2 u1} (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, succ (max u2 u1)} Type.{max u2 u1} (CategoryTheory.Category.toCategoryStruct.{max u2 u1, succ (max u2 u1)} Type.{max u2 u1} CategoryTheory.types.{max u2 u1})) (CategoryTheory.Functor.toPrefunctor.{max u2 u1, max u2 u1, succ (max u2 u1), succ (max u2 u1)} TopCat.{max u2 u1} instTopCatLargeCategory.{max u2 u1} Type.{max u2 u1} CategoryTheory.types.{max u2 u1} (CategoryTheory.forget.{succ (max u2 u1), max u2 u1, max u2 u1} TopCat.{max u2 u1} instTopCatLargeCategory.{max u2 u1} TopCat.concreteCategory.{max u2 u1})) (CategoryTheory.Limits.limit.{u1, u1, max u2 u1, max (succ u2) (succ u1)} J _inst_1 TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} F (CategoryTheory.Limits.hasLimitOfHasLimitsOfShape.{u1, u1, max u2 u1, max (succ u2) (succ u1)} TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} J _inst_1 (CategoryTheory.Limits.hasLimitsOfShapeOfHasLimits.{u1, u1, max u2 u1, max (succ u2) (succ u1)} TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} J _inst_1 TopCat.topCat_hasLimitsOfSize.{u1, u2}) F))) (Prefunctor.obj.{succ (max u2 u1), succ (max u2 u1), succ (max u2 u1), succ (max u2 u1)} TopCat.{max u2 u1} (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, succ (max u2 u1)} TopCat.{max u2 u1} (CategoryTheory.Category.toCategoryStruct.{max u2 u1, succ (max u2 u1)} TopCat.{max u2 u1} instTopCatLargeCategory.{max u2 u1})) Type.{max u2 u1} (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, succ (max u2 u1)} Type.{max u2 u1} (CategoryTheory.Category.toCategoryStruct.{max u2 u1, succ (max u2 u1)} Type.{max u2 u1} CategoryTheory.types.{max u2 u1})) (CategoryTheory.Functor.toPrefunctor.{max u2 u1, max u2 u1, succ (max u2 u1), succ (max u2 u1)} TopCat.{max u2 u1} instTopCatLargeCategory.{max u2 u1} Type.{max u2 u1} CategoryTheory.types.{max u2 u1} (CategoryTheory.forget.{succ (max u2 u1), max u2 u1, max u2 u1} TopCat.{max u2 u1} instTopCatLargeCategory.{max u2 u1} TopCat.concreteCategory.{max u2 u1})) (Prefunctor.obj.{succ u1, succ (max u2 u1), u1, max (succ u2) (succ u1)} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_1)) TopCatMax.{u1, u2} (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max (succ u2) (succ u1)} TopCatMax.{u1, u2} (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max (succ u2) (succ u1)} TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1})) (CategoryTheory.Functor.toPrefunctor.{u1, max u2 u1, u1, max (succ u2) (succ u1)} J _inst_1 TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} F) j)) (Prefunctor.map.{succ (max u2 u1), succ (max u2 u1), succ (max u2 u1), succ (max u2 u1)} TopCat.{max u2 u1} (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, succ (max u2 u1)} TopCat.{max u2 u1} (CategoryTheory.Category.toCategoryStruct.{max u2 u1, succ (max u2 u1)} TopCat.{max u2 u1} instTopCatLargeCategory.{max u2 u1})) Type.{max u2 u1} (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, succ (max u2 u1)} Type.{max u2 u1} (CategoryTheory.Category.toCategoryStruct.{max u2 u1, succ (max u2 u1)} Type.{max u2 u1} CategoryTheory.types.{max u2 u1})) (CategoryTheory.Functor.toPrefunctor.{max u2 u1, max u2 u1, succ (max u2 u1), succ (max u2 u1)} TopCat.{max u2 u1} instTopCatLargeCategory.{max u2 u1} Type.{max u2 u1} CategoryTheory.types.{max u2 u1} (CategoryTheory.forget.{succ (max u2 u1), max u2 u1, max u2 u1} TopCat.{max u2 u1} instTopCatLargeCategory.{max u2 u1} TopCat.concreteCategory.{max u2 u1})) (CategoryTheory.Limits.limit.{u1, u1, max u2 u1, max (succ u2) (succ u1)} J _inst_1 TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} F (CategoryTheory.Limits.hasLimitOfHasLimitsOfShape.{u1, u1, max u2 u1, max (succ u2) (succ u1)} TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} J _inst_1 (CategoryTheory.Limits.hasLimitsOfShapeOfHasLimits.{u1, u1, max u2 u1, max (succ u2) (succ u1)} TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} J _inst_1 TopCat.topCat_hasLimitsOfSize.{u1, u2}) F)) (Prefunctor.obj.{succ u1, succ (max u2 u1), u1, max (succ u2) (succ u1)} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_1)) TopCatMax.{u1, u2} (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max (succ u2) (succ u1)} TopCatMax.{u1, u2} (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max (succ u2) (succ u1)} TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1})) (CategoryTheory.Functor.toPrefunctor.{u1, max u2 u1, u1, max (succ u2) (succ u1)} J _inst_1 TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} F) j) (CategoryTheory.Limits.limit.π.{u1, u1, max u2 u1, max (succ u2) (succ u1)} J _inst_1 TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} F (CategoryTheory.Limits.hasLimitOfHasLimitsOfShape.{u1, u1, max u2 u1, max (succ u2) (succ u1)} TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} J _inst_1 (CategoryTheory.Limits.hasLimitsOfShapeOfHasLimits.{u1, u1, max u2 u1, max (succ u2) (succ u1)} TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} J _inst_1 TopCat.topCat_hasLimitsOfSize.{u1, u2}) F) j)) (CategoryTheory.Bundled.str.{max u2 u1, max u2 u1} TopologicalSpace.{max u1 u2} (Prefunctor.obj.{succ u1, max (succ u2) (succ u1), u1, max (succ u2) (succ u1)} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_1)) TopCatMax.{u1, u2} (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max (succ u2) (succ u1)} TopCatMax.{u1, u2} (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max (succ u2) (succ u1)} TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1})) (CategoryTheory.Functor.toPrefunctor.{u1, max u2 u1, u1, max (succ u2) (succ u1)} J _inst_1 TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} F) j))))
 Case conversion may be inaccurate. Consider using '#align Top.limit_topology TopCat.limit_topologyₓ'. -/
 theorem limit_topology (F : J ⥤ TopCat.{max v u}) :
     (limit F).TopologicalSpace = ⨅ j, (F.obj j).TopologicalSpace.induced (limit.π F j) :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/2f8347015b12b0864dfaf366ec4909eb70c78740

@@ -363,9 +363,9 @@ theorem prodIsoProd_inv_snd (X Y : TopCat.{u}) :
 
 /- warning: Top.prod_topology -> TopCat.prod_topology is a dubious translation:
 lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align Top.prod_topology TopCat.prod_topologyₓ'. -/
 theorem prod_topology {X Y : TopCat} :
     (X ⨯ Y).TopologicalSpace =
@@ -409,9 +409,9 @@ theorem range_prod_map {W X Y Z : TopCat.{u}} (f : W ⟶ Y) (g : X ⟶ Z) :
 
 /- warning: Top.inducing_prod_map -> TopCat.inducing_prod_map 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 Top.inducing_prod_map TopCat.inducing_prod_mapₓ'. -/
 theorem inducing_prod_map {W X Y Z : TopCat} {f : W ⟶ X} {g : Y ⟶ Z} (hf : Inducing f)
     (hg : Inducing g) : Inducing (Limits.prod.map f g) :=
@@ -425,9 +425,9 @@ theorem inducing_prod_map {W X Y Z : TopCat} {f : W ⟶ X} {g : Y ⟶ Z} (hf : I
 
 /- warning: Top.embedding_prod_map -> TopCat.embedding_prod_map is a dubious translation:
 lean 3 declaration is
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TopCat.largeCategory.{u1} (CategoryTheory.Discrete.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.discreteCategory.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.Limits.hasLimitsOfShapeOfHasLimits.{0, 0, u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} (CategoryTheory.Discrete.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.discreteCategory.{0} CategoryTheory.Limits.WalkingPair) TopCat.topCat_hasLimitsOfSize.{u1, 0}) (CategoryTheory.Limits.pair.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1} X Z)) f g)))
 but is expected to have type
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TopCat.concreteCategory.{0})) W) (Prefunctor.obj.{1, 1, 1, 1} TopCat.{0} (CategoryTheory.CategoryStruct.toQuiver.{0, 1} TopCat.{0} (CategoryTheory.Category.toCategoryStruct.{0, 1} TopCat.{0} instTopCatLargeCategory.{0})) Type (CategoryTheory.CategoryStruct.toQuiver.{0, 1} Type (CategoryTheory.Category.toCategoryStruct.{0, 1} Type CategoryTheory.types.{0})) (CategoryTheory.Functor.toPrefunctor.{0, 0, 1, 1} TopCat.{0} instTopCatLargeCategory.{0} Type CategoryTheory.types.{0} (CategoryTheory.forget.{1, 0, 0} TopCat.{0} instTopCatLargeCategory.{0} TopCat.concreteCategory.{0})) X) (TopCat.topologicalSpace_forget.{0} W) (TopCat.topologicalSpace_forget.{0} X) (Prefunctor.map.{1, 1, 1, 1} TopCat.{0} (CategoryTheory.CategoryStruct.toQuiver.{0, 1} TopCat.{0} (CategoryTheory.Category.toCategoryStruct.{0, 1} TopCat.{0} instTopCatLargeCategory.{0})) Type (CategoryTheory.CategoryStruct.toQuiver.{0, 1} Type (CategoryTheory.Category.toCategoryStruct.{0, 1} Type CategoryTheory.types.{0})) (CategoryTheory.Functor.toPrefunctor.{0, 0, 1, 1} TopCat.{0} instTopCatLargeCategory.{0} Type CategoryTheory.types.{0} (CategoryTheory.forget.{1, 0, 0} TopCat.{0} instTopCatLargeCategory.{0} TopCat.concreteCategory.{0})) W X f)) -> (Embedding.{0, 0} (Prefunctor.obj.{1, 1, 1, 1} TopCat.{0} (CategoryTheory.CategoryStruct.toQuiver.{0, 1} TopCat.{0} (CategoryTheory.Category.toCategoryStruct.{0, 1} TopCat.{0} instTopCatLargeCategory.{0})) Type (CategoryTheory.CategoryStruct.toQuiver.{0, 1} Type (CategoryTheory.Category.toCategoryStruct.{0, 1} Type CategoryTheory.types.{0})) (CategoryTheory.Functor.toPrefunctor.{0, 0, 1, 1} TopCat.{0} instTopCatLargeCategory.{0} Type CategoryTheory.types.{0} (CategoryTheory.forget.{1, 0, 0} TopCat.{0} instTopCatLargeCategory.{0} TopCat.concreteCategory.{0})) Y) (Prefunctor.obj.{1, 1, 1, 1} TopCat.{0} (CategoryTheory.CategoryStruct.toQuiver.{0, 1} TopCat.{0} (CategoryTheory.Category.toCategoryStruct.{0, 1} TopCat.{0} instTopCatLargeCategory.{0})) Type (CategoryTheory.CategoryStruct.toQuiver.{0, 1} Type (CategoryTheory.Category.toCategoryStruct.{0, 1} Type CategoryTheory.types.{0})) (CategoryTheory.Functor.toPrefunctor.{0, 0, 1, 1} TopCat.{0} instTopCatLargeCategory.{0} Type CategoryTheory.types.{0} (CategoryTheory.forget.{1, 0, 0} TopCat.{0} instTopCatLargeCategory.{0} TopCat.concreteCategory.{0})) Z) (TopCat.topologicalSpace_forget.{0} Y) (TopCat.topologicalSpace_forget.{0} Z) (Prefunctor.map.{1, 1, 1, 1} TopCat.{0} (CategoryTheory.CategoryStruct.toQuiver.{0, 1} TopCat.{0} (CategoryTheory.Category.toCategoryStruct.{0, 1} TopCat.{0} instTopCatLargeCategory.{0})) Type (CategoryTheory.CategoryStruct.toQuiver.{0, 1} Type (CategoryTheory.Category.toCategoryStruct.{0, 1} Type CategoryTheory.types.{0})) (CategoryTheory.Functor.toPrefunctor.{0, 0, 1, 1} TopCat.{0} instTopCatLargeCategory.{0} Type CategoryTheory.types.{0} (CategoryTheory.forget.{1, 0, 0} TopCat.{0} instTopCatLargeCategory.{0} TopCat.concreteCategory.{0})) Y Z g)) -> (Embedding.{0, 0} (Prefunctor.obj.{1, 1, 1, 1} TopCat.{0} (CategoryTheory.CategoryStruct.toQuiver.{0, 1} TopCat.{0} (CategoryTheory.Category.toCategoryStruct.{0, 1} TopCat.{0} instTopCatLargeCategory.{0})) Type (CategoryTheory.CategoryStruct.toQuiver.{0, 1} Type (CategoryTheory.Category.toCategoryStruct.{0, 1} Type CategoryTheory.types.{0})) (CategoryTheory.Functor.toPrefunctor.{0, 0, 1, 1} TopCat.{0} instTopCatLargeCategory.{0} Type CategoryTheory.types.{0} (CategoryTheory.forget.{1, 0, 0} TopCat.{0} instTopCatLargeCategory.{0} TopCat.concreteCategory.{0})) (CategoryTheory.Limits.prod.{0, 1} TopCat.{0} instTopCatLargeCategory.{0} W Y (CategoryTheory.Limits.hasLimitOfHasLimitsOfShape.{0, 0, 0, 1} TopCat.{0} instTopCatLargeCategory.{0} (CategoryTheory.Discrete.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.discreteCategory.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.Limits.hasLimitsOfShapeOfHasLimits.{0, 0, 0, 1} TopCat.{0} instTopCatLargeCategory.{0} (CategoryTheory.Discrete.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.discreteCategory.{0} CategoryTheory.Limits.WalkingPair) TopCat.topCat_hasLimits.{0}) (CategoryTheory.Limits.pair.{0, 1} TopCat.{0} instTopCatLargeCategory.{0} W Y)))) (Prefunctor.obj.{1, 1, 1, 1} TopCat.{0} (CategoryTheory.CategoryStruct.toQuiver.{0, 1} TopCat.{0} (CategoryTheory.Category.toCategoryStruct.{0, 1} TopCat.{0} instTopCatLargeCategory.{0})) Type (CategoryTheory.CategoryStruct.toQuiver.{0, 1} Type (CategoryTheory.Category.toCategoryStruct.{0, 1} Type CategoryTheory.types.{0})) (CategoryTheory.Functor.toPrefunctor.{0, 0, 1, 1} TopCat.{0} instTopCatLargeCategory.{0} Type CategoryTheory.types.{0} (CategoryTheory.forget.{1, 0, 0} TopCat.{0} instTopCatLargeCategory.{0} TopCat.concreteCategory.{0})) (CategoryTheory.Limits.prod.{0, 1} TopCat.{0} instTopCatLargeCategory.{0} X Z (CategoryTheory.Limits.hasLimitOfHasLimitsOfShape.{0, 0, 0, 1} TopCat.{0} instTopCatLargeCategory.{0} (CategoryTheory.Discrete.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.discreteCategory.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.Limits.hasLimitsOfShapeOfHasLimits.{0, 0, 0, 1} TopCat.{0} instTopCatLargeCategory.{0} (CategoryTheory.Discrete.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.discreteCategory.{0} CategoryTheory.Limits.WalkingPair) TopCat.topCat_hasLimits.{0}) (CategoryTheory.Limits.pair.{0, 1} TopCat.{0} instTopCatLargeCategory.{0} X Z)))) (TopCat.topologicalSpace_forget.{0} (CategoryTheory.Limits.prod.{0, 1} TopCat.{0} instTopCatLargeCategory.{0} W Y (CategoryTheory.Limits.hasLimitOfHasLimitsOfShape.{0, 0, 0, 1} TopCat.{0} instTopCatLargeCategory.{0} (CategoryTheory.Discrete.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.discreteCategory.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.Limits.hasLimitsOfShapeOfHasLimits.{0, 0, 0, 1} TopCat.{0} instTopCatLargeCategory.{0} (CategoryTheory.Discrete.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.discreteCategory.{0} CategoryTheory.Limits.WalkingPair) TopCat.topCat_hasLimits.{0}) (CategoryTheory.Limits.pair.{0, 1} TopCat.{0} instTopCatLargeCategory.{0} W Y)))) (TopCat.topologicalSpace_forget.{0} (CategoryTheory.Limits.prod.{0, 1} TopCat.{0} instTopCatLargeCategory.{0} X Z (CategoryTheory.Limits.hasLimitOfHasLimitsOfShape.{0, 0, 0, 1} TopCat.{0} instTopCatLargeCategory.{0} (CategoryTheory.Discrete.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.discreteCategory.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.Limits.hasLimitsOfShapeOfHasLimits.{0, 0, 0, 1} TopCat.{0} instTopCatLargeCategory.{0} (CategoryTheory.Discrete.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.discreteCategory.{0} CategoryTheory.Limits.WalkingPair) TopCat.topCat_hasLimits.{0}) (CategoryTheory.Limits.pair.{0, 1} TopCat.{0} instTopCatLargeCategory.{0} X Z)))) (Prefunctor.map.{1, 1, 1, 1} TopCat.{0} (CategoryTheory.CategoryStruct.toQuiver.{0, 1} TopCat.{0} (CategoryTheory.Category.toCategoryStruct.{0, 1} TopCat.{0} instTopCatLargeCategory.{0})) Type (CategoryTheory.CategoryStruct.toQuiver.{0, 1} Type (CategoryTheory.Category.toCategoryStruct.{0, 1} Type CategoryTheory.types.{0})) (CategoryTheory.Functor.toPrefunctor.{0, 0, 1, 1} TopCat.{0} instTopCatLargeCategory.{0} Type CategoryTheory.types.{0} (CategoryTheory.forget.{1, 0, 0} TopCat.{0} instTopCatLargeCategory.{0} TopCat.concreteCategory.{0})) (CategoryTheory.Limits.prod.{0, 1} TopCat.{0} instTopCatLargeCategory.{0} W Y (CategoryTheory.Limits.hasLimitOfHasLimitsOfShape.{0, 0, 0, 1} TopCat.{0} instTopCatLargeCategory.{0} (CategoryTheory.Discrete.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.discreteCategory.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.Limits.hasLimitsOfShapeOfHasLimits.{0, 0, 0, 1} TopCat.{0} instTopCatLargeCategory.{0} (CategoryTheory.Discrete.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.discreteCategory.{0} CategoryTheory.Limits.WalkingPair) TopCat.topCat_hasLimits.{0}) (CategoryTheory.Limits.pair.{0, 1} TopCat.{0} instTopCatLargeCategory.{0} W Y))) (CategoryTheory.Limits.prod.{0, 1} TopCat.{0} instTopCatLargeCategory.{0} X Z (CategoryTheory.Limits.hasLimitOfHasLimitsOfShape.{0, 0, 0, 1} TopCat.{0} instTopCatLargeCategory.{0} (CategoryTheory.Discrete.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.discreteCategory.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.Limits.hasLimitsOfShapeOfHasLimits.{0, 0, 0, 1} TopCat.{0} instTopCatLargeCategory.{0} (CategoryTheory.Discrete.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.discreteCategory.{0} CategoryTheory.Limits.WalkingPair) TopCat.topCat_hasLimits.{0}) (CategoryTheory.Limits.pair.{0, 1} TopCat.{0} instTopCatLargeCategory.{0} X Z))) (CategoryTheory.Limits.prod.map.{0, 1} TopCat.{0} instTopCatLargeCategory.{0} W Y X Z (CategoryTheory.Limits.hasLimitOfHasLimitsOfShape.{0, 0, 0, 1} TopCat.{0} instTopCatLargeCategory.{0} (CategoryTheory.Discrete.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.discreteCategory.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.Limits.hasLimitsOfShapeOfHasLimits.{0, 0, 0, 1} TopCat.{0} instTopCatLargeCategory.{0} (CategoryTheory.Discrete.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.discreteCategory.{0} CategoryTheory.Limits.WalkingPair) TopCat.topCat_hasLimits.{0}) (CategoryTheory.Limits.pair.{0, 1} TopCat.{0} instTopCatLargeCategory.{0} W Y)) (CategoryTheory.Limits.hasLimitOfHasLimitsOfShape.{0, 0, 0, 1} TopCat.{0} instTopCatLargeCategory.{0} (CategoryTheory.Discrete.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.discreteCategory.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.Limits.hasLimitsOfShapeOfHasLimits.{0, 0, 0, 1} TopCat.{0} instTopCatLargeCategory.{0} (CategoryTheory.Discrete.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.discreteCategory.{0} CategoryTheory.Limits.WalkingPair) TopCat.topCat_hasLimits.{0}) (CategoryTheory.Limits.pair.{0, 1} TopCat.{0} instTopCatLargeCategory.{0} X Z)) f g)))
+  forall {W : TopCat.{u1}} {X : TopCat.{u1}} {Y : TopCat.{u1}} {Z : TopCat.{u1}} {f : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) W X} {g : Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Y Z}, (Embedding.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) W) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) X) (TopCat.topologicalSpace_forget.{u1} W) (TopCat.topologicalSpace_forget.{u1} X) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) W X f)) -> (Embedding.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y) (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Z) (TopCat.topologicalSpace_forget.{u1} Y) (TopCat.topologicalSpace_forget.{u1} Z) (Prefunctor.map.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) Y Z g)) -> (Embedding.{u1, u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) Type.{u1} 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 Case conversion may be inaccurate. Consider using '#align Top.embedding_prod_map TopCat.embedding_prod_mapₓ'. -/
 theorem embedding_prod_map {W X Y Z : TopCat} {f : W ⟶ X} {g : Y ⟶ Z} (hf : Embedding f)
     (hg : Embedding g) : Embedding (Limits.prod.map f g) :=
@@ -440,11 +440,14 @@ theorem embedding_prod_map {W X Y Z : TopCat} {f : W ⟶ X} {g : Y ⟶ Z} (hf :
 
 end Prod
 
+#print TopCat.binaryCofan /-
 /-- The binary coproduct cofan in `Top`. -/
 protected def binaryCofan (X Y : TopCat.{u}) : BinaryCofan X Y :=
   BinaryCofan.mk (⟨Sum.inl⟩ : X ⟶ TopCat.of (Sum X Y)) ⟨Sum.inr⟩
 #align Top.binary_cofan TopCat.binaryCofan
+-/
 
+#print TopCat.binaryCofanIsColimit /-
 /-- The constructed binary coproduct cofan in `Top` is the coproduct. -/
 def binaryCofanIsColimit (X Y : TopCat.{u}) : IsColimit (TopCat.binaryCofan X Y) :=
   by
@@ -459,7 +462,14 @@ def binaryCofanIsColimit (X Y : TopCat.{u}) : IsColimit (TopCat.binaryCofan X Y)
     ext (x | x)
     exacts[(concrete_category.congr_hom h₁ x : _), (concrete_category.congr_hom h₂ x : _)]
 #align Top.binary_cofan_is_colimit TopCat.binaryCofanIsColimit
+-/
 
+/- warning: Top.binary_cofan_is_colimit_iff -> TopCat.binaryCofan_isColimit_iff is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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instTopCatLargeCategory.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1})) (Prefunctor.obj.{1, succ u1, 0, succ u1} (CategoryTheory.Discrete.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (CategoryTheory.Discrete.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.Category.toCategoryStruct.{0, 0} (CategoryTheory.Discrete.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.discreteCategory.{0} CategoryTheory.Limits.WalkingPair))) TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, succ u1} (CategoryTheory.Discrete.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.discreteCategory.{0} CategoryTheory.Limits.WalkingPair) TopCat.{u1} instTopCatLargeCategory.{u1} (CategoryTheory.Limits.pair.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y)) (CategoryTheory.Discrete.mk.{0} CategoryTheory.Limits.WalkingPair CategoryTheory.Limits.WalkingPair.right)) (Prefunctor.obj.{1, succ u1, 0, succ u1} (CategoryTheory.Discrete.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (CategoryTheory.Discrete.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.Category.toCategoryStruct.{0, 0} (CategoryTheory.Discrete.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.discreteCategory.{0} CategoryTheory.Limits.WalkingPair))) TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, succ u1} (CategoryTheory.Discrete.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.discreteCategory.{0} CategoryTheory.Limits.WalkingPair) TopCat.{u1} instTopCatLargeCategory.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) (CategoryTheory.Functor.{0, u1, 0, succ u1} (CategoryTheory.Discrete.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.discreteCategory.{0} CategoryTheory.Limits.WalkingPair) TopCat.{u1} instTopCatLargeCategory.{u1}) (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} (CategoryTheory.Functor.{0, u1, 0, succ u1} (CategoryTheory.Discrete.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.discreteCategory.{0} CategoryTheory.Limits.WalkingPair) TopCat.{u1} instTopCatLargeCategory.{u1}) (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} (CategoryTheory.Functor.{0, u1, 0, succ u1} (CategoryTheory.Discrete.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.discreteCategory.{0} CategoryTheory.Limits.WalkingPair) TopCat.{u1} instTopCatLargeCategory.{u1}) (CategoryTheory.Functor.category.{0, u1, 0, succ u1} (CategoryTheory.Discrete.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.discreteCategory.{0} CategoryTheory.Limits.WalkingPair) TopCat.{u1} instTopCatLargeCategory.{u1}))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} (CategoryTheory.Functor.{0, u1, 0, succ u1} (CategoryTheory.Discrete.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.discreteCategory.{0} CategoryTheory.Limits.WalkingPair) TopCat.{u1} instTopCatLargeCategory.{u1}) (CategoryTheory.Functor.category.{0, u1, 0, succ u1} (CategoryTheory.Discrete.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.discreteCategory.{0} CategoryTheory.Limits.WalkingPair) TopCat.{u1} instTopCatLargeCategory.{u1}) (CategoryTheory.Functor.const.{0, u1, 0, succ u1} (CategoryTheory.Discrete.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.discreteCategory.{0} CategoryTheory.Limits.WalkingPair) TopCat.{u1} instTopCatLargeCategory.{u1})) (CategoryTheory.Limits.Cocone.pt.{0, u1, 0, succ u1} (CategoryTheory.Discrete.{0} CategoryTheory.Limits.WalkingPair) (CategoryTheory.discreteCategory.{0} CategoryTheory.Limits.WalkingPair) TopCat.{u1} instTopCatLargeCategory.{u1} (CategoryTheory.Limits.pair.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y) c))) (CategoryTheory.Discrete.mk.{0} CategoryTheory.Limits.WalkingPair CategoryTheory.Limits.WalkingPair.right)) (CategoryTheory.Limits.BinaryCofan.inr.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1} X Y c))))))
+Case conversion may be inaccurate. Consider using '#align Top.binary_cofan_is_colimit_iff TopCat.binaryCofan_isColimit_iffₓ'. -/
 theorem binaryCofan_isColimit_iff {X Y : TopCat} (c : BinaryCofan X Y) :
     Nonempty (IsColimit c) ↔
       OpenEmbedding c.inl ∧ OpenEmbedding c.inr ∧ IsCompl (Set.range c.inl) (Set.range c.inr) :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/2f8347015b12b0864dfaf366ec4909eb70c78740

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Patrick Massot, Scott Morrison, Mario Carneiro, Andrew Yang
 
 ! This file was ported from Lean 3 source module topology.category.Top.limits.products
-! leanprover-community/mathlib commit 178a32653e369dce2da68dc6b2694e385d484ef1
+! leanprover-community/mathlib commit 781cb2eed038c4caf53bdbd8d20a95e5822d77df
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.Topology.Category.Top.Limits.Basic
 /-!
 # Products and coproducts in the category of topological spaces
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 -/
 
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/28b2a92f2996d28e580450863c130955de0ed398

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Patrick Massot, Scott Morrison, Mario Carneiro, Andrew Yang
 
 ! This file was ported from Lean 3 source module topology.category.Top.limits.products
-! leanprover-community/mathlib commit 781cb2eed038c4caf53bdbd8d20a95e5822d77df
+! leanprover-community/mathlib commit 178a32653e369dce2da68dc6b2694e385d484ef1
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,9 +14,6 @@ import Mathbin.Topology.Category.Top.Limits.Basic
 /-!
 # Products and coproducts in the category of topological spaces
 
-> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
-> Any changes to this file require a corresponding PR to mathlib4.
-
 -/
 
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/2f8347015b12b0864dfaf366ec4909eb70c78740

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Patrick Massot, Scott Morrison, Mario Carneiro, Andrew Yang
 
 ! This file was ported from Lean 3 source module topology.category.Top.limits.products
-! leanprover-community/mathlib commit 178a32653e369dce2da68dc6b2694e385d484ef1
+! leanprover-community/mathlib commit 781cb2eed038c4caf53bdbd8d20a95e5822d77df
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.Topology.Category.Top.Limits.Basic
 /-!
 # Products and coproducts in the category of topological spaces
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 -/
 
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/cc5dd6244981976cc9da7afc4eee5682b037a013

@@ -31,17 +31,35 @@ namespace TopCat
 
 variable {J : Type v} [SmallCategory J]
 
+/- warning: Top.pi_π -> TopCat.piπ is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u2}} (α : ι -> TopCat.{max u2 u1}) (i : ι), Quiver.Hom.{succ (max u2 u1), succ (max u2 u1)} TopCat.{max u2 u1} (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, succ (max u2 u1)} TopCat.{max u2 u1} (CategoryTheory.Category.toCategoryStruct.{max u2 u1, succ (max u2 u1)} TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1})) (TopCat.of.{max u2 u1} (forall (i : ι), coeSort.{succ (succ (max u2 u1)), succ (succ (max u2 u1))} TopCat.{max u2 u1} Type.{max u2 u1} TopCat.hasCoeToSort.{max u2 u1} (α i)) (Pi.topologicalSpace.{u2, max u2 u1} ι (fun (i : ι) => coeSort.{succ (succ (max u2 u1)), succ (succ (max u2 u1))} TopCat.{max u2 u1} Type.{max u2 u1} TopCat.hasCoeToSort.{max u2 u1} (α i)) (fun (a : ι) => TopCat.topologicalSpace.{max u2 u1} (α a)))) (α i)
+but is expected to have type
+  forall {ι : Type.{u1}} (α : ι -> TopCatMax.{u1, u2}) (i : ι), Quiver.Hom.{max (succ u2) (succ u1), succ (max u2 u1)} TopCat.{max u2 u1} (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max (succ u2) (succ u1)} TopCat.{max u2 u1} (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max (succ u2) (succ u1)} TopCat.{max u2 u1} instTopCatLargeCategory.{max u2 u1})) (TopCat.of.{max u2 u1} (forall (i : ι), CategoryTheory.Bundled.α.{max u2 u1, max u2 u1} TopologicalSpace.{max u2 u1} (α i)) (Pi.topologicalSpace.{u1, max u2 u1} ι (fun (i : ι) => CategoryTheory.Bundled.α.{max u2 u1, max u2 u1} TopologicalSpace.{max u2 u1} (α i)) (fun (a : ι) => TopCat.topologicalSpace_coe.{max u2 u1} (α a)))) (α i)
+Case conversion may be inaccurate. Consider using '#align Top.pi_π TopCat.piπₓ'. -/
 /-- The projection from the product as a bundled continous map. -/
 abbrev piπ {ι : Type v} (α : ι → TopCat.{max v u}) (i : ι) : TopCat.of (∀ i, α i) ⟶ α i :=
   ⟨fun f => f i, continuous_apply i⟩
 #align Top.pi_π TopCat.piπ
 
+/- warning: Top.pi_fan -> TopCat.piFan is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u2}} (α : ι -> TopCat.{max u2 u1}), CategoryTheory.Limits.Fan.{u2, max u2 u1, succ (max u2 u1)} ι TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} α
+but is expected to have type
+  forall {ι : Type.{u1}} (α : ι -> TopCatMax.{u1, u2}), CategoryTheory.Limits.Fan.{u1, max u2 u1, max (succ u2) (succ u1)} ι TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} α
+Case conversion may be inaccurate. Consider using '#align Top.pi_fan TopCat.piFanₓ'. -/
 /-- The explicit fan of a family of topological spaces given by the pi type. -/
 @[simps pt π_app]
 def piFan {ι : Type v} (α : ι → TopCat.{max v u}) : Fan α :=
   Fan.mk (TopCat.of (∀ i, α i)) (piπ α)
 #align Top.pi_fan TopCat.piFan
 
+/- warning: Top.pi_fan_is_limit -> TopCat.piFanIsLimit is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u2}} (α : ι -> TopCat.{max u2 u1}), CategoryTheory.Limits.IsLimit.{u2, max u2 u1, u2, succ (max u2 u1)} (CategoryTheory.Discrete.{u2} ι) (CategoryTheory.discreteCategory.{u2} ι) TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} (CategoryTheory.Discrete.functor.{max u2 u1, u2, succ (max u2 u1)} TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} ι α) (TopCat.piFan.{u1, u2} ι α)
+but is expected to have type
+  forall {ι : Type.{u1}} (α : ι -> TopCatMax.{u1, u2}), CategoryTheory.Limits.IsLimit.{u1, max u2 u1, u1, max (succ u2) (succ u1)} (CategoryTheory.Discrete.{u1} ι) (CategoryTheory.discreteCategory.{u1} ι) TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} (CategoryTheory.Discrete.functor.{max u2 u1, u1, max (succ u2) (succ u1)} TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} ι α) (TopCat.piFan.{u1, u2} ι α)
+Case conversion may be inaccurate. Consider using '#align Top.pi_fan_is_limit TopCat.piFanIsLimitₓ'. -/
 /-- The constructed fan is indeed a limit -/
 def piFanIsLimit {ι : Type v} (α : ι → TopCat.{max v u}) : IsLimit (piFan α)
     where
@@ -55,6 +73,12 @@ def piFanIsLimit {ι : Type v} (α : ι → TopCat.{max v u}) : IsLimit (piFan 
     tidy
 #align Top.pi_fan_is_limit TopCat.piFanIsLimit
 
+/- warning: Top.pi_iso_pi -> TopCat.piIsoPi is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u2}} (α : ι -> TopCat.{max u2 u1}), CategoryTheory.Iso.{max u2 u1, succ (max u2 u1)} TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} (CategoryTheory.Limits.piObj.{u2, max u2 u1, succ (max u2 u1)} ι TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} α (TopCat.piIsoPi._proof_1.{u1, u2} ι α)) (TopCat.of.{max u2 u1} (forall (i : ι), coeSort.{succ (succ (max u2 u1)), succ (succ (max u2 u1))} TopCat.{max u2 u1} Type.{max u2 u1} TopCat.hasCoeToSort.{max u2 u1} (α i)) (Pi.topologicalSpace.{u2, max u2 u1} ι (fun (i : ι) => coeSort.{succ (succ (max u2 u1)), succ (succ (max u2 u1))} TopCat.{max u2 u1} Type.{max u2 u1} TopCat.hasCoeToSort.{max u2 u1} (α i)) (fun (a : ι) => TopCat.topologicalSpace.{max u2 u1} (α a))))
+but is expected to have type
+  forall {ι : Type.{u1}} (α : ι -> TopCatMax.{u1, u2}), CategoryTheory.Iso.{max u2 u1, max (succ u2) (succ u1)} TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} (CategoryTheory.Limits.piObj.{u1, max u2 u1, max (succ u2) (succ u1)} ι TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} α (CategoryTheory.Limits.hasLimitOfHasLimitsOfShape.{u1, u1, max u2 u1, max (succ u2) (succ u1)} TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} (CategoryTheory.Discrete.{u1} ι) (CategoryTheory.discreteCategory.{u1} ι) (CategoryTheory.Limits.hasLimitsOfShapeOfHasLimits.{u1, u1, max u2 u1, max (succ u2) (succ u1)} TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} (CategoryTheory.Discrete.{u1} ι) (CategoryTheory.discreteCategory.{u1} ι) TopCat.topCat_hasLimitsOfSize.{u1, u2}) (CategoryTheory.Discrete.functor.{max u2 u1, u1, max (succ u2) (succ u1)} TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} ι α))) (TopCat.of.{max u2 u1} (forall (i : ι), CategoryTheory.Bundled.α.{max u2 u1, max u2 u1} TopologicalSpace.{max u2 u1} (α i)) (Pi.topologicalSpace.{u1, max u2 u1} ι (fun (i : ι) => CategoryTheory.Bundled.α.{max u2 u1, max u2 u1} TopologicalSpace.{max u2 u1} (α i)) (fun (a : ι) => TopCat.topologicalSpace_coe.{max u2 u1} (α a))))
+Case conversion may be inaccurate. Consider using '#align Top.pi_iso_pi TopCat.piIsoPiₓ'. -/
 /-- The product is homeomorphic to the product of the underlying spaces,
 equipped with the product topology.
 -/
@@ -62,17 +86,35 @@ def piIsoPi {ι : Type v} (α : ι → TopCat.{max v u}) : ∏ α ≅ TopCat.of
   (limit.isLimit _).conePointUniqueUpToIso (piFanIsLimit α)
 #align Top.pi_iso_pi TopCat.piIsoPi
 
+/- warning: Top.pi_iso_pi_inv_π -> TopCat.piIsoPi_inv_π is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align Top.pi_iso_pi_inv_π TopCat.piIsoPi_inv_πₓ'. -/
 @[simp, reassoc.1]
 theorem piIsoPi_inv_π {ι : Type v} (α : ι → TopCat.{max v u}) (i : ι) :
     (piIsoPi α).inv ≫ Pi.π α i = piπ α i := by simp [pi_iso_pi]
 #align Top.pi_iso_pi_inv_π TopCat.piIsoPi_inv_π
 
+/- warning: Top.pi_iso_pi_inv_π_apply -> TopCat.piIsoPi_inv_π_apply is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align Top.pi_iso_pi_inv_π_apply TopCat.piIsoPi_inv_π_applyₓ'. -/
 @[simp]
 theorem piIsoPi_inv_π_apply {ι : Type v} (α : ι → TopCat.{max v u}) (i : ι) (x : ∀ i, α i) :
     (Pi.π α i : _) ((piIsoPi α).inv x) = x i :=
   ConcreteCategory.congr_hom (piIsoPi_inv_π α i) x
 #align Top.pi_iso_pi_inv_π_apply TopCat.piIsoPi_inv_π_apply
 
+/- warning: Top.pi_iso_pi_hom_apply -> TopCat.piIsoPi_hom_apply is a dubious translation:
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(ContinuousMap.hasCoeToFun.{max u2 u1, max u2 u1} (coeSort.{succ (succ (max u2 u1)), succ (succ (max u2 u1))} (CategoryTheory.Bundled.{max u2 u1, max u2 u1} TopologicalSpace.{max u2 u1}) Type.{max u2 u1} (CategoryTheory.Bundled.hasCoeToSort.{max u2 u1, max u2 u1} TopologicalSpace.{max u2 u1}) (CategoryTheory.Limits.piObj.{u2, max u2 u1, succ (max u2 u1)} ι TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} α (CategoryTheory.Limits.hasLimitOfHasLimitsOfShape.{u2, u2, max u2 u1, succ (max u2 u1)} TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} (CategoryTheory.Discrete.{u2} ι) (CategoryTheory.discreteCategory.{u2} ι) (CategoryTheory.Limits.hasLimitsOfShapeOfHasLimits.{u2, u2, max u2 u1, succ (max u2 u1)} TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} (CategoryTheory.Discrete.{u2} ι) (CategoryTheory.discreteCategory.{u2} ι) TopCat.topCat_hasLimitsOfSize.{u1, u2}) (CategoryTheory.Discrete.functor.{max u2 u1, u2, succ (max u2 u1)} TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} ι α)))) (coeSort.{succ (succ (max u2 u1)), succ (succ (max u2 u1))} (CategoryTheory.Bundled.{max u2 u1, max u2 u1} TopologicalSpace.{max u2 u1}) Type.{max u2 u1} (CategoryTheory.Bundled.hasCoeToSort.{max u2 u1, max u2 u1} TopologicalSpace.{max u2 u1}) (α i)) (CategoryTheory.Bundled.str.{max u2 u1, max u2 u1} TopologicalSpace.{max u2 u1} (CategoryTheory.Limits.piObj.{u2, max u2 u1, succ (max u2 u1)} ι TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} α (CategoryTheory.Limits.hasLimitOfHasLimitsOfShape.{u2, u2, max u2 u1, succ (max u2 u1)} TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} (CategoryTheory.Discrete.{u2} ι) (CategoryTheory.discreteCategory.{u2} ι) (CategoryTheory.Limits.hasLimitsOfShapeOfHasLimits.{u2, u2, max u2 u1, succ (max u2 u1)} TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} (CategoryTheory.Discrete.{u2} ι) (CategoryTheory.discreteCategory.{u2} ι) TopCat.topCat_hasLimitsOfSize.{u1, u2}) (CategoryTheory.Discrete.functor.{max u2 u1, u2, succ (max u2 u1)} 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+but is expected to have type
+  forall {ι : Type.{u1}} (α : ι -> TopCatMax.{u1, u2}) (i : ι) (x : CategoryTheory.Bundled.α.{max u2 u1, max u2 u1} TopologicalSpace.{max u2 u1} (CategoryTheory.Limits.piObj.{u1, max u2 u1, max (succ u2) (succ u1)} ι TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} α (CategoryTheory.Limits.hasLimitOfHasLimitsOfShape.{u1, u1, max u2 u1, max (succ u2) (succ u1)} TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} (CategoryTheory.Discrete.{u1} ι) (CategoryTheory.discreteCategory.{u1} ι) (CategoryTheory.Limits.hasLimitsOfShapeOfHasLimits.{u1, u1, max u2 u1, max (succ u2) (succ u1)} TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} (CategoryTheory.Discrete.{u1} ι) (CategoryTheory.discreteCategory.{u1} ι) TopCat.topCat_hasLimitsOfSize.{u1, u2}) (CategoryTheory.Discrete.functor.{max u2 u1, u1, max (succ u2) (succ u1)} TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} ι α)))), Eq.{max (succ u2) (succ u1)} (CategoryTheory.Bundled.α.{max u2 u1, max u2 u1} 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max (succ u2) (succ u1)} ι TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} α (CategoryTheory.Limits.hasLimitOfHasLimitsOfShape.{u1, u1, max u2 u1, max (succ u2) (succ u1)} TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} (CategoryTheory.Discrete.{u1} ι) (CategoryTheory.discreteCategory.{u1} ι) (CategoryTheory.Limits.hasLimitsOfShapeOfHasLimits.{u1, u1, max u2 u1, max (succ u2) (succ u1)} TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} (CategoryTheory.Discrete.{u1} ι) (CategoryTheory.discreteCategory.{u1} ι) TopCat.topCat_hasLimitsOfSize.{u1, u2}) (CategoryTheory.Discrete.functor.{max u2 u1, u1, max (succ u2) (succ u1)} TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} ι α)) i) x)
+Case conversion may be inaccurate. Consider using '#align Top.pi_iso_pi_hom_apply TopCat.piIsoPi_hom_applyₓ'. -/
 @[simp]
 theorem piIsoPi_hom_apply {ι : Type v} (α : ι → TopCat.{max v u}) (i : ι) (x : ∏ α) :
     (piIsoPi α).Hom x i = (Pi.π α i : _) x :=
@@ -82,17 +124,35 @@ theorem piIsoPi_hom_apply {ι : Type v} (α : ι → TopCat.{max v u}) (i : ι)
   exact concrete_category.congr_hom this x
 #align Top.pi_iso_pi_hom_apply TopCat.piIsoPi_hom_apply
 
+/- warning: Top.sigma_ι -> TopCat.sigmaι is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u2}} (α : ι -> TopCat.{max u2 u1}) (i : ι), Quiver.Hom.{succ (max u2 u1), succ (max u2 u1)} TopCat.{max u2 u1} (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, succ (max u2 u1)} TopCat.{max u2 u1} (CategoryTheory.Category.toCategoryStruct.{max u2 u1, succ (max u2 u1)} TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1})) (α i) (TopCat.of.{max u2 u1} (Sigma.{u2, max u2 u1} ι (fun (i : ι) => coeSort.{succ (succ (max u2 u1)), succ (succ (max u2 u1))} TopCat.{max u2 u1} Type.{max u2 u1} TopCat.hasCoeToSort.{max u2 u1} (α i))) (Sigma.topologicalSpace.{u2, max u2 u1} ι (fun (i : ι) => coeSort.{succ (succ (max u2 u1)), succ (succ (max u2 u1))} TopCat.{max u2 u1} Type.{max u2 u1} TopCat.hasCoeToSort.{max u2 u1} (α i)) (fun (a : ι) => TopCat.topologicalSpace.{max u2 u1} (α a))))
+but is expected to have type
+  forall {ι : Type.{u1}} (α : ι -> TopCatMax.{u1, u2}) (i : ι), Quiver.Hom.{max (succ u2) (succ u1), max (succ u2) (succ u1)} TopCatMax.{u1, u2} (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max (succ u2) (succ u1)} TopCatMax.{u1, u2} (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max (succ u2) (succ u1)} TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1})) (α i) (TopCat.of.{max u2 u1} (Sigma.{u1, max u2 u1} ι (fun (i : ι) => CategoryTheory.Bundled.α.{max u2 u1, max u2 u1} TopologicalSpace.{max u2 u1} (α i))) (instTopologicalSpaceSigma.{u1, max u2 u1} ι (fun (i : ι) => CategoryTheory.Bundled.α.{max u2 u1, max u2 u1} TopologicalSpace.{max u2 u1} (α i)) (fun (a : ι) => TopCat.topologicalSpace_coe.{max u2 u1} (α a))))
+Case conversion may be inaccurate. Consider using '#align Top.sigma_ι TopCat.sigmaιₓ'. -/
 /-- The inclusion to the coproduct as a bundled continous map. -/
 abbrev sigmaι {ι : Type v} (α : ι → TopCat.{max v u}) (i : ι) : α i ⟶ TopCat.of (Σi, α i) :=
   ⟨Sigma.mk i⟩
 #align Top.sigma_ι TopCat.sigmaι
 
+/- warning: Top.sigma_cofan -> TopCat.sigmaCofan is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u2}} (α : ι -> TopCat.{max u2 u1}), CategoryTheory.Limits.Cofan.{u2, max u2 u1, succ (max u2 u1)} ι TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} α
+but is expected to have type
+  forall {ι : Type.{u1}} (α : ι -> TopCatMax.{u1, u2}), CategoryTheory.Limits.Cofan.{u1, max u2 u1, max (succ u2) (succ u1)} ι TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} α
+Case conversion may be inaccurate. Consider using '#align Top.sigma_cofan TopCat.sigmaCofanₓ'. -/
 /-- The explicit cofan of a family of topological spaces given by the sigma type. -/
 @[simps pt ι_app]
 def sigmaCofan {ι : Type v} (α : ι → TopCat.{max v u}) : Cofan α :=
   Cofan.mk (TopCat.of (Σi, α i)) (sigmaι α)
 #align Top.sigma_cofan TopCat.sigmaCofan
 
+/- warning: Top.sigma_cofan_is_colimit -> TopCat.sigmaCofanIsColimit is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u2}} (α : ι -> TopCat.{max u2 u1}), CategoryTheory.Limits.IsColimit.{u2, max u2 u1, u2, succ (max u2 u1)} (CategoryTheory.Discrete.{u2} ι) (CategoryTheory.discreteCategory.{u2} ι) TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} (CategoryTheory.Discrete.functor.{max u2 u1, u2, succ (max u2 u1)} TopCat.{max u2 u1} TopCat.largeCategory.{max u2 u1} ι α) (TopCat.sigmaCofan.{u1, u2} ι α)
+but is expected to have type
+  forall {ι : Type.{u1}} (α : ι -> TopCatMax.{u1, u2}), CategoryTheory.Limits.IsColimit.{u1, max u2 u1, u1, max (succ u2) (succ u1)} (CategoryTheory.Discrete.{u1} ι) (CategoryTheory.discreteCategory.{u1} ι) TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} (CategoryTheory.Discrete.functor.{max u2 u1, u1, max (succ u2) (succ u1)} TopCatMax.{u1, u2} instTopCatLargeCategory.{max u2 u1} ι α) (TopCat.sigmaCofan.{u1, u2} ι α)
+Case conversion may be inaccurate. Consider using '#align Top.sigma_cofan_is_colimit TopCat.sigmaCofanIsColimitₓ'. -/
 /-- The constructed cofan is indeed a colimit -/
 def sigmaCofanIsColimit {ι : Type v} (α : ι → TopCat.{max v u}) : IsColimit (sigmaCofan α)
     where
@@ -108,23 +168,47 @@ def sigmaCofanIsColimit {ι : Type v} (α : ι → TopCat.{max v u}) : IsColimit
     tidy
 #align Top.sigma_cofan_is_colimit TopCat.sigmaCofanIsColimit
 
+/- warning: Top.sigma_iso_sigma -> TopCat.sigmaIsoSigma is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align Top.sigma_iso_sigma TopCat.sigmaIsoSigmaₓ'. -/
 /-- The coproduct is homeomorphic to the disjoint union of the topological spaces.
 -/
 def sigmaIsoSigma {ι : Type v} (α : ι → TopCat.{max v u}) : ∐ α ≅ TopCat.of (Σi, α i) :=
   (colimit.isColimit _).coconePointUniqueUpToIso (sigmaCofanIsColimit α)
 #align Top.sigma_iso_sigma TopCat.sigmaIsoSigma
 
+/- warning: Top.sigma_iso_sigma_hom_ι -> TopCat.sigmaIsoSigma_hom_ι is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align Top.sigma_iso_sigma_hom_ι TopCat.sigmaIsoSigma_hom_ιₓ'. -/
 @[simp, reassoc.1]
 theorem sigmaIsoSigma_hom_ι {ι : Type v} (α : ι → TopCat.{max v u}) (i : ι) :
     Sigma.ι α i ≫ (sigmaIsoSigma α).Hom = sigmaι α i := by simp [sigma_iso_sigma]
 #align Top.sigma_iso_sigma_hom_ι TopCat.sigmaIsoSigma_hom_ι
 
+/- warning: Top.sigma_iso_sigma_hom_ι_apply -> TopCat.sigmaIsoSigma_hom_ι_apply is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align Top.sigma_iso_sigma_hom_ι_apply TopCat.sigmaIsoSigma_hom_ι_applyₓ'. -/
 @[simp]
 theorem sigmaIsoSigma_hom_ι_apply {ι : Type v} (α : ι → TopCat.{max v u}) (i : ι) (x : α i) :
     (sigmaIsoSigma α).Hom ((Sigma.ι α i : _) x) = Sigma.mk i x :=
   ConcreteCategory.congr_hom (sigmaIsoSigma_hom_ι α i) x
 #align Top.sigma_iso_sigma_hom_ι_apply TopCat.sigmaIsoSigma_hom_ι_apply
 
+/- warning: Top.sigma_iso_sigma_inv_apply -> TopCat.sigmaIsoSigma_inv_apply 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 Top.sigma_iso_sigma_inv_apply TopCat.sigmaIsoSigma_inv_applyₓ'. -/
 @[simp]
 theorem sigmaIsoSigma_inv_apply {ι : Type v} (α : ι → TopCat.{max v u}) (i : ι) (x : α i) :
     (sigmaIsoSigma α).inv ⟨i, x⟩ = (Sigma.ι α i : _) x :=
@@ -133,6 +217,12 @@ theorem sigmaIsoSigma_inv_apply {ι : Type v} (α : ι → TopCat.{max v u}) (i
   simp
 #align Top.sigma_iso_sigma_inv_apply TopCat.sigmaIsoSigma_inv_apply
 
+/- warning: Top.induced_of_is_limit -> TopCat.induced_of_isLimit 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 Top.induced_of_is_limit TopCat.induced_of_isLimitₓ'. -/
 theorem induced_of_isLimit {F : J ⥤ TopCat.{max v u}} (C : Cone F) (hC : IsLimit C) :
     C.pt.TopologicalSpace = ⨅ j, (F.obj j).TopologicalSpace.induced (C.π.app j) :=
   by
@@ -142,6 +232,12 @@ theorem induced_of_isLimit {F : J ⥤ TopCat.{max v u}} (C : Cone F) (hC : IsLim
   simpa [induced_infᵢ, induced_compose]
 #align Top.induced_of_is_limit TopCat.induced_of_isLimit
 
+/- warning: Top.limit_topology -> TopCat.limit_topology is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align Top.limit_topology TopCat.limit_topologyₓ'. -/
 theorem limit_topology (F : J ⥤ TopCat.{max v u}) :
     (limit F).TopologicalSpace = ⨅ j, (F.obj j).TopologicalSpace.induced (limit.π F j) :=
   induced_of_isLimit _ (limit.isLimit F)
@@ -149,21 +245,36 @@ theorem limit_topology (F : J ⥤ TopCat.{max v u}) :
 
 section Prod
 
+/- warning: Top.prod_fst -> TopCat.prodFst is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align Top.prod_fst TopCat.prodFstₓ'. -/
 /-- The first projection from the product. -/
 abbrev prodFst {X Y : TopCat.{u}} : TopCat.of (X × Y) ⟶ X :=
   ⟨Prod.fst⟩
 #align Top.prod_fst TopCat.prodFst
 
+/- warning: Top.prod_snd -> TopCat.prodSnd is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align Top.prod_snd TopCat.prodSndₓ'. -/
 /-- The second projection from the product. -/
 abbrev prodSnd {X Y : TopCat.{u}} : TopCat.of (X × Y) ⟶ Y :=
   ⟨Prod.snd⟩
 #align Top.prod_snd TopCat.prodSnd
 
+#print TopCat.prodBinaryFan /-
 /-- The explicit binary cofan of `X, Y` given by `X × Y`. -/
 def prodBinaryFan (X Y : TopCat.{u}) : BinaryFan X Y :=
   BinaryFan.mk prodFst prodSnd
 #align Top.prod_binary_fan TopCat.prodBinaryFan
+-/
 
+#print TopCat.prodBinaryFanIsLimit /-
 /-- The constructed binary fan is indeed a limit -/
 def prodBinaryFanIsLimit (X Y : TopCat.{u}) : IsLimit (prodBinaryFan X Y)
     where
@@ -181,7 +292,14 @@ def prodBinaryFanIsLimit (X Y : TopCat.{u}) : IsLimit (prodBinaryFan X Y)
       apply_fun fun e => e x  at h
       exact h
 #align Top.prod_binary_fan_is_limit TopCat.prodBinaryFanIsLimit
+-/
 
+/- warning: Top.prod_iso_prod -> TopCat.prodIsoProd is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align Top.prod_iso_prod TopCat.prodIsoProdₓ'. -/
 /-- The homeomorphism between `X ⨯ Y` and the set-theoretic product of `X` and `Y`,
 equipped with the product topology.
 -/
@@ -189,16 +307,26 @@ def prodIsoProd (X Y : TopCat.{u}) : X ⨯ Y ≅ TopCat.of (X × Y) :=
   (limit.isLimit _).conePointUniqueUpToIso (prodBinaryFanIsLimit X Y)
 #align Top.prod_iso_prod TopCat.prodIsoProd
 
+#print TopCat.prodIsoProd_hom_fst /-
 @[simp, reassoc.1]
 theorem prodIsoProd_hom_fst (X Y : TopCat.{u}) :
     (prodIsoProd X Y).Hom ≫ prodFst = Limits.prod.fst := by simpa [← iso.eq_inv_comp, prod_iso_prod]
 #align Top.prod_iso_prod_hom_fst TopCat.prodIsoProd_hom_fst
+-/
 
+#print TopCat.prodIsoProd_hom_snd /-
 @[simp, reassoc.1]
 theorem prodIsoProd_hom_snd (X Y : TopCat.{u}) :
     (prodIsoProd X Y).Hom ≫ prodSnd = Limits.prod.snd := by simpa [← iso.eq_inv_comp, prod_iso_prod]
 #align Top.prod_iso_prod_hom_snd TopCat.prodIsoProd_hom_snd
+-/
 
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+Case conversion may be inaccurate. Consider using '#align Top.prod_iso_prod_hom_apply TopCat.prodIsoProd_hom_applyₓ'. -/
 @[simp]
 theorem prodIsoProd_hom_apply {X Y : TopCat.{u}} (x : X ⨯ Y) :
     (prodIsoProd X Y).Hom x = ((Limits.prod.fst : X ⨯ Y ⟶ _) x, (Limits.prod.snd : X ⨯ Y ⟶ _) x) :=
@@ -208,16 +336,34 @@ theorem prodIsoProd_hom_apply {X Y : TopCat.{u}} (x : X ⨯ Y) :
   · exact concrete_category.congr_hom (prod_iso_prod_hom_snd X Y) x
 #align Top.prod_iso_prod_hom_apply TopCat.prodIsoProd_hom_apply
 
+/- warning: Top.prod_iso_prod_inv_fst -> TopCat.prodIsoProd_inv_fst is a dubious translation:
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 @[simp, reassoc.1, elementwise]
 theorem prodIsoProd_inv_fst (X Y : TopCat.{u}) :
     (prodIsoProd X Y).inv ≫ Limits.prod.fst = prodFst := by simp [iso.inv_comp_eq]
 #align Top.prod_iso_prod_inv_fst TopCat.prodIsoProd_inv_fst
 
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+Case conversion may be inaccurate. Consider using '#align Top.prod_iso_prod_inv_snd TopCat.prodIsoProd_inv_sndₓ'. -/
 @[simp, reassoc.1, elementwise]
 theorem prodIsoProd_inv_snd (X Y : TopCat.{u}) :
     (prodIsoProd X Y).inv ≫ Limits.prod.snd = prodSnd := by simp [iso.inv_comp_eq]
 #align Top.prod_iso_prod_inv_snd TopCat.prodIsoProd_inv_snd
 
+/- warning: Top.prod_topology -> TopCat.prod_topology 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 Top.prod_topology TopCat.prod_topologyₓ'. -/
 theorem prod_topology {X Y : TopCat} :
     (X ⨯ Y).TopologicalSpace =
       induced (Limits.prod.fst : X ⨯ Y ⟶ _) X.TopologicalSpace ⊓
@@ -229,6 +375,12 @@ theorem prod_topology {X Y : TopCat} :
   simpa [induced_compose]
 #align Top.prod_topology TopCat.prod_topology
 
+/- warning: Top.range_prod_map -> TopCat.range_prod_map is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align Top.range_prod_map TopCat.range_prod_mapₓ'. -/
 theorem range_prod_map {W X Y Z : TopCat.{u}} (f : W ⟶ Y) (g : X ⟶ Z) :
     Set.range (Limits.prod.map f g) =
       (Limits.prod.fst : Y ⨯ Z ⟶ _) ⁻¹' Set.range f ∩
@@ -252,6 +404,12 @@ theorem range_prod_map {W X Y Z : TopCat.{u}} (f : W ⟶ Y) (g : X ⟶ Z) :
       simp [hx₂]
 #align Top.range_prod_map TopCat.range_prod_map
 
+/- warning: Top.inducing_prod_map -> TopCat.inducing_prod_map 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 Top.inducing_prod_map TopCat.inducing_prod_mapₓ'. -/
 theorem inducing_prod_map {W X Y Z : TopCat} {f : W ⟶ X} {g : Y ⟶ Z} (hf : Inducing f)
     (hg : Inducing g) : Inducing (Limits.prod.map f g) :=
   by
@@ -262,6 +420,12 @@ theorem inducing_prod_map {W X Y Z : TopCat} {f : W ⟶ X} {g : Y ⟶ Z} (hf : I
   rw [← @induced_compose _ _ _ _ _ f, ← @induced_compose _ _ _ _ _ g, ← hf.induced, ← hg.induced]
 #align Top.inducing_prod_map TopCat.inducing_prod_map
 
+/- warning: Top.embedding_prod_map -> TopCat.embedding_prod_map is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {W : TopCat.{0}} {X : TopCat.{0}} {Y : TopCat.{0}} {Z : TopCat.{0}} {f : Quiver.Hom.{1, 1} TopCat.{0} (CategoryTheory.CategoryStruct.toQuiver.{0, 1} TopCat.{0} (CategoryTheory.Category.toCategoryStruct.{0, 1} TopCat.{0} instTopCatLargeCategory.{0})) W X} {g : Quiver.Hom.{1, 1} TopCat.{0} (CategoryTheory.CategoryStruct.toQuiver.{0, 1} TopCat.{0} (CategoryTheory.Category.toCategoryStruct.{0, 1} TopCat.{0} instTopCatLargeCategory.{0})) Y Z}, (Embedding.{0, 0} (Prefunctor.obj.{1, 1, 1, 1} TopCat.{0} (CategoryTheory.CategoryStruct.toQuiver.{0, 1} TopCat.{0} (CategoryTheory.Category.toCategoryStruct.{0, 1} TopCat.{0} instTopCatLargeCategory.{0})) Type (CategoryTheory.CategoryStruct.toQuiver.{0, 1} Type (CategoryTheory.Category.toCategoryStruct.{0, 1} Type CategoryTheory.types.{0})) (CategoryTheory.Functor.toPrefunctor.{0, 0, 1, 1} TopCat.{0} instTopCatLargeCategory.{0} Type CategoryTheory.types.{0} (CategoryTheory.forget.{1, 0, 0} TopCat.{0} instTopCatLargeCategory.{0} 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TopCat.topCat_hasLimits.{0}) (CategoryTheory.Limits.pair.{0, 1} TopCat.{0} instTopCatLargeCategory.{0} X Z)) f g)))
+Case conversion may be inaccurate. Consider using '#align Top.embedding_prod_map TopCat.embedding_prod_mapₓ'. -/
 theorem embedding_prod_map {W X Y Z : TopCat} {f : W ⟶ X} {g : Y ⟶ Z} (hf : Embedding f)
     (hg : Embedding g) : Embedding (Limits.prod.map f g) :=
   ⟨inducing_prod_map hf.to_inducing hg.to_inducing,

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

Moves definition of and lemmas related to Set.Subsingleton and Set.Nontrivial to a new file, so that Basic can be shorter.

@@ -7,7 +7,7 @@ import Mathlib.Topology.Category.TopCat.EpiMono
 import Mathlib.Topology.Category.TopCat.Limits.Basic
 import Mathlib.CategoryTheory.Limits.Shapes.Products
 import Mathlib.CategoryTheory.Limits.ConcreteCategory
-import Mathlib.Data.Set.Basic
+import Mathlib.Data.Set.Subsingleton
 
 #align_import topology.category.Top.limits.products from "leanprover-community/mathlib"@"178a32653e369dce2da68dc6b2694e385d484ef1"
 

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

@@ -179,7 +179,7 @@ def prodBinaryFanIsLimit (X Y : TopCat.{u}) : IsLimit (prodBinaryFan X Y) where
     toFun := fun s => (S.fst s, S.snd s)
     -- Porting note: continuity failed again here. Lean cannot infer
     -- ContinuousMapClass (X ⟶ Y) X Y for X Y : TopCat which may be one of the problems
-    continuous_toFun := (Continuous.prod_mk)
+    continuous_toFun := Continuous.prod_mk
       (BinaryFan.fst S).continuous_toFun (BinaryFan.snd S).continuous_toFun }
   fac := by
     rintro S (_ | _) <;> {dsimp; ext; rfl}

All these lemmas refer to the range of some function being open/range (i.e. isOpen or isClosed).

@@ -354,7 +354,7 @@ theorem binaryCofan_isColimit_iff {X Y : TopCat} (c : BinaryCofan X Y) :
             apply Continuous.comp
             · exact f.continuous_toFun
             · continuity
-          · exact h₁.open_range
+          · exact h₁.isOpen_range
         · revert h x
           apply (IsOpen.continuousOn_iff _).mp
           · rw [continuousOn_iff_continuous_restrict]
@@ -373,7 +373,7 @@ theorem binaryCofan_isColimit_iff {X Y : TopCat} (c : BinaryCofan X Y) :
                 exact continuous_subtype_val
           · change IsOpen (Set.range c.inl)ᶜ
             rw [← eq_compl_iff_isCompl.mpr h₃.symm]
-            exact h₂.open_range
+            exact h₂.isOpen_range
       · intro T f g
         ext x
         refine' (dif_pos _).trans _

This is a very large PR, but it has been reviewed piecemeal already in PRs to the bump/v4.7.0 branch as we update to intermediate nightlies.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: damiano <adomani@gmail.com>

@@ -52,6 +52,7 @@ def piFanIsLimit {ι : Type v} (α : ι → TopCatMax.{v, u}) : IsLimit (piFan 
     intro S m h
     apply ContinuousMap.ext; intro x
     funext i
+    set_option tactic.skipAssignedInstances false in
     dsimp
     rw [ContinuousMap.coe_mk, ← h ⟨i⟩]
     rfl

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

• converts "--porting note" into "-- Porting note";
• converts "porting note" into "Porting note".

@@ -184,7 +184,7 @@ def prodBinaryFanIsLimit (X Y : TopCat.{u}) : IsLimit (prodBinaryFan X Y) where
     rintro S (_ | _) <;> {dsimp; ext; rfl}
   uniq := by
     intro S m h
-    -- porting note: used to be `ext x`
+    -- Porting note: used to be `ext x`
     refine' ContinuousMap.ext (fun (x : ↥(S.pt)) => Prod.ext _ _)
     · specialize h ⟨WalkingPair.left⟩
       apply_fun fun e => e x at h

• Remove Data.Set.Basic from scripts/noshake.json.
• Remove an exception that was used by examples only, move these examples to a new test file.
• Drop an exception for Order.Filter.Basic dependency on Control.Traversable.Instances, as the relevant parts were moved to Order.Filter.ListTraverse.
• Run lake exe shake --fix.

@@ -7,6 +7,7 @@ import Mathlib.Topology.Category.TopCat.EpiMono
 import Mathlib.Topology.Category.TopCat.Limits.Basic
 import Mathlib.CategoryTheory.Limits.Shapes.Products
 import Mathlib.CategoryTheory.Limits.ConcreteCategory
+import Mathlib.Data.Set.Basic
 
 #align_import topology.category.Top.limits.products from "leanprover-community/mathlib"@"178a32653e369dce2da68dc6b2694e385d484ef1"
 

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: Patrick Massot, Scott Morrison, Mario Carneiro, Andrew Yang
 import Mathlib.Topology.Category.TopCat.EpiMono
 import Mathlib.Topology.Category.TopCat.Limits.Basic
 import Mathlib.CategoryTheory.Limits.Shapes.Products
+import Mathlib.CategoryTheory.Limits.ConcreteCategory
 
 #align_import topology.category.Top.limits.products from "leanprover-community/mathlib"@"178a32653e369dce2da68dc6b2694e385d484ef1"
 

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

@@ -133,7 +133,7 @@ theorem sigmaIsoSigma_hom_ι_apply {ι : Type v} (α : ι → TopCatMax.{v, u})
 @[simp]
 theorem sigmaIsoSigma_inv_apply {ι : Type v} (α : ι → TopCatMax.{v, u}) (i : ι) (x : α i) :
     (sigmaIsoSigma α).inv ⟨i, x⟩ = (Sigma.ι α i : _) x := by
-  rw [← sigmaIsoSigma_hom_ι_apply, ← comp_app, ←comp_app, Iso.hom_inv_id,
+  rw [← sigmaIsoSigma_hom_ι_apply, ← comp_app, ← comp_app, Iso.hom_inv_id,
     Category.comp_id]
 #align Top.sigma_iso_sigma_inv_apply TopCat.sigmaIsoSigma_inv_apply
 

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

@@ -5,6 +5,7 @@ Authors: Patrick Massot, Scott Morrison, Mario Carneiro, Andrew Yang
 -/
 import Mathlib.Topology.Category.TopCat.EpiMono
 import Mathlib.Topology.Category.TopCat.Limits.Basic
+import Mathlib.CategoryTheory.Limits.Shapes.Products
 
 #align_import topology.category.Top.limits.products from "leanprover-community/mathlib"@"178a32653e369dce2da68dc6b2694e385d484ef1"
 

I've also got a change to make this required, but I'd like to land this first.

@@ -340,7 +340,7 @@ theorem binaryCofan_isColimit_iff {X Y : TopCat} (c : BinaryCofan X Y) :
             else g ((Equiv.ofInjective _ h₂.inj).symm ⟨x, (this x).resolve_left h⟩)
         rw [continuous_iff_continuousAt]
         intro x
-        by_cases x ∈ Set.range c.inl
+        by_cases h : x ∈ Set.range c.inl
         · revert h x
           apply (IsOpen.continuousOn_iff _).mp
           · rw [continuousOn_iff_continuous_restrict]

This eliminates (fun a ↦ β) α in the type when applying a FunLike.

Co-authored-by: Matthew Ballard <matt@mrb.email> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -132,7 +132,7 @@ theorem sigmaIsoSigma_hom_ι_apply {ι : Type v} (α : ι → TopCatMax.{v, u})
 @[simp]
 theorem sigmaIsoSigma_inv_apply {ι : Type v} (α : ι → TopCatMax.{v, u}) (i : ι) (x : α i) :
     (sigmaIsoSigma α).inv ⟨i, x⟩ = (Sigma.ι α i : _) x := by
-  rw [← sigmaIsoSigma_hom_ι_apply, ← comp_app, ←comp_app, Category.assoc, Iso.hom_inv_id,
+  rw [← sigmaIsoSigma_hom_ι_apply, ← comp_app, ←comp_app, Iso.hom_inv_id,
     Category.comp_id]
 #align Top.sigma_iso_sigma_inv_apply TopCat.sigmaIsoSigma_inv_apply
 

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

@@ -58,8 +58,7 @@ def piFanIsLimit {ι : Type v} (α : ι → TopCatMax.{v, u}) : IsLimit (piFan 
 /-- The product is homeomorphic to the product of the underlying spaces,
 equipped with the product topology.
 -/
-def piIsoPi {ι : Type v} (α : ι → TopCatMax.{v, u}) :
-  ∏ α ≅ TopCat.of (∀ i, α i) :=
+def piIsoPi {ι : Type v} (α : ι → TopCatMax.{v, u}) : ∏ α ≅ TopCat.of (∀ i, α i) :=
   (limit.isLimit _).conePointUniqueUpToIso (piFanIsLimit α)
 #align Top.pi_iso_pi TopCat.piIsoPi
 

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

@@ -325,8 +325,6 @@ theorem binaryCofan_isColimit_iff {X Y : TopCat} (c : BinaryCofan X Y) :
         (binaryCofanIsColimit X Y)).symm.openEmbedding.comp openEmbedding_inl,
           (homeoOfIso <| h.coconePointUniqueUpToIso
             (binaryCofanIsColimit X Y)).symm.openEmbedding.comp openEmbedding_inr, _⟩
-      simp only [Functor.map_comp]
-
       erw [Set.range_comp, ← eq_compl_iff_isCompl, coe_comp, coe_comp, Set.range_comp _ Sum.inr,
         ← Set.image_compl_eq (homeoOfIso <| h.coconePointUniqueUpToIso
             (binaryCofanIsColimit X Y)).symm.bijective, Set.compl_range_inr, Set.image_comp]

• depends on: #5966

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

@@ -2,15 +2,12 @@
 Copyright (c) 2017 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Patrick Massot, Scott Morrison, Mario Carneiro, Andrew Yang
-
-! This file was ported from Lean 3 source module topology.category.Top.limits.products
-! 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.Topology.Category.TopCat.EpiMono
 import Mathlib.Topology.Category.TopCat.Limits.Basic
 
+#align_import topology.category.Top.limits.products from "leanprover-community/mathlib"@"178a32653e369dce2da68dc6b2694e385d484ef1"
+
 /-!
 # Products and coproducts in the category of topological spaces
 -/

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

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

@@ -178,7 +178,7 @@ def prodBinaryFanIsLimit (X Y : TopCat.{u}) : IsLimit (prodBinaryFan X Y) where
   lift := fun S : BinaryFan X Y => {
     toFun := fun s => (S.fst s, S.snd s)
     -- Porting note: continuity failed again here. Lean cannot infer
-    -- ContinuousMapClass (X ⟶  Y) X Y for X Y : TopCat which may be one of the problems
+    -- ContinuousMapClass (X ⟶ Y) X Y for X Y : TopCat which may be one of the problems
     continuous_toFun := (Continuous.prod_mk)
       (BinaryFan.fst S).continuous_toFun (BinaryFan.snd S).continuous_toFun }
   fac := by

Co-authored-by: Yury G. Kudryashov <urkud@urkud.name>

@@ -361,7 +361,7 @@ theorem binaryCofan_isColimit_iff {X Y : TopCat} (c : BinaryCofan X Y) :
           apply (IsOpen.continuousOn_iff _).mp
           · rw [continuousOn_iff_continuous_restrict]
             have : ∀ a, a ∉ Set.range c.inl → a ∈ Set.range c.inr := by
-              rintro a (h : a ∈ Set.range c.inlᶜ)
+              rintro a (h : a ∈ (Set.range c.inl)ᶜ)
               rwa [eq_compl_iff_isCompl.mpr h₃.symm]
             convert_to Continuous
                 (g ∘ (Homeomorph.ofEmbedding _ h₂.toEmbedding).symm ∘ Subtype.map _ this)
@@ -373,7 +373,7 @@ theorem binaryCofan_isColimit_iff {X Y : TopCat} (c : BinaryCofan X Y) :
               · continuity
               · rw [embedding_subtype_val.toInducing.continuous_iff]
                 exact continuous_subtype_val
-          · change IsOpen (Set.range c.inlᶜ)
+          · change IsOpen (Set.range c.inl)ᶜ
             rw [← eq_compl_iff_isCompl.mpr h₃.symm]
             exact h₂.open_range
       · intro T f g

Changes are of the form

• some_tactic at h⊢ -> some_tactic at h ⊢
• some_tactic at h -> some_tactic at h

@@ -188,10 +188,10 @@ def prodBinaryFanIsLimit (X Y : TopCat.{u}) : IsLimit (prodBinaryFan X Y) where
     -- porting note: used to be `ext x`
     refine' ContinuousMap.ext (fun (x : ↥(S.pt)) => Prod.ext _ _)
     · specialize h ⟨WalkingPair.left⟩
-      apply_fun fun e => e x  at h
+      apply_fun fun e => e x at h
       exact h
     · specialize h ⟨WalkingPair.right⟩
-      apply_fun fun e => e x  at h
+      apply_fun fun e => e x at h
       exact h
 #align Top.prod_binary_fan_is_limit TopCat.prodBinaryFanIsLimit
 

@@ -136,8 +136,8 @@ theorem sigmaIsoSigma_hom_ι_apply {ι : Type v} (α : ι → TopCatMax.{v, u})
 @[simp]
 theorem sigmaIsoSigma_inv_apply {ι : Type v} (α : ι → TopCatMax.{v, u}) (i : ι) (x : α i) :
     (sigmaIsoSigma α).inv ⟨i, x⟩ = (Sigma.ι α i : _) x := by
-  rw [← sigmaIsoSigma_hom_ι_apply, ← comp_app]
-  simp
+  rw [← sigmaIsoSigma_hom_ι_apply, ← comp_app, ←comp_app, Category.assoc, Iso.hom_inv_id,
+    Category.comp_id]
 #align Top.sigma_iso_sigma_inv_apply TopCat.sigmaIsoSigma_inv_apply
 
 -- Porting note: cannot use .topologicalSpace in place .str
@@ -265,13 +265,11 @@ theorem range_prod_map {W X Y Z : TopCat.{u}} (f : W ⟶ Y) (g : X ⟶ Z) :
     · simp only [← comp_apply, Category.assoc]
       erw [Limits.prod.map_fst]
       rw [TopCat.prodIsoProd_inv_fst_assoc,TopCat.comp_app]
-      have : (forget TopCat).map prodFst (x₁, x₂) = x₁ := rfl
-      rw [this, hx₁]
+      exact hx₁
     · simp only [← comp_apply, Category.assoc]
       erw [Limits.prod.map_snd]
       rw [TopCat.prodIsoProd_inv_snd_assoc,TopCat.comp_app]
-      have : (forget TopCat).map prodSnd (x₁, x₂) = x₂ := rfl
-      rw [this, hx₂]
+      exact hx₂
 #align Top.range_prod_map TopCat.range_prod_map
 
 theorem inducing_prod_map {W X Y Z : TopCat.{u}} {f : W ⟶ X} {g : Y ⟶ Z} (hf : Inducing f)
@@ -331,10 +329,11 @@ theorem binaryCofan_isColimit_iff {X Y : TopCat} (c : BinaryCofan X Y) :
           (homeoOfIso <| h.coconePointUniqueUpToIso
             (binaryCofanIsColimit X Y)).symm.openEmbedding.comp openEmbedding_inr, _⟩
       simp only [Functor.map_comp]
-      erw [Set.range_comp, ← eq_compl_iff_isCompl, Set.range_comp _ Sum.inr,
+
+      erw [Set.range_comp, ← eq_compl_iff_isCompl, coe_comp, coe_comp, Set.range_comp _ Sum.inr,
         ← Set.image_compl_eq (homeoOfIso <| h.coconePointUniqueUpToIso
-          (binaryCofanIsColimit X Y)).symm.bijective, Set.compl_range_inr.symm]
-      congr 1
+            (binaryCofanIsColimit X Y)).symm.bijective, Set.compl_range_inr, Set.image_comp]
+      aesop
     · rintro ⟨h₁, h₂, h₃⟩
       have : ∀ x, x ∈ Set.range c.inl ∨ x ∈ Set.range c.inr := by
         rw [eq_compl_iff_isCompl.mpr h₃.symm]

Too often tempted to change these during other PRs, so doing a mass edit here.

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

@@ -312,7 +312,7 @@ def binaryCofanIsColimit (X Y : TopCat.{u}) : IsColimit (TopCat.binaryCofan X Y)
     rfl
   · intro s m h₁ h₂
     ext (x | x)
-    exacts[(ConcreteCategory.congr_hom h₁ x : _), (ConcreteCategory.congr_hom h₂ x : _)]
+    exacts [(ConcreteCategory.congr_hom h₁ x : _), (ConcreteCategory.congr_hom h₂ x : _)]
 #align Top.binary_cofan_is_colimit TopCat.binaryCofanIsColimit
 
 theorem binaryCofan_isColimit_iff {X Y : TopCat} (c : BinaryCofan X Y) :
@@ -394,5 +394,3 @@ theorem binaryCofan_isColimit_iff {X Y : TopCat} (c : BinaryCofan X Y) :
         change m x = dite _ _ _
         split_ifs <;> exact congr_arg _ (Equiv.apply_ofInjective_symm _ ⟨_, _⟩).symm
 #align Top.binary_cofan_is_colimit_iff TopCat.binaryCofan_isColimit_iff
-
-

Run codespell Mathlib and keep some suggestions.

@@ -32,7 +32,7 @@ namespace TopCat
 
 variable {J : Type v} [SmallCategory J]
 
-/-- The projection from the product as a bundled continous map. -/
+/-- The projection from the product as a bundled continuous map. -/
 abbrev piπ {ι : Type v} (α : ι → TopCatMax.{v, u}) (i : ι) : TopCat.of (∀ i, α i) ⟶ α i :=
   ⟨fun f => f i, continuous_apply i⟩
 #align Top.pi_π TopCat.piπ
@@ -87,7 +87,7 @@ theorem piIsoPi_hom_apply {ι : Type v} (α : ι → TopCatMax.{v, u}) (i : ι)
 #align Top.pi_iso_pi_hom_apply TopCat.piIsoPi_hom_apply
 
 -- Porting note: Lean doesn't automatically reduce TopCat.of X|>.α to X now
-/-- The inclusion to the coproduct as a bundled continous map. -/
+/-- The inclusion to the coproduct as a bundled continuous map. -/
 abbrev sigmaι {ι : Type v} (α : ι → TopCatMax.{v,u}) (i : ι) : α i ⟶ TopCat.of (Σi, α i) := by
   refine ContinuousMap.mk ?_ ?_
   · dsimp

@@ -8,8 +8,8 @@ Authors: Patrick Massot, Scott Morrison, Mario Carneiro, Andrew Yang
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
-import Mathlib.Topology.Category.Top.EpiMono
-import Mathlib.Topology.Category.Top.Limits.Basic
+import Mathlib.Topology.Category.TopCat.EpiMono
+import Mathlib.Topology.Category.TopCat.Limits.Basic
 
 /-!
 # Products and coproducts in the category of topological spaces

As discussed on Zulip

Renames

• supₛ → sSup
• infₛ → sInf
• supᵢ → iSup
• infᵢ → iInf
• bsupₛ → bsSup
• binfₛ → bsInf
• bsupᵢ → biSup
• binfᵢ → biInf
• csupₛ → csSup
• cinfₛ → csInf
• csupᵢ → ciSup
• cinfᵢ → ciInf
• unionₛ → sUnion
• interₛ → sInter
• unionᵢ → iUnion
• interᵢ → iInter
• bunionₛ → bsUnion
• binterₛ → bsInter
• bunionᵢ → biUnion
• binterᵢ → biInter

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

@@ -146,7 +146,7 @@ theorem induced_of_isLimit {F : J ⥤ TopCatMax.{v, u}} (C : Cone F) (hC : IsLim
   let homeo := homeoOfIso (hC.conePointUniqueUpToIso (limitConeInfiIsLimit F))
   refine' homeo.inducing.induced.trans _
   change induced homeo (⨅ j : J, _) = _
-  simp [induced_infᵢ, induced_compose]
+  simp [induced_iInf, induced_compose]
   rfl
 #align Top.induced_of_is_limit TopCat.induced_of_isLimit
 

Co-authored-by: Moritz Firsching <firsching@google.com> Co-authored-by: Matthew Robert Ballard <100034030+mattrobball@users.noreply.github.com> Co-authored-by: ChrisHughes24 <chrishughes24@gmail.com>

@@ -237,7 +237,7 @@ theorem prodIsoProd_inv_snd (X Y : TopCat.{u}) :
     (prodIsoProd X Y).inv ≫ Limits.prod.snd = prodSnd := by simp [Iso.inv_comp_eq]
 #align Top.prod_iso_prod_inv_snd TopCat.prodIsoProd_inv_snd
 
-theorem prod_topology {X Y : TopCat} :
+theorem prod_topology {X Y : TopCat.{u}} :
     (X ⨯ Y).str =
       induced (Limits.prod.fst : X ⨯ Y ⟶ _) X.str ⊓
         induced (Limits.prod.snd : X ⨯ Y ⟶ _) Y.str := by
@@ -274,7 +274,7 @@ theorem range_prod_map {W X Y Z : TopCat.{u}} (f : W ⟶ Y) (g : X ⟶ Z) :
       rw [this, hx₂]
 #align Top.range_prod_map TopCat.range_prod_map
 
-theorem inducing_prod_map {W X Y Z : TopCat} {f : W ⟶ X} {g : Y ⟶ Z} (hf : Inducing f)
+theorem inducing_prod_map {W X Y Z : TopCat.{u}} {f : W ⟶ X} {g : Y ⟶ Z} (hf : Inducing f)
     (hg : Inducing g) : Inducing (Limits.prod.map f g) := by
   constructor
   simp only [prod_topology, induced_compose, ← coe_comp, Limits.prod.map_fst, Limits.prod.map_snd,
@@ -283,7 +283,7 @@ theorem inducing_prod_map {W X Y Z : TopCat} {f : W ⟶ X} {g : Y ⟶ Z} (hf : I
   rw [← @induced_compose _ _ _ _ _ f, ← @induced_compose _ _ _ _ _ g, ← hf.induced, ← hg.induced]
 #align Top.inducing_prod_map TopCat.inducing_prod_map
 
-theorem embedding_prod_map {W X Y Z : TopCat} {f : W ⟶ X} {g : Y ⟶ Z} (hf : Embedding f)
+theorem embedding_prod_map {W X Y Z : TopCat.{u}} {f : W ⟶ X} {g : Y ⟶ Z} (hf : Embedding f)
     (hg : Embedding g) : Embedding (Limits.prod.map f g) :=
   ⟨inducing_prod_map hf.toInducing hg.toInducing, by
     haveI := (TopCat.mono_iff_injective _).mpr hf.inj
@@ -292,3 +292,107 @@ theorem embedding_prod_map {W X Y Z : TopCat} {f : W ⟶ X} {g : Y ⟶ Z} (hf :
 #align Top.embedding_prod_map TopCat.embedding_prod_map
 
 end Prod
+
+/-- The binary coproduct cofan in `TopCat`. -/
+protected def binaryCofan (X Y : TopCat.{u}) : BinaryCofan X Y :=
+  BinaryCofan.mk (⟨Sum.inl, by continuity⟩ : X ⟶ TopCat.of (Sum X Y)) ⟨Sum.inr, by continuity⟩
+#align Top.binary_cofan TopCat.binaryCofan
+
+/-- The constructed binary coproduct cofan in `TopCat` is the coproduct. -/
+def binaryCofanIsColimit (X Y : TopCat.{u}) : IsColimit (TopCat.binaryCofan X Y) := by
+  refine' Limits.BinaryCofan.isColimitMk (fun s =>
+    {toFun := Sum.elim s.inl s.inr, continuous_toFun := _ }) _ _ _
+  · apply
+      Continuous.sum_elim (BinaryCofan.inl s).continuous_toFun (BinaryCofan.inr s).continuous_toFun
+  · intro s
+    ext
+    rfl
+  · intro s
+    ext
+    rfl
+  · intro s m h₁ h₂
+    ext (x | x)
+    exacts[(ConcreteCategory.congr_hom h₁ x : _), (ConcreteCategory.congr_hom h₂ x : _)]
+#align Top.binary_cofan_is_colimit TopCat.binaryCofanIsColimit
+
+theorem binaryCofan_isColimit_iff {X Y : TopCat} (c : BinaryCofan X Y) :
+    Nonempty (IsColimit c) ↔
+      OpenEmbedding c.inl ∧ OpenEmbedding c.inr ∧ IsCompl (Set.range c.inl) (Set.range c.inr) := by
+  classical
+    constructor
+    · rintro ⟨h⟩
+      rw [← show _ = c.inl from
+          h.comp_coconePointUniqueUpToIso_inv (binaryCofanIsColimit X Y) ⟨WalkingPair.left⟩,
+        ← show _ = c.inr from
+          h.comp_coconePointUniqueUpToIso_inv (binaryCofanIsColimit X Y) ⟨WalkingPair.right⟩]
+      dsimp
+      refine' ⟨(homeoOfIso <| h.coconePointUniqueUpToIso
+        (binaryCofanIsColimit X Y)).symm.openEmbedding.comp openEmbedding_inl,
+          (homeoOfIso <| h.coconePointUniqueUpToIso
+            (binaryCofanIsColimit X Y)).symm.openEmbedding.comp openEmbedding_inr, _⟩
+      simp only [Functor.map_comp]
+      erw [Set.range_comp, ← eq_compl_iff_isCompl, Set.range_comp _ Sum.inr,
+        ← Set.image_compl_eq (homeoOfIso <| h.coconePointUniqueUpToIso
+          (binaryCofanIsColimit X Y)).symm.bijective, Set.compl_range_inr.symm]
+      congr 1
+    · rintro ⟨h₁, h₂, h₃⟩
+      have : ∀ x, x ∈ Set.range c.inl ∨ x ∈ Set.range c.inr := by
+        rw [eq_compl_iff_isCompl.mpr h₃.symm]
+        exact fun _ => or_not
+      refine' ⟨BinaryCofan.IsColimit.mk _ _ _ _ _⟩
+      · intro T f g
+        refine' ContinuousMap.mk _ _
+        · exact fun x =>
+            if h : x ∈ Set.range c.inl then f ((Equiv.ofInjective _ h₁.inj).symm ⟨x, h⟩)
+            else g ((Equiv.ofInjective _ h₂.inj).symm ⟨x, (this x).resolve_left h⟩)
+        rw [continuous_iff_continuousAt]
+        intro x
+        by_cases x ∈ Set.range c.inl
+        · revert h x
+          apply (IsOpen.continuousOn_iff _).mp
+          · rw [continuousOn_iff_continuous_restrict]
+            convert_to Continuous (f ∘ (Homeomorph.ofEmbedding _ h₁.toEmbedding).symm)
+            · ext ⟨x, hx⟩
+              exact dif_pos hx
+            apply Continuous.comp
+            · exact f.continuous_toFun
+            · continuity
+          · exact h₁.open_range
+        · revert h x
+          apply (IsOpen.continuousOn_iff _).mp
+          · rw [continuousOn_iff_continuous_restrict]
+            have : ∀ a, a ∉ Set.range c.inl → a ∈ Set.range c.inr := by
+              rintro a (h : a ∈ Set.range c.inlᶜ)
+              rwa [eq_compl_iff_isCompl.mpr h₃.symm]
+            convert_to Continuous
+                (g ∘ (Homeomorph.ofEmbedding _ h₂.toEmbedding).symm ∘ Subtype.map _ this)
+            · ext ⟨x, hx⟩
+              exact dif_neg hx
+            apply Continuous.comp
+            · exact g.continuous_toFun
+            · apply Continuous.comp
+              · continuity
+              · rw [embedding_subtype_val.toInducing.continuous_iff]
+                exact continuous_subtype_val
+          · change IsOpen (Set.range c.inlᶜ)
+            rw [← eq_compl_iff_isCompl.mpr h₃.symm]
+            exact h₂.open_range
+      · intro T f g
+        ext x
+        refine' (dif_pos _).trans _
+        · exact ⟨x, rfl⟩
+        · dsimp; conv_lhs => erw [Equiv.ofInjective_symm_apply]
+      · intro T f g
+        ext x
+        refine' (dif_neg _).trans _
+        · rintro ⟨y, e⟩
+          have : c.inr x ∈ Set.range c.inl ⊓ Set.range c.inr := ⟨⟨_, e⟩, ⟨_, rfl⟩⟩
+          rwa [disjoint_iff.mp h₃.1] at this
+        · exact congr_arg g (Equiv.ofInjective_symm_apply _ _)
+      · rintro T _ _ m rfl rfl
+        ext x
+        change m x = dite _ _ _
+        split_ifs <;> exact congr_arg _ (Equiv.apply_ofInjective_symm _ ⟨_, _⟩).symm
+#align Top.binary_cofan_is_colimit_iff TopCat.binaryCofan_isColimit_iff
+
+

Co-authored-by: Moritz Firsching <firsching@google.com> Co-authored-by: Matthew Robert Ballard <100034030+mattrobball@users.noreply.github.com>