category_theory.filtered ⟷ Mathlib.CategoryTheory.Filtered.Basic

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

@@ -3,11 +3,11 @@ Copyright (c) 2019 Reid Barton. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Reid Barton, Scott Morrison
 -/
-import CategoryTheory.FinCategory
+import CategoryTheory.FinCategory.Basic
 import CategoryTheory.Limits.Cones
 import CategoryTheory.Adjunction.Basic
 import CategoryTheory.Category.Preorder
-import CategoryTheory.Category.Ulift
+import CategoryTheory.Category.ULift
 
 #align_import category_theory.filtered from "leanprover-community/mathlib"@"ee05e9ce1322178f0c12004eb93c00d2c8c00ed2"
 

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

@@ -261,7 +261,7 @@ theorem sup_exists :
       apply Finset.mem_of_mem_insert_of_ne mf'
       contrapose! h
       obtain ⟨rfl, h⟩ := h
-      rw [heq_iff_eq, PSigma.mk.inj_iff] at h 
+      rw [heq_iff_eq, PSigma.mk.inj_iff] at h
       exact ⟨rfl, h.1.symm⟩
 #align category_theory.is_filtered.sup_exists CategoryTheory.IsFiltered.sup_exists
 -/
@@ -476,7 +476,7 @@ theorem bowtie {j₁ j₂ k₁ k₂ : C} (f₁ : j₁ ⟶ k₁) (g₁ : j₁ ⟶
   by
   obtain ⟨t, k₁t, k₂t, ht⟩ := span f₁ g₁
   obtain ⟨s, ts, hs⟩ := cocone_maps (f₂ ≫ k₁t) (g₂ ≫ k₂t)
-  simp_rw [category.assoc] at hs 
+  simp_rw [category.assoc] at hs
   exact ⟨s, k₁t ≫ ts, k₂t ≫ ts, by rw [reassoc_of ht], hs⟩
 #align category_theory.is_filtered.bowtie CategoryTheory.IsFiltered.bowtie
 -/
@@ -733,7 +733,7 @@ theorem inf_exists :
       apply Finset.mem_of_mem_insert_of_ne mf'
       contrapose! h
       obtain ⟨rfl, h⟩ := h
-      rw [heq_iff_eq, PSigma.mk.inj_iff] at h 
+      rw [heq_iff_eq, PSigma.mk.inj_iff] at h
       exact ⟨rfl, h.1.symm⟩
 #align category_theory.is_cofiltered.inf_exists CategoryTheory.IsCofiltered.inf_exists
 -/

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

@@ -216,7 +216,16 @@ variable {C} [IsFiltered C]
 #print CategoryTheory.IsFiltered.sup_objs_exists /-
 /-- Any finite collection of objects in a filtered category has an object "to the right".
 -/
-theorem sup_objs_exists (O : Finset C) : ∃ S : C, ∀ {X}, X ∈ O → Nonempty (X ⟶ S) := by classical
+theorem sup_objs_exists (O : Finset C) : ∃ S : C, ∀ {X}, X ∈ O → Nonempty (X ⟶ S) := by
+  classical
+  apply Finset.induction_on O
+  · exact ⟨is_filtered.nonempty.some, by rintro - ⟨⟩⟩
+  · rintro X O' nm ⟨S', w'⟩
+    use max X S'
+    rintro Y mY
+    obtain rfl | h := eq_or_ne Y X
+    · exact ⟨left_to_max _ _⟩
+    · exact ⟨(w' (Finset.mem_of_mem_insert_of_ne mY h)).some ≫ right_to_max _ _⟩
 #align category_theory.is_filtered.sup_objs_exists CategoryTheory.IsFiltered.sup_objs_exists
 -/
 
@@ -232,7 +241,28 @@ theorem sup_exists :
     ∃ (S : C) (T : ∀ {X : C}, X ∈ O → (X ⟶ S)),
       ∀ {X Y : C} (mX : X ∈ O) (mY : Y ∈ O) {f : X ⟶ Y},
         (⟨X, Y, mX, mY, f⟩ : Σ' (X Y : C) (mX : X ∈ O) (mY : Y ∈ O), X ⟶ Y) ∈ H → f ≫ T mY = T mX :=
-  by classical
+  by
+  classical
+  apply Finset.induction_on H
+  · obtain ⟨S, f⟩ := sup_objs_exists O
+    refine' ⟨S, fun X mX => (f mX).some, _⟩
+    rintro - - - - - ⟨⟩
+  · rintro ⟨X, Y, mX, mY, f⟩ H' nmf ⟨S', T', w'⟩
+    refine' ⟨coeq (f ≫ T' mY) (T' mX), fun Z mZ => T' mZ ≫ coeq_hom (f ≫ T' mY) (T' mX), _⟩
+    intro X' Y' mX' mY' f' mf'
+    rw [← category.assoc]
+    by_cases h : X = X' ∧ Y = Y'
+    · rcases h with ⟨rfl, rfl⟩
+      by_cases hf : f = f'
+      · subst hf
+        apply coeq_condition
+      · rw [@w' _ _ mX mY f' (by simpa [hf ∘ Eq.symm] using mf')]
+    · rw [@w' _ _ mX' mY' f' _]
+      apply Finset.mem_of_mem_insert_of_ne mf'
+      contrapose! h
+      obtain ⟨rfl, h⟩ := h
+      rw [heq_iff_eq, PSigma.mk.inj_iff] at h 
+      exact ⟨rfl, h.1.symm⟩
 #align category_theory.is_filtered.sup_exists CategoryTheory.IsFiltered.sup_exists
 -/
 
@@ -270,7 +300,22 @@ variable {J : Type v} [SmallCategory J] [FinCategory J]
 /-- If we have `is_filtered C`, then for any functor `F : J ⥤ C` with `fin_category J`,
 there exists a cocone over `F`.
 -/
-theorem cocone_nonempty (F : J ⥤ C) : Nonempty (Cocone F) := by classical
+theorem cocone_nonempty (F : J ⥤ C) : Nonempty (Cocone F) := by
+  classical
+  let O := finset.univ.image F.obj
+  let H : Finset (Σ' (X Y : C) (mX : X ∈ O) (mY : Y ∈ O), X ⟶ Y) :=
+    finset.univ.bUnion fun X : J =>
+      finset.univ.bUnion fun Y : J =>
+        finset.univ.image fun f : X ⟶ Y => ⟨F.obj X, F.obj Y, by simp, by simp, F.map f⟩
+  obtain ⟨Z, f, w⟩ := sup_exists O H
+  refine' ⟨⟨Z, ⟨fun X => f (by simp), _⟩⟩⟩
+  intro j j' g
+  dsimp
+  simp only [category.comp_id]
+  apply w
+  simp only [Finset.mem_univ, Finset.mem_biUnion, exists_and_left, exists_prop_of_true,
+    Finset.mem_image]
+  exact ⟨j, rfl, j', g, by simp⟩
 #align category_theory.is_filtered.cocone_nonempty CategoryTheory.IsFiltered.cocone_nonempty
 -/
 
@@ -643,7 +688,16 @@ variable {C} [IsCofiltered C]
 #print CategoryTheory.IsCofiltered.inf_objs_exists /-
 /-- Any finite collection of objects in a cofiltered category has an object "to the left".
 -/
-theorem inf_objs_exists (O : Finset C) : ∃ S : C, ∀ {X}, X ∈ O → Nonempty (S ⟶ X) := by classical
+theorem inf_objs_exists (O : Finset C) : ∃ S : C, ∀ {X}, X ∈ O → Nonempty (S ⟶ X) := by
+  classical
+  apply Finset.induction_on O
+  · exact ⟨is_cofiltered.nonempty.some, by rintro - ⟨⟩⟩
+  · rintro X O' nm ⟨S', w'⟩
+    use min X S'
+    rintro Y mY
+    obtain rfl | h := eq_or_ne Y X
+    · exact ⟨min_to_left _ _⟩
+    · exact ⟨min_to_right _ _ ≫ (w' (Finset.mem_of_mem_insert_of_ne mY h)).some⟩
 #align category_theory.is_cofiltered.inf_objs_exists CategoryTheory.IsCofiltered.inf_objs_exists
 -/
 
@@ -659,7 +713,28 @@ theorem inf_exists :
     ∃ (S : C) (T : ∀ {X : C}, X ∈ O → (S ⟶ X)),
       ∀ {X Y : C} (mX : X ∈ O) (mY : Y ∈ O) {f : X ⟶ Y},
         (⟨X, Y, mX, mY, f⟩ : Σ' (X Y : C) (mX : X ∈ O) (mY : Y ∈ O), X ⟶ Y) ∈ H → T mX ≫ f = T mY :=
-  by classical
+  by
+  classical
+  apply Finset.induction_on H
+  · obtain ⟨S, f⟩ := inf_objs_exists O
+    refine' ⟨S, fun X mX => (f mX).some, _⟩
+    rintro - - - - - ⟨⟩
+  · rintro ⟨X, Y, mX, mY, f⟩ H' nmf ⟨S', T', w'⟩
+    refine' ⟨Eq (T' mX ≫ f) (T' mY), fun Z mZ => eq_hom (T' mX ≫ f) (T' mY) ≫ T' mZ, _⟩
+    intro X' Y' mX' mY' f' mf'
+    rw [category.assoc]
+    by_cases h : X = X' ∧ Y = Y'
+    · rcases h with ⟨rfl, rfl⟩
+      by_cases hf : f = f'
+      · subst hf
+        apply eq_condition
+      · rw [@w' _ _ mX mY f' (by simpa [hf ∘ Eq.symm] using mf')]
+    · rw [@w' _ _ mX' mY' f' _]
+      apply Finset.mem_of_mem_insert_of_ne mf'
+      contrapose! h
+      obtain ⟨rfl, h⟩ := h
+      rw [heq_iff_eq, PSigma.mk.inj_iff] at h 
+      exact ⟨rfl, h.1.symm⟩
 #align category_theory.is_cofiltered.inf_exists CategoryTheory.IsCofiltered.inf_exists
 -/
 
@@ -697,7 +772,23 @@ variable {J : Type w} [SmallCategory J] [FinCategory J]
 /-- If we have `is_cofiltered C`, then for any functor `F : J ⥤ C` with `fin_category J`,
 there exists a cone over `F`.
 -/
-theorem cone_nonempty (F : J ⥤ C) : Nonempty (Cone F) := by classical
+theorem cone_nonempty (F : J ⥤ C) : Nonempty (Cone F) := by
+  classical
+  let O := finset.univ.image F.obj
+  let H : Finset (Σ' (X Y : C) (mX : X ∈ O) (mY : Y ∈ O), X ⟶ Y) :=
+    finset.univ.bUnion fun X : J =>
+      finset.univ.bUnion fun Y : J =>
+        finset.univ.image fun f : X ⟶ Y => ⟨F.obj X, F.obj Y, by simp, by simp, F.map f⟩
+  obtain ⟨Z, f, w⟩ := inf_exists O H
+  refine' ⟨⟨Z, ⟨fun X => f (by simp), _⟩⟩⟩
+  intro j j' g
+  dsimp
+  simp only [category.id_comp]
+  symm
+  apply w
+  simp only [Finset.mem_univ, Finset.mem_biUnion, exists_and_left, exists_prop_of_true,
+    Finset.mem_image]
+  exact ⟨j, rfl, j', g, by simp⟩
 #align category_theory.is_cofiltered.cone_nonempty CategoryTheory.IsCofiltered.cone_nonempty
 -/
 

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

@@ -216,16 +216,7 @@ variable {C} [IsFiltered C]
 #print CategoryTheory.IsFiltered.sup_objs_exists /-
 /-- Any finite collection of objects in a filtered category has an object "to the right".
 -/
-theorem sup_objs_exists (O : Finset C) : ∃ S : C, ∀ {X}, X ∈ O → Nonempty (X ⟶ S) := by
-  classical
-  apply Finset.induction_on O
-  · exact ⟨is_filtered.nonempty.some, by rintro - ⟨⟩⟩
-  · rintro X O' nm ⟨S', w'⟩
-    use max X S'
-    rintro Y mY
-    obtain rfl | h := eq_or_ne Y X
-    · exact ⟨left_to_max _ _⟩
-    · exact ⟨(w' (Finset.mem_of_mem_insert_of_ne mY h)).some ≫ right_to_max _ _⟩
+theorem sup_objs_exists (O : Finset C) : ∃ S : C, ∀ {X}, X ∈ O → Nonempty (X ⟶ S) := by classical
 #align category_theory.is_filtered.sup_objs_exists CategoryTheory.IsFiltered.sup_objs_exists
 -/
 
@@ -241,28 +232,7 @@ theorem sup_exists :
     ∃ (S : C) (T : ∀ {X : C}, X ∈ O → (X ⟶ S)),
       ∀ {X Y : C} (mX : X ∈ O) (mY : Y ∈ O) {f : X ⟶ Y},
         (⟨X, Y, mX, mY, f⟩ : Σ' (X Y : C) (mX : X ∈ O) (mY : Y ∈ O), X ⟶ Y) ∈ H → f ≫ T mY = T mX :=
-  by
-  classical
-  apply Finset.induction_on H
-  · obtain ⟨S, f⟩ := sup_objs_exists O
-    refine' ⟨S, fun X mX => (f mX).some, _⟩
-    rintro - - - - - ⟨⟩
-  · rintro ⟨X, Y, mX, mY, f⟩ H' nmf ⟨S', T', w'⟩
-    refine' ⟨coeq (f ≫ T' mY) (T' mX), fun Z mZ => T' mZ ≫ coeq_hom (f ≫ T' mY) (T' mX), _⟩
-    intro X' Y' mX' mY' f' mf'
-    rw [← category.assoc]
-    by_cases h : X = X' ∧ Y = Y'
-    · rcases h with ⟨rfl, rfl⟩
-      by_cases hf : f = f'
-      · subst hf
-        apply coeq_condition
-      · rw [@w' _ _ mX mY f' (by simpa [hf ∘ Eq.symm] using mf')]
-    · rw [@w' _ _ mX' mY' f' _]
-      apply Finset.mem_of_mem_insert_of_ne mf'
-      contrapose! h
-      obtain ⟨rfl, h⟩ := h
-      rw [heq_iff_eq, PSigma.mk.inj_iff] at h 
-      exact ⟨rfl, h.1.symm⟩
+  by classical
 #align category_theory.is_filtered.sup_exists CategoryTheory.IsFiltered.sup_exists
 -/
 
@@ -300,22 +270,7 @@ variable {J : Type v} [SmallCategory J] [FinCategory J]
 /-- If we have `is_filtered C`, then for any functor `F : J ⥤ C` with `fin_category J`,
 there exists a cocone over `F`.
 -/
-theorem cocone_nonempty (F : J ⥤ C) : Nonempty (Cocone F) := by
-  classical
-  let O := finset.univ.image F.obj
-  let H : Finset (Σ' (X Y : C) (mX : X ∈ O) (mY : Y ∈ O), X ⟶ Y) :=
-    finset.univ.bUnion fun X : J =>
-      finset.univ.bUnion fun Y : J =>
-        finset.univ.image fun f : X ⟶ Y => ⟨F.obj X, F.obj Y, by simp, by simp, F.map f⟩
-  obtain ⟨Z, f, w⟩ := sup_exists O H
-  refine' ⟨⟨Z, ⟨fun X => f (by simp), _⟩⟩⟩
-  intro j j' g
-  dsimp
-  simp only [category.comp_id]
-  apply w
-  simp only [Finset.mem_univ, Finset.mem_biUnion, exists_and_left, exists_prop_of_true,
-    Finset.mem_image]
-  exact ⟨j, rfl, j', g, by simp⟩
+theorem cocone_nonempty (F : J ⥤ C) : Nonempty (Cocone F) := by classical
 #align category_theory.is_filtered.cocone_nonempty CategoryTheory.IsFiltered.cocone_nonempty
 -/
 
@@ -688,16 +643,7 @@ variable {C} [IsCofiltered C]
 #print CategoryTheory.IsCofiltered.inf_objs_exists /-
 /-- Any finite collection of objects in a cofiltered category has an object "to the left".
 -/
-theorem inf_objs_exists (O : Finset C) : ∃ S : C, ∀ {X}, X ∈ O → Nonempty (S ⟶ X) := by
-  classical
-  apply Finset.induction_on O
-  · exact ⟨is_cofiltered.nonempty.some, by rintro - ⟨⟩⟩
-  · rintro X O' nm ⟨S', w'⟩
-    use min X S'
-    rintro Y mY
-    obtain rfl | h := eq_or_ne Y X
-    · exact ⟨min_to_left _ _⟩
-    · exact ⟨min_to_right _ _ ≫ (w' (Finset.mem_of_mem_insert_of_ne mY h)).some⟩
+theorem inf_objs_exists (O : Finset C) : ∃ S : C, ∀ {X}, X ∈ O → Nonempty (S ⟶ X) := by classical
 #align category_theory.is_cofiltered.inf_objs_exists CategoryTheory.IsCofiltered.inf_objs_exists
 -/
 
@@ -713,28 +659,7 @@ theorem inf_exists :
     ∃ (S : C) (T : ∀ {X : C}, X ∈ O → (S ⟶ X)),
       ∀ {X Y : C} (mX : X ∈ O) (mY : Y ∈ O) {f : X ⟶ Y},
         (⟨X, Y, mX, mY, f⟩ : Σ' (X Y : C) (mX : X ∈ O) (mY : Y ∈ O), X ⟶ Y) ∈ H → T mX ≫ f = T mY :=
-  by
-  classical
-  apply Finset.induction_on H
-  · obtain ⟨S, f⟩ := inf_objs_exists O
-    refine' ⟨S, fun X mX => (f mX).some, _⟩
-    rintro - - - - - ⟨⟩
-  · rintro ⟨X, Y, mX, mY, f⟩ H' nmf ⟨S', T', w'⟩
-    refine' ⟨Eq (T' mX ≫ f) (T' mY), fun Z mZ => eq_hom (T' mX ≫ f) (T' mY) ≫ T' mZ, _⟩
-    intro X' Y' mX' mY' f' mf'
-    rw [category.assoc]
-    by_cases h : X = X' ∧ Y = Y'
-    · rcases h with ⟨rfl, rfl⟩
-      by_cases hf : f = f'
-      · subst hf
-        apply eq_condition
-      · rw [@w' _ _ mX mY f' (by simpa [hf ∘ Eq.symm] using mf')]
-    · rw [@w' _ _ mX' mY' f' _]
-      apply Finset.mem_of_mem_insert_of_ne mf'
-      contrapose! h
-      obtain ⟨rfl, h⟩ := h
-      rw [heq_iff_eq, PSigma.mk.inj_iff] at h 
-      exact ⟨rfl, h.1.symm⟩
+  by classical
 #align category_theory.is_cofiltered.inf_exists CategoryTheory.IsCofiltered.inf_exists
 -/
 
@@ -772,23 +697,7 @@ variable {J : Type w} [SmallCategory J] [FinCategory J]
 /-- If we have `is_cofiltered C`, then for any functor `F : J ⥤ C` with `fin_category J`,
 there exists a cone over `F`.
 -/
-theorem cone_nonempty (F : J ⥤ C) : Nonempty (Cone F) := by
-  classical
-  let O := finset.univ.image F.obj
-  let H : Finset (Σ' (X Y : C) (mX : X ∈ O) (mY : Y ∈ O), X ⟶ Y) :=
-    finset.univ.bUnion fun X : J =>
-      finset.univ.bUnion fun Y : J =>
-        finset.univ.image fun f : X ⟶ Y => ⟨F.obj X, F.obj Y, by simp, by simp, F.map f⟩
-  obtain ⟨Z, f, w⟩ := inf_exists O H
-  refine' ⟨⟨Z, ⟨fun X => f (by simp), _⟩⟩⟩
-  intro j j' g
-  dsimp
-  simp only [category.id_comp]
-  symm
-  apply w
-  simp only [Finset.mem_univ, Finset.mem_biUnion, exists_and_left, exists_prop_of_true,
-    Finset.mem_image]
-  exact ⟨j, rfl, j', g, by simp⟩
+theorem cone_nonempty (F : J ⥤ C) : Nonempty (Cone F) := by classical
 #align category_theory.is_cofiltered.cone_nonempty CategoryTheory.IsCofiltered.cone_nonempty
 -/
 

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

@@ -3,11 +3,11 @@ Copyright (c) 2019 Reid Barton. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Reid Barton, Scott Morrison
 -/
-import Mathbin.CategoryTheory.FinCategory
-import Mathbin.CategoryTheory.Limits.Cones
-import Mathbin.CategoryTheory.Adjunction.Basic
-import Mathbin.CategoryTheory.Category.Preorder
-import Mathbin.CategoryTheory.Category.Ulift
+import CategoryTheory.FinCategory
+import CategoryTheory.Limits.Cones
+import CategoryTheory.Adjunction.Basic
+import CategoryTheory.Category.Preorder
+import CategoryTheory.Category.Ulift
 
 #align_import category_theory.filtered from "leanprover-community/mathlib"@"ee05e9ce1322178f0c12004eb93c00d2c8c00ed2"
 

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

@@ -2,11 +2,6 @@
 Copyright (c) 2019 Reid Barton. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Reid Barton, Scott Morrison
-
-! This file was ported from Lean 3 source module category_theory.filtered
-! leanprover-community/mathlib commit ee05e9ce1322178f0c12004eb93c00d2c8c00ed2
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.CategoryTheory.FinCategory
 import Mathbin.CategoryTheory.Limits.Cones
@@ -14,6 +9,8 @@ import Mathbin.CategoryTheory.Adjunction.Basic
 import Mathbin.CategoryTheory.Category.Preorder
 import Mathbin.CategoryTheory.Category.Ulift
 
+#align_import category_theory.filtered from "leanprover-community/mathlib"@"ee05e9ce1322178f0c12004eb93c00d2c8c00ed2"
+
 /-!
 # Filtered categories
 

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

@@ -352,10 +352,12 @@ theorem of_isRightAdjoint (R : C ⥤ D) [IsRightAdjoint R] : IsFiltered D :=
 #align category_theory.is_filtered.of_is_right_adjoint CategoryTheory.IsFiltered.of_isRightAdjoint
 -/
 
+#print CategoryTheory.IsFiltered.of_equivalence /-
 /-- Being filtered is preserved by equivalence of categories. -/
 theorem of_equivalence (h : C ≌ D) : IsFiltered D :=
   of_right_adjoint h.symm.toAdjunction
 #align category_theory.is_filtered.of_equivalence CategoryTheory.IsFiltered.of_equivalence
+-/
 
 end Nonempty
 
@@ -669,12 +671,14 @@ theorem cospan {i j j' : C} (f : j ⟶ i) (f' : j' ⟶ i) :
 #align category_theory.is_cofiltered.cospan CategoryTheory.IsCofiltered.cospan
 -/
 
+#print CategoryTheory.Functor.ranges_directed /-
 theorem CategoryTheory.Functor.ranges_directed (F : C ⥤ Type _) (j : C) :
     Directed (· ⊇ ·) fun f : Σ' i, i ⟶ j => Set.range (F.map f.2) := fun ⟨i, ij⟩ ⟨k, kj⟩ =>
   by
   let ⟨l, li, lk, e⟩ := cospan ij kj
   refine' ⟨⟨l, lk ≫ kj⟩, e ▸ _, _⟩ <;> simp_rw [F.map_comp] <;> apply Set.range_comp_subset_range
 #align category_theory.functor.ranges_directed CategoryTheory.Functor.ranges_directed
+-/
 
 end AllowEmpty
 
@@ -823,10 +827,12 @@ theorem of_isLeftAdjoint (L : C ⥤ D) [IsLeftAdjoint L] : IsCofiltered D :=
 #align category_theory.is_cofiltered.of_is_left_adjoint CategoryTheory.IsCofiltered.of_isLeftAdjoint
 -/
 
+#print CategoryTheory.IsCofiltered.of_equivalence /-
 /-- Being cofiltered is preserved by equivalence of categories. -/
 theorem of_equivalence (h : C ≌ D) : IsCofiltered D :=
   of_left_adjoint h.toAdjunction
 #align category_theory.is_cofiltered.of_equivalence CategoryTheory.IsCofiltered.of_equivalence
+-/
 
 end Nonempty
 

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

@@ -221,14 +221,14 @@ variable {C} [IsFiltered C]
 -/
 theorem sup_objs_exists (O : Finset C) : ∃ S : C, ∀ {X}, X ∈ O → Nonempty (X ⟶ S) := by
   classical
-    apply Finset.induction_on O
-    · exact ⟨is_filtered.nonempty.some, by rintro - ⟨⟩⟩
-    · rintro X O' nm ⟨S', w'⟩
-      use max X S'
-      rintro Y mY
-      obtain rfl | h := eq_or_ne Y X
-      · exact ⟨left_to_max _ _⟩
-      · exact ⟨(w' (Finset.mem_of_mem_insert_of_ne mY h)).some ≫ right_to_max _ _⟩
+  apply Finset.induction_on O
+  · exact ⟨is_filtered.nonempty.some, by rintro - ⟨⟩⟩
+  · rintro X O' nm ⟨S', w'⟩
+    use max X S'
+    rintro Y mY
+    obtain rfl | h := eq_or_ne Y X
+    · exact ⟨left_to_max _ _⟩
+    · exact ⟨(w' (Finset.mem_of_mem_insert_of_ne mY h)).some ≫ right_to_max _ _⟩
 #align category_theory.is_filtered.sup_objs_exists CategoryTheory.IsFiltered.sup_objs_exists
 -/
 
@@ -246,26 +246,26 @@ theorem sup_exists :
         (⟨X, Y, mX, mY, f⟩ : Σ' (X Y : C) (mX : X ∈ O) (mY : Y ∈ O), X ⟶ Y) ∈ H → f ≫ T mY = T mX :=
   by
   classical
-    apply Finset.induction_on H
-    · obtain ⟨S, f⟩ := sup_objs_exists O
-      refine' ⟨S, fun X mX => (f mX).some, _⟩
-      rintro - - - - - ⟨⟩
-    · rintro ⟨X, Y, mX, mY, f⟩ H' nmf ⟨S', T', w'⟩
-      refine' ⟨coeq (f ≫ T' mY) (T' mX), fun Z mZ => T' mZ ≫ coeq_hom (f ≫ T' mY) (T' mX), _⟩
-      intro X' Y' mX' mY' f' mf'
-      rw [← category.assoc]
-      by_cases h : X = X' ∧ Y = Y'
-      · rcases h with ⟨rfl, rfl⟩
-        by_cases hf : f = f'
-        · subst hf
-          apply coeq_condition
-        · rw [@w' _ _ mX mY f' (by simpa [hf ∘ Eq.symm] using mf')]
-      · rw [@w' _ _ mX' mY' f' _]
-        apply Finset.mem_of_mem_insert_of_ne mf'
-        contrapose! h
-        obtain ⟨rfl, h⟩ := h
-        rw [heq_iff_eq, PSigma.mk.inj_iff] at h 
-        exact ⟨rfl, h.1.symm⟩
+  apply Finset.induction_on H
+  · obtain ⟨S, f⟩ := sup_objs_exists O
+    refine' ⟨S, fun X mX => (f mX).some, _⟩
+    rintro - - - - - ⟨⟩
+  · rintro ⟨X, Y, mX, mY, f⟩ H' nmf ⟨S', T', w'⟩
+    refine' ⟨coeq (f ≫ T' mY) (T' mX), fun Z mZ => T' mZ ≫ coeq_hom (f ≫ T' mY) (T' mX), _⟩
+    intro X' Y' mX' mY' f' mf'
+    rw [← category.assoc]
+    by_cases h : X = X' ∧ Y = Y'
+    · rcases h with ⟨rfl, rfl⟩
+      by_cases hf : f = f'
+      · subst hf
+        apply coeq_condition
+      · rw [@w' _ _ mX mY f' (by simpa [hf ∘ Eq.symm] using mf')]
+    · rw [@w' _ _ mX' mY' f' _]
+      apply Finset.mem_of_mem_insert_of_ne mf'
+      contrapose! h
+      obtain ⟨rfl, h⟩ := h
+      rw [heq_iff_eq, PSigma.mk.inj_iff] at h 
+      exact ⟨rfl, h.1.symm⟩
 #align category_theory.is_filtered.sup_exists CategoryTheory.IsFiltered.sup_exists
 -/
 
@@ -305,20 +305,20 @@ there exists a cocone over `F`.
 -/
 theorem cocone_nonempty (F : J ⥤ C) : Nonempty (Cocone F) := by
   classical
-    let O := finset.univ.image F.obj
-    let H : Finset (Σ' (X Y : C) (mX : X ∈ O) (mY : Y ∈ O), X ⟶ Y) :=
-      finset.univ.bUnion fun X : J =>
-        finset.univ.bUnion fun Y : J =>
-          finset.univ.image fun f : X ⟶ Y => ⟨F.obj X, F.obj Y, by simp, by simp, F.map f⟩
-    obtain ⟨Z, f, w⟩ := sup_exists O H
-    refine' ⟨⟨Z, ⟨fun X => f (by simp), _⟩⟩⟩
-    intro j j' g
-    dsimp
-    simp only [category.comp_id]
-    apply w
-    simp only [Finset.mem_univ, Finset.mem_biUnion, exists_and_left, exists_prop_of_true,
-      Finset.mem_image]
-    exact ⟨j, rfl, j', g, by simp⟩
+  let O := finset.univ.image F.obj
+  let H : Finset (Σ' (X Y : C) (mX : X ∈ O) (mY : Y ∈ O), X ⟶ Y) :=
+    finset.univ.bUnion fun X : J =>
+      finset.univ.bUnion fun Y : J =>
+        finset.univ.image fun f : X ⟶ Y => ⟨F.obj X, F.obj Y, by simp, by simp, F.map f⟩
+  obtain ⟨Z, f, w⟩ := sup_exists O H
+  refine' ⟨⟨Z, ⟨fun X => f (by simp), _⟩⟩⟩
+  intro j j' g
+  dsimp
+  simp only [category.comp_id]
+  apply w
+  simp only [Finset.mem_univ, Finset.mem_biUnion, exists_and_left, exists_prop_of_true,
+    Finset.mem_image]
+  exact ⟨j, rfl, j', g, by simp⟩
 #align category_theory.is_filtered.cocone_nonempty CategoryTheory.IsFiltered.cocone_nonempty
 -/
 
@@ -689,14 +689,14 @@ variable {C} [IsCofiltered C]
 -/
 theorem inf_objs_exists (O : Finset C) : ∃ S : C, ∀ {X}, X ∈ O → Nonempty (S ⟶ X) := by
   classical
-    apply Finset.induction_on O
-    · exact ⟨is_cofiltered.nonempty.some, by rintro - ⟨⟩⟩
-    · rintro X O' nm ⟨S', w'⟩
-      use min X S'
-      rintro Y mY
-      obtain rfl | h := eq_or_ne Y X
-      · exact ⟨min_to_left _ _⟩
-      · exact ⟨min_to_right _ _ ≫ (w' (Finset.mem_of_mem_insert_of_ne mY h)).some⟩
+  apply Finset.induction_on O
+  · exact ⟨is_cofiltered.nonempty.some, by rintro - ⟨⟩⟩
+  · rintro X O' nm ⟨S', w'⟩
+    use min X S'
+    rintro Y mY
+    obtain rfl | h := eq_or_ne Y X
+    · exact ⟨min_to_left _ _⟩
+    · exact ⟨min_to_right _ _ ≫ (w' (Finset.mem_of_mem_insert_of_ne mY h)).some⟩
 #align category_theory.is_cofiltered.inf_objs_exists CategoryTheory.IsCofiltered.inf_objs_exists
 -/
 
@@ -714,26 +714,26 @@ theorem inf_exists :
         (⟨X, Y, mX, mY, f⟩ : Σ' (X Y : C) (mX : X ∈ O) (mY : Y ∈ O), X ⟶ Y) ∈ H → T mX ≫ f = T mY :=
   by
   classical
-    apply Finset.induction_on H
-    · obtain ⟨S, f⟩ := inf_objs_exists O
-      refine' ⟨S, fun X mX => (f mX).some, _⟩
-      rintro - - - - - ⟨⟩
-    · rintro ⟨X, Y, mX, mY, f⟩ H' nmf ⟨S', T', w'⟩
-      refine' ⟨Eq (T' mX ≫ f) (T' mY), fun Z mZ => eq_hom (T' mX ≫ f) (T' mY) ≫ T' mZ, _⟩
-      intro X' Y' mX' mY' f' mf'
-      rw [category.assoc]
-      by_cases h : X = X' ∧ Y = Y'
-      · rcases h with ⟨rfl, rfl⟩
-        by_cases hf : f = f'
-        · subst hf
-          apply eq_condition
-        · rw [@w' _ _ mX mY f' (by simpa [hf ∘ Eq.symm] using mf')]
-      · rw [@w' _ _ mX' mY' f' _]
-        apply Finset.mem_of_mem_insert_of_ne mf'
-        contrapose! h
-        obtain ⟨rfl, h⟩ := h
-        rw [heq_iff_eq, PSigma.mk.inj_iff] at h 
-        exact ⟨rfl, h.1.symm⟩
+  apply Finset.induction_on H
+  · obtain ⟨S, f⟩ := inf_objs_exists O
+    refine' ⟨S, fun X mX => (f mX).some, _⟩
+    rintro - - - - - ⟨⟩
+  · rintro ⟨X, Y, mX, mY, f⟩ H' nmf ⟨S', T', w'⟩
+    refine' ⟨Eq (T' mX ≫ f) (T' mY), fun Z mZ => eq_hom (T' mX ≫ f) (T' mY) ≫ T' mZ, _⟩
+    intro X' Y' mX' mY' f' mf'
+    rw [category.assoc]
+    by_cases h : X = X' ∧ Y = Y'
+    · rcases h with ⟨rfl, rfl⟩
+      by_cases hf : f = f'
+      · subst hf
+        apply eq_condition
+      · rw [@w' _ _ mX mY f' (by simpa [hf ∘ Eq.symm] using mf')]
+    · rw [@w' _ _ mX' mY' f' _]
+      apply Finset.mem_of_mem_insert_of_ne mf'
+      contrapose! h
+      obtain ⟨rfl, h⟩ := h
+      rw [heq_iff_eq, PSigma.mk.inj_iff] at h 
+      exact ⟨rfl, h.1.symm⟩
 #align category_theory.is_cofiltered.inf_exists CategoryTheory.IsCofiltered.inf_exists
 -/
 
@@ -773,21 +773,21 @@ there exists a cone over `F`.
 -/
 theorem cone_nonempty (F : J ⥤ C) : Nonempty (Cone F) := by
   classical
-    let O := finset.univ.image F.obj
-    let H : Finset (Σ' (X Y : C) (mX : X ∈ O) (mY : Y ∈ O), X ⟶ Y) :=
-      finset.univ.bUnion fun X : J =>
-        finset.univ.bUnion fun Y : J =>
-          finset.univ.image fun f : X ⟶ Y => ⟨F.obj X, F.obj Y, by simp, by simp, F.map f⟩
-    obtain ⟨Z, f, w⟩ := inf_exists O H
-    refine' ⟨⟨Z, ⟨fun X => f (by simp), _⟩⟩⟩
-    intro j j' g
-    dsimp
-    simp only [category.id_comp]
-    symm
-    apply w
-    simp only [Finset.mem_univ, Finset.mem_biUnion, exists_and_left, exists_prop_of_true,
-      Finset.mem_image]
-    exact ⟨j, rfl, j', g, by simp⟩
+  let O := finset.univ.image F.obj
+  let H : Finset (Σ' (X Y : C) (mX : X ∈ O) (mY : Y ∈ O), X ⟶ Y) :=
+    finset.univ.bUnion fun X : J =>
+      finset.univ.bUnion fun Y : J =>
+        finset.univ.image fun f : X ⟶ Y => ⟨F.obj X, F.obj Y, by simp, by simp, F.map f⟩
+  obtain ⟨Z, f, w⟩ := inf_exists O H
+  refine' ⟨⟨Z, ⟨fun X => f (by simp), _⟩⟩⟩
+  intro j j' g
+  dsimp
+  simp only [category.id_comp]
+  symm
+  apply w
+  simp only [Finset.mem_univ, Finset.mem_biUnion, exists_and_left, exists_prop_of_true,
+    Finset.mem_image]
+  exact ⟨j, rfl, j', g, by simp⟩
 #align category_theory.is_cofiltered.cone_nonempty CategoryTheory.IsCofiltered.cone_nonempty
 -/
 

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

@@ -73,8 +73,8 @@ variable (C : Type u) [Category.{v} C]
    are equal.
 -/
 class IsFilteredOrEmpty : Prop where
-  cocone_objs : ∀ X Y : C, ∃ (Z : _)(f : X ⟶ Z)(g : Y ⟶ Z), True
-  cocone_maps : ∀ ⦃X Y : C⦄ (f g : X ⟶ Y), ∃ (Z : _)(h : Y ⟶ Z), f ≫ h = g ≫ h
+  cocone_objs : ∀ X Y : C, ∃ (Z : _) (f : X ⟶ Z) (g : Y ⟶ Z), True
+  cocone_maps : ∀ ⦃X Y : C⦄ (f g : X ⟶ Y), ∃ (Z : _) (h : Y ⟶ Z), f ≫ h = g ≫ h
 #align category_theory.is_filtered_or_empty CategoryTheory.IsFilteredOrEmpty
 -/
 
@@ -141,11 +141,11 @@ section AllowEmpty
 
 variable {C} [IsFilteredOrEmpty C]
 
-theorem cocone_objs : ∀ X Y : C, ∃ (Z : _)(f : X ⟶ Z)(g : Y ⟶ Z), True :=
+theorem cocone_objs : ∀ X Y : C, ∃ (Z : _) (f : X ⟶ Z) (g : Y ⟶ Z), True :=
   IsFilteredOrEmpty.cocone_objs
 #align category_theory.is_filtered.cocone_objs CategoryTheory.IsFiltered.cocone_objs
 
-theorem cocone_maps : ∀ ⦃X Y : C⦄ (f g : X ⟶ Y), ∃ (Z : _)(h : Y ⟶ Z), f ≫ h = g ≫ h :=
+theorem cocone_maps : ∀ ⦃X Y : C⦄ (f g : X ⟶ Y), ∃ (Z : _) (h : Y ⟶ Z), f ≫ h = g ≫ h :=
   IsFilteredOrEmpty.cocone_maps
 #align category_theory.is_filtered.cocone_maps CategoryTheory.IsFiltered.cocone_maps
 
@@ -232,7 +232,7 @@ theorem sup_objs_exists (O : Finset C) : ∃ S : C, ∀ {X}, X ∈ O → Nonempt
 #align category_theory.is_filtered.sup_objs_exists CategoryTheory.IsFiltered.sup_objs_exists
 -/
 
-variable (O : Finset C) (H : Finset (Σ'(X Y : C)(mX : X ∈ O)(mY : Y ∈ O), X ⟶ Y))
+variable (O : Finset C) (H : Finset (Σ' (X Y : C) (mX : X ∈ O) (mY : Y ∈ O), X ⟶ Y))
 
 #print CategoryTheory.IsFiltered.sup_exists /-
 /-- Given any `finset` of objects `{X, ...}` and
@@ -241,9 +241,9 @@ there exists an object `S`, with a morphism `T X : X ⟶ S` from each `X`,
 such that the triangles commute: `f ≫ T Y = T X`, for `f : X ⟶ Y` in the `finset`.
 -/
 theorem sup_exists :
-    ∃ (S : C)(T : ∀ {X : C}, X ∈ O → (X ⟶ S)),
+    ∃ (S : C) (T : ∀ {X : C}, X ∈ O → (X ⟶ S)),
       ∀ {X Y : C} (mX : X ∈ O) (mY : Y ∈ O) {f : X ⟶ Y},
-        (⟨X, Y, mX, mY, f⟩ : Σ'(X Y : C)(mX : X ∈ O)(mY : Y ∈ O), X ⟶ Y) ∈ H → f ≫ T mY = T mX :=
+        (⟨X, Y, mX, mY, f⟩ : Σ' (X Y : C) (mX : X ∈ O) (mY : Y ∈ O), X ⟶ Y) ∈ H → f ≫ T mY = T mX :=
   by
   classical
     apply Finset.induction_on H
@@ -264,7 +264,7 @@ theorem sup_exists :
         apply Finset.mem_of_mem_insert_of_ne mf'
         contrapose! h
         obtain ⟨rfl, h⟩ := h
-        rw [heq_iff_eq, PSigma.mk.inj_iff] at h
+        rw [heq_iff_eq, PSigma.mk.inj_iff] at h 
         exact ⟨rfl, h.1.symm⟩
 #align category_theory.is_filtered.sup_exists CategoryTheory.IsFiltered.sup_exists
 -/
@@ -291,7 +291,7 @@ noncomputable def toSup {X : C} (m : X ∈ O) : X ⟶ sup O H :=
 /-- The triangles of consisting of a morphism in `H` and the maps to `sup O H` commute.
 -/
 theorem toSup_commutes {X Y : C} (mX : X ∈ O) (mY : Y ∈ O) {f : X ⟶ Y}
-    (mf : (⟨X, Y, mX, mY, f⟩ : Σ'(X Y : C)(mX : X ∈ O)(mY : Y ∈ O), X ⟶ Y) ∈ H) :
+    (mf : (⟨X, Y, mX, mY, f⟩ : Σ' (X Y : C) (mX : X ∈ O) (mY : Y ∈ O), X ⟶ Y) ∈ H) :
     f ≫ toSup O H mY = toSup O H mX :=
   (sup_exists O H).choose_spec.choose_spec mX mY mf
 #align category_theory.is_filtered.to_sup_commutes CategoryTheory.IsFiltered.toSup_commutes
@@ -306,7 +306,7 @@ there exists a cocone over `F`.
 theorem cocone_nonempty (F : J ⥤ C) : Nonempty (Cocone F) := by
   classical
     let O := finset.univ.image F.obj
-    let H : Finset (Σ'(X Y : C)(mX : X ∈ O)(mY : Y ∈ O), X ⟶ Y) :=
+    let H : Finset (Σ' (X Y : C) (mX : X ∈ O) (mY : Y ∈ O), X ⟶ Y) :=
       finset.univ.bUnion fun X : J =>
         finset.univ.bUnion fun Y : J =>
           finset.univ.image fun f : X ⟶ Y => ⟨F.obj X, F.obj Y, by simp, by simp, F.map f⟩
@@ -451,10 +451,10 @@ theorem coeq₃_condition₃ {j₁ j₂ : C} (f g h : j₁ ⟶ j₂) : f ≫ coe
 /-- For every span `j ⟵ i ⟶ j'`, there
    exists a cocone `j ⟶ k ⟵ j'` such that the square commutes. -/
 theorem span {i j j' : C} (f : i ⟶ j) (f' : i ⟶ j') :
-    ∃ (k : C)(g : j ⟶ k)(g' : j' ⟶ k), f ≫ g = f' ≫ g' :=
+    ∃ (k : C) (g : j ⟶ k) (g' : j' ⟶ k), f ≫ g = f' ≫ g' :=
   let ⟨K, G, G', _⟩ := cocone_objs j j'
   let ⟨k, e, he⟩ := cocone_maps (f ≫ G) (f' ≫ G')
-  ⟨k, G ≫ e, G' ≫ e, by simpa only [← category.assoc] ⟩
+  ⟨k, G ≫ e, G' ≫ e, by simpa only [← category.assoc]⟩
 #align category_theory.is_filtered.span CategoryTheory.IsFiltered.span
 -/
 
@@ -473,11 +473,11 @@ in a filtered category, we can construct an object `s` and two morphisms from `k
 making the resulting squares commute.
 -/
 theorem bowtie {j₁ j₂ k₁ k₂ : C} (f₁ : j₁ ⟶ k₁) (g₁ : j₁ ⟶ k₂) (f₂ : j₂ ⟶ k₁) (g₂ : j₂ ⟶ k₂) :
-    ∃ (s : C)(α : k₁ ⟶ s)(β : k₂ ⟶ s), f₁ ≫ α = g₁ ≫ β ∧ f₂ ≫ α = g₂ ≫ β :=
+    ∃ (s : C) (α : k₁ ⟶ s) (β : k₂ ⟶ s), f₁ ≫ α = g₁ ≫ β ∧ f₂ ≫ α = g₂ ≫ β :=
   by
   obtain ⟨t, k₁t, k₂t, ht⟩ := span f₁ g₁
   obtain ⟨s, ts, hs⟩ := cocone_maps (f₂ ≫ k₁t) (g₂ ≫ k₂t)
-  simp_rw [category.assoc] at hs
+  simp_rw [category.assoc] at hs 
   exact ⟨s, k₁t ≫ ts, k₂t ≫ ts, by rw [reassoc_of ht], hs⟩
 #align category_theory.is_filtered.bowtie CategoryTheory.IsFiltered.bowtie
 -/
@@ -502,7 +502,7 @@ to `s`, making the resulting squares commute.
 -/
 theorem tulip {j₁ j₂ j₃ k₁ k₂ l : C} (f₁ : j₁ ⟶ k₁) (f₂ : j₂ ⟶ k₁) (f₃ : j₂ ⟶ k₂) (f₄ : j₃ ⟶ k₂)
     (g₁ : j₁ ⟶ l) (g₂ : j₃ ⟶ l) :
-    ∃ (s : C)(α : k₁ ⟶ s)(β : l ⟶ s)(γ : k₂ ⟶ s),
+    ∃ (s : C) (α : k₁ ⟶ s) (β : l ⟶ s) (γ : k₂ ⟶ s),
       f₁ ≫ α = g₁ ≫ β ∧ f₂ ≫ α = f₃ ≫ γ ∧ f₄ ≫ γ = g₂ ≫ β :=
   by
   obtain ⟨l', k₁l, k₂l, hl⟩ := span f₂ f₃
@@ -523,8 +523,8 @@ end IsFiltered
    are equal.
 -/
 class IsCofilteredOrEmpty : Prop where
-  cone_objs : ∀ X Y : C, ∃ (W : _)(f : W ⟶ X)(g : W ⟶ Y), True
-  cone_maps : ∀ ⦃X Y : C⦄ (f g : X ⟶ Y), ∃ (W : _)(h : W ⟶ X), h ≫ f = h ≫ g
+  cone_objs : ∀ X Y : C, ∃ (W : _) (f : W ⟶ X) (g : W ⟶ Y), True
+  cone_maps : ∀ ⦃X Y : C⦄ (f g : X ⟶ Y), ∃ (W : _) (h : W ⟶ X), h ≫ f = h ≫ g
 #align category_theory.is_cofiltered_or_empty CategoryTheory.IsCofilteredOrEmpty
 -/
 
@@ -591,11 +591,11 @@ section AllowEmpty
 
 variable {C} [IsCofilteredOrEmpty C]
 
-theorem cone_objs : ∀ X Y : C, ∃ (W : _)(f : W ⟶ X)(g : W ⟶ Y), True :=
+theorem cone_objs : ∀ X Y : C, ∃ (W : _) (f : W ⟶ X) (g : W ⟶ Y), True :=
   IsCofilteredOrEmpty.cone_objs
 #align category_theory.is_cofiltered.cone_objs CategoryTheory.IsCofiltered.cone_objs
 
-theorem cone_maps : ∀ ⦃X Y : C⦄ (f g : X ⟶ Y), ∃ (W : _)(h : W ⟶ X), h ≫ f = h ≫ g :=
+theorem cone_maps : ∀ ⦃X Y : C⦄ (f g : X ⟶ Y), ∃ (W : _) (h : W ⟶ X), h ≫ f = h ≫ g :=
   IsCofilteredOrEmpty.cone_maps
 #align category_theory.is_cofiltered.cone_maps CategoryTheory.IsCofiltered.cone_maps
 
@@ -662,7 +662,7 @@ theorem eq_condition {j j' : C} (f f' : j ⟶ j') : eqHom f f' ≫ f = eqHom f f
 /-- For every cospan `j ⟶ i ⟵ j'`,
  there exists a cone `j ⟵ k ⟶ j'` such that the square commutes. -/
 theorem cospan {i j j' : C} (f : j ⟶ i) (f' : j' ⟶ i) :
-    ∃ (k : C)(g : k ⟶ j)(g' : k ⟶ j'), g ≫ f = g' ≫ f' :=
+    ∃ (k : C) (g : k ⟶ j) (g' : k ⟶ j'), g ≫ f = g' ≫ f' :=
   let ⟨K, G, G', _⟩ := cone_objs j j'
   let ⟨k, e, he⟩ := cone_maps (G ≫ f) (G' ≫ f')
   ⟨k, e ≫ G, e ≫ G', by simpa only [category.assoc] using he⟩
@@ -670,7 +670,7 @@ theorem cospan {i j j' : C} (f : j ⟶ i) (f' : j' ⟶ i) :
 -/
 
 theorem CategoryTheory.Functor.ranges_directed (F : C ⥤ Type _) (j : C) :
-    Directed (· ⊇ ·) fun f : Σ'i, i ⟶ j => Set.range (F.map f.2) := fun ⟨i, ij⟩ ⟨k, kj⟩ =>
+    Directed (· ⊇ ·) fun f : Σ' i, i ⟶ j => Set.range (F.map f.2) := fun ⟨i, ij⟩ ⟨k, kj⟩ =>
   by
   let ⟨l, li, lk, e⟩ := cospan ij kj
   refine' ⟨⟨l, lk ≫ kj⟩, e ▸ _, _⟩ <;> simp_rw [F.map_comp] <;> apply Set.range_comp_subset_range
@@ -700,7 +700,7 @@ theorem inf_objs_exists (O : Finset C) : ∃ S : C, ∀ {X}, X ∈ O → Nonempt
 #align category_theory.is_cofiltered.inf_objs_exists CategoryTheory.IsCofiltered.inf_objs_exists
 -/
 
-variable (O : Finset C) (H : Finset (Σ'(X Y : C)(mX : X ∈ O)(mY : Y ∈ O), X ⟶ Y))
+variable (O : Finset C) (H : Finset (Σ' (X Y : C) (mX : X ∈ O) (mY : Y ∈ O), X ⟶ Y))
 
 #print CategoryTheory.IsCofiltered.inf_exists /-
 /-- Given any `finset` of objects `{X, ...}` and
@@ -709,9 +709,9 @@ there exists an object `S`, with a morphism `T X : S ⟶ X` from each `X`,
 such that the triangles commute: `T X ≫ f = T Y`, for `f : X ⟶ Y` in the `finset`.
 -/
 theorem inf_exists :
-    ∃ (S : C)(T : ∀ {X : C}, X ∈ O → (S ⟶ X)),
+    ∃ (S : C) (T : ∀ {X : C}, X ∈ O → (S ⟶ X)),
       ∀ {X Y : C} (mX : X ∈ O) (mY : Y ∈ O) {f : X ⟶ Y},
-        (⟨X, Y, mX, mY, f⟩ : Σ'(X Y : C)(mX : X ∈ O)(mY : Y ∈ O), X ⟶ Y) ∈ H → T mX ≫ f = T mY :=
+        (⟨X, Y, mX, mY, f⟩ : Σ' (X Y : C) (mX : X ∈ O) (mY : Y ∈ O), X ⟶ Y) ∈ H → T mX ≫ f = T mY :=
   by
   classical
     apply Finset.induction_on H
@@ -732,7 +732,7 @@ theorem inf_exists :
         apply Finset.mem_of_mem_insert_of_ne mf'
         contrapose! h
         obtain ⟨rfl, h⟩ := h
-        rw [heq_iff_eq, PSigma.mk.inj_iff] at h
+        rw [heq_iff_eq, PSigma.mk.inj_iff] at h 
         exact ⟨rfl, h.1.symm⟩
 #align category_theory.is_cofiltered.inf_exists CategoryTheory.IsCofiltered.inf_exists
 -/
@@ -759,7 +759,7 @@ noncomputable def infTo {X : C} (m : X ∈ O) : inf O H ⟶ X :=
 /-- The triangles consisting of a morphism in `H` and the maps from `inf O H` commute.
 -/
 theorem infTo_commutes {X Y : C} (mX : X ∈ O) (mY : Y ∈ O) {f : X ⟶ Y}
-    (mf : (⟨X, Y, mX, mY, f⟩ : Σ'(X Y : C)(mX : X ∈ O)(mY : Y ∈ O), X ⟶ Y) ∈ H) :
+    (mf : (⟨X, Y, mX, mY, f⟩ : Σ' (X Y : C) (mX : X ∈ O) (mY : Y ∈ O), X ⟶ Y) ∈ H) :
     infTo O H mX ≫ f = infTo O H mY :=
   (inf_exists O H).choose_spec.choose_spec mX mY mf
 #align category_theory.is_cofiltered.inf_to_commutes CategoryTheory.IsCofiltered.infTo_commutes
@@ -774,7 +774,7 @@ there exists a cone over `F`.
 theorem cone_nonempty (F : J ⥤ C) : Nonempty (Cone F) := by
   classical
     let O := finset.univ.image F.obj
-    let H : Finset (Σ'(X Y : C)(mX : X ∈ O)(mY : Y ∈ O), X ⟶ Y) :=
+    let H : Finset (Σ' (X Y : C) (mX : X ∈ O) (mY : Y ∈ O), X ⟶ Y) :=
       finset.univ.bUnion fun X : J =>
         finset.univ.bUnion fun Y : J =>
           finset.univ.image fun f : X ⟶ Y => ⟨F.obj X, F.obj Y, by simp, by simp, F.map f⟩

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

@@ -107,6 +107,7 @@ instance (priority := 100) isFiltered_of_semilatticeSup_nonempty (α : Type u) [
 #align category_theory.is_filtered_of_semilattice_sup_nonempty CategoryTheory.isFiltered_of_semilatticeSup_nonempty
 -/
 
+#print CategoryTheory.isFilteredOrEmpty_of_directed_le /-
 instance (priority := 100) isFilteredOrEmpty_of_directed_le (α : Type u) [Preorder α]
     [IsDirected α (· ≤ ·)] : IsFilteredOrEmpty α
     where
@@ -115,10 +116,13 @@ instance (priority := 100) isFilteredOrEmpty_of_directed_le (α : Type u) [Preor
     ⟨Z, homOfLE h1, homOfLE h2, trivial⟩
   cocone_maps X Y f g := ⟨Y, 𝟙 _, by simp⟩
 #align category_theory.is_filtered_or_empty_of_directed_le CategoryTheory.isFilteredOrEmpty_of_directed_le
+-/
 
+#print CategoryTheory.isFiltered_of_directed_le_nonempty /-
 instance (priority := 100) isFiltered_of_directed_le_nonempty (α : Type u) [Preorder α]
     [IsDirected α (· ≤ ·)] [Nonempty α] : IsFiltered α where
 #align category_theory.is_filtered_of_directed_le_nonempty CategoryTheory.isFiltered_of_directed_le_nonempty
+-/
 
 -- Sanity checks
 example (α : Type u) [SemilatticeSup α] [OrderBot α] : IsFiltered α := by infer_instance
@@ -553,6 +557,7 @@ instance (priority := 100) isCofiltered_of_semilatticeInf_nonempty (α : Type u)
 #align category_theory.is_cofiltered_of_semilattice_inf_nonempty CategoryTheory.isCofiltered_of_semilatticeInf_nonempty
 -/
 
+#print CategoryTheory.isCofilteredOrEmpty_of_directed_ge /-
 instance (priority := 100) isCofilteredOrEmpty_of_directed_ge (α : Type u) [Preorder α]
     [IsDirected α (· ≥ ·)] : IsCofilteredOrEmpty α
     where
@@ -561,10 +566,13 @@ instance (priority := 100) isCofilteredOrEmpty_of_directed_ge (α : Type u) [Pre
     ⟨Z, homOfLE hX, homOfLE hY, trivial⟩
   cone_maps X Y f g := ⟨X, 𝟙 _, by simp⟩
 #align category_theory.is_cofiltered_or_empty_of_directed_ge CategoryTheory.isCofilteredOrEmpty_of_directed_ge
+-/
 
+#print CategoryTheory.isCofiltered_of_directed_ge_nonempty /-
 instance (priority := 100) isCofiltered_of_directed_ge_nonempty (α : Type u) [Preorder α]
     [IsDirected α (· ≥ ·)] [Nonempty α] : IsCofiltered α where
 #align category_theory.is_cofiltered_of_directed_ge_nonempty CategoryTheory.isCofiltered_of_directed_ge_nonempty
+-/
 
 -- Sanity checks
 example (α : Type u) [SemilatticeInf α] [OrderBot α] : IsCofiltered α := by infer_instance

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

@@ -107,12 +107,6 @@ instance (priority := 100) isFiltered_of_semilatticeSup_nonempty (α : Type u) [
 #align category_theory.is_filtered_of_semilattice_sup_nonempty CategoryTheory.isFiltered_of_semilatticeSup_nonempty
 -/
 
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align category_theory.is_filtered_or_empty_of_directed_le CategoryTheory.isFilteredOrEmpty_of_directed_leₓ'. -/
 instance (priority := 100) isFilteredOrEmpty_of_directed_le (α : Type u) [Preorder α]
     [IsDirected α (· ≤ ·)] : IsFilteredOrEmpty α
     where
@@ -122,12 +116,6 @@ instance (priority := 100) isFilteredOrEmpty_of_directed_le (α : Type u) [Preor
   cocone_maps X Y f g := ⟨Y, 𝟙 _, by simp⟩
 #align category_theory.is_filtered_or_empty_of_directed_le CategoryTheory.isFilteredOrEmpty_of_directed_le
 
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align category_theory.is_filtered_of_directed_le_nonempty CategoryTheory.isFiltered_of_directed_le_nonemptyₓ'. -/
 instance (priority := 100) isFiltered_of_directed_le_nonempty (α : Type u) [Preorder α]
     [IsDirected α (· ≤ ·)] [Nonempty α] : IsFiltered α where
 #align category_theory.is_filtered_of_directed_le_nonempty CategoryTheory.isFiltered_of_directed_le_nonempty
@@ -360,12 +348,6 @@ theorem of_isRightAdjoint (R : C ⥤ D) [IsRightAdjoint R] : IsFiltered D :=
 #align category_theory.is_filtered.of_is_right_adjoint CategoryTheory.IsFiltered.of_isRightAdjoint
 -/
 
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-lean 3 declaration is
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.IsFiltered.{u1, u3} C _inst_1] {D : Type.{u4}} [_inst_5 : CategoryTheory.Category.{u2, u4} D], (CategoryTheory.Equivalence.{u1, u2, u3, u4} C _inst_1 D _inst_5) -> (CategoryTheory.IsFiltered.{u2, u4} D _inst_5)
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-Case conversion may be inaccurate. Consider using '#align category_theory.is_filtered.of_equivalence CategoryTheory.IsFiltered.of_equivalenceₓ'. -/
 /-- Being filtered is preserved by equivalence of categories. -/
 theorem of_equivalence (h : C ≌ D) : IsFiltered D :=
   of_right_adjoint h.symm.toAdjunction
@@ -571,12 +553,6 @@ instance (priority := 100) isCofiltered_of_semilatticeInf_nonempty (α : Type u)
 #align category_theory.is_cofiltered_of_semilattice_inf_nonempty CategoryTheory.isCofiltered_of_semilatticeInf_nonempty
 -/
 
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-Case conversion may be inaccurate. Consider using '#align category_theory.is_cofiltered_or_empty_of_directed_ge CategoryTheory.isCofilteredOrEmpty_of_directed_geₓ'. -/
 instance (priority := 100) isCofilteredOrEmpty_of_directed_ge (α : Type u) [Preorder α]
     [IsDirected α (· ≥ ·)] : IsCofilteredOrEmpty α
     where
@@ -586,12 +562,6 @@ instance (priority := 100) isCofilteredOrEmpty_of_directed_ge (α : Type u) [Pre
   cone_maps X Y f g := ⟨X, 𝟙 _, by simp⟩
 #align category_theory.is_cofiltered_or_empty_of_directed_ge CategoryTheory.isCofilteredOrEmpty_of_directed_ge
 
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 instance (priority := 100) isCofiltered_of_directed_ge_nonempty (α : Type u) [Preorder α]
     [IsDirected α (· ≥ ·)] [Nonempty α] : IsCofiltered α where
 #align category_theory.is_cofiltered_of_directed_ge_nonempty CategoryTheory.isCofiltered_of_directed_ge_nonempty
@@ -691,12 +661,6 @@ theorem cospan {i j j' : C} (f : j ⟶ i) (f' : j' ⟶ i) :
 #align category_theory.is_cofiltered.cospan CategoryTheory.IsCofiltered.cospan
 -/
 
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PSigma.{succ u3, succ u2} C (fun (i : C) => Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) i j)) => Set.range.{u1, succ u1} (Prefunctor.obj.{succ u2, succ u1, u3, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u3, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} F) j) (Prefunctor.obj.{succ u2, succ u1, u3, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u3, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} F) (PSigma.fst.{succ u3, succ u2} C (fun (i : C) => Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) i j) f)) (Prefunctor.map.{succ u2, succ u1, u3, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u3, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} F) (PSigma.fst.{succ u3, succ u2} C (fun (i : C) => Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) i j) f) j (PSigma.snd.{succ u3, succ u2} C (fun (i : C) => Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) i j) f)))
-Case conversion may be inaccurate. Consider using '#align category_theory.functor.ranges_directed CategoryTheory.Functor.ranges_directedₓ'. -/
 theorem CategoryTheory.Functor.ranges_directed (F : C ⥤ Type _) (j : C) :
     Directed (· ⊇ ·) fun f : Σ'i, i ⟶ j => Set.range (F.map f.2) := fun ⟨i, ij⟩ ⟨k, kj⟩ =>
   by
@@ -851,12 +815,6 @@ theorem of_isLeftAdjoint (L : C ⥤ D) [IsLeftAdjoint L] : IsCofiltered D :=
 #align category_theory.is_cofiltered.of_is_left_adjoint CategoryTheory.IsCofiltered.of_isLeftAdjoint
 -/
 
-/- warning: category_theory.is_cofiltered.of_equivalence -> CategoryTheory.IsCofiltered.of_equivalence is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.IsCofiltered.{u1, u3} C _inst_1] {D : Type.{u4}} [_inst_5 : CategoryTheory.Category.{u2, u4} D], (CategoryTheory.Equivalence.{u1, u2, u3, u4} C _inst_1 D _inst_5) -> (CategoryTheory.IsCofiltered.{u2, u4} D _inst_5)
-but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.IsCofiltered.{u1, u3} C _inst_1] {D : Type.{u4}} [_inst_5 : CategoryTheory.Category.{u2, u4} D], (CategoryTheory.Equivalence.{u1, u2, u3, u4} C D _inst_1 _inst_5) -> (CategoryTheory.IsCofiltered.{u2, u4} D _inst_5)
-Case conversion may be inaccurate. Consider using '#align category_theory.is_cofiltered.of_equivalence CategoryTheory.IsCofiltered.of_equivalenceₓ'. -/
 /-- Being cofiltered is preserved by equivalence of categories. -/
 theorem of_equivalence (h : C ≌ D) : IsCofiltered D :=
   of_left_adjoint h.toAdjunction

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

@@ -210,7 +210,7 @@ noncomputable def coeqHom {j j' : C} (f f' : j ⟶ j') : j' ⟶ coeq f f' :=
 /-- `coeq_condition f f'`, for morphisms `f f' : j ⟶ j'`, is the proof that
 `f ≫ coeq_hom f f' = f' ≫ coeq_hom f f'`.
 -/
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem coeq_condition {j j' : C} (f f' : j ⟶ j') : f ≫ coeqHom f f' = f' ≫ coeqHom f f' :=
   (cocone_maps f f').choose_spec.choose_spec
 #align category_theory.is_filtered.coeq_condition CategoryTheory.IsFiltered.coeq_condition
@@ -674,7 +674,7 @@ noncomputable def eqHom {j j' : C} (f f' : j ⟶ j') : eq f f' ⟶ j :=
 /-- `eq_condition f f'`, for morphisms `f f' : j ⟶ j'`, is the proof that
 `eq_hom f f' ≫ f = eq_hom f f' ≫ f'`.
 -/
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem eq_condition {j j' : C} (f f' : j ⟶ j') : eqHom f f' ≫ f = eqHom f f' ≫ f' :=
   (cone_maps f f').choose_spec.choose_spec
 #align category_theory.is_cofiltered.eq_condition CategoryTheory.IsCofiltered.eq_condition

mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8

@@ -107,7 +107,12 @@ instance (priority := 100) isFiltered_of_semilatticeSup_nonempty (α : Type u) [
 #align category_theory.is_filtered_of_semilattice_sup_nonempty CategoryTheory.isFiltered_of_semilatticeSup_nonempty
 -/
 
-#print CategoryTheory.isFilteredOrEmpty_of_directed_le /-
+/- warning: category_theory.is_filtered_or_empty_of_directed_le -> CategoryTheory.isFilteredOrEmpty_of_directed_le is a dubious translation:
+lean 3 declaration is
+  forall (α : Type.{u1}) [_inst_2 : Preorder.{u1} α] [_inst_3 : IsDirected.{u1} α (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))], CategoryTheory.IsFilteredOrEmpty.{u1, u1} α (Preorder.smallCategory.{u1} α _inst_2)
+but is expected to have type
+  forall (α : Type.{u1}) [_inst_2 : Preorder.{u1} α] [_inst_3 : IsDirected.{u1} α (fun (x._@.Mathlib.CategoryTheory.Filtered._hyg.210 : α) (x._@.Mathlib.CategoryTheory.Filtered._hyg.212 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.CategoryTheory.Filtered._hyg.210 x._@.Mathlib.CategoryTheory.Filtered._hyg.212)], CategoryTheory.IsFilteredOrEmpty.{u1, u1} α (Preorder.smallCategory.{u1} α _inst_2)
+Case conversion may be inaccurate. Consider using '#align category_theory.is_filtered_or_empty_of_directed_le CategoryTheory.isFilteredOrEmpty_of_directed_leₓ'. -/
 instance (priority := 100) isFilteredOrEmpty_of_directed_le (α : Type u) [Preorder α]
     [IsDirected α (· ≤ ·)] : IsFilteredOrEmpty α
     where
@@ -116,13 +121,16 @@ instance (priority := 100) isFilteredOrEmpty_of_directed_le (α : Type u) [Preor
     ⟨Z, homOfLE h1, homOfLE h2, trivial⟩
   cocone_maps X Y f g := ⟨Y, 𝟙 _, by simp⟩
 #align category_theory.is_filtered_or_empty_of_directed_le CategoryTheory.isFilteredOrEmpty_of_directed_le
--/
 
-#print CategoryTheory.isFiltered_of_directed_le_nonempty /-
+/- warning: category_theory.is_filtered_of_directed_le_nonempty -> CategoryTheory.isFiltered_of_directed_le_nonempty is a dubious translation:
+lean 3 declaration is
+  forall (α : Type.{u1}) [_inst_2 : Preorder.{u1} α] [_inst_3 : IsDirected.{u1} α (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] [_inst_4 : Nonempty.{succ u1} α], CategoryTheory.IsFiltered.{u1, u1} α (Preorder.smallCategory.{u1} α _inst_2)
+but is expected to have type
+  forall (α : Type.{u1}) [_inst_2 : Preorder.{u1} α] [_inst_3 : IsDirected.{u1} α (fun (x._@.Mathlib.CategoryTheory.Filtered._hyg.309 : α) (x._@.Mathlib.CategoryTheory.Filtered._hyg.311 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.CategoryTheory.Filtered._hyg.309 x._@.Mathlib.CategoryTheory.Filtered._hyg.311)] [_inst_4 : Nonempty.{succ u1} α], CategoryTheory.IsFiltered.{u1, u1} α (Preorder.smallCategory.{u1} α _inst_2)
+Case conversion may be inaccurate. Consider using '#align category_theory.is_filtered_of_directed_le_nonempty CategoryTheory.isFiltered_of_directed_le_nonemptyₓ'. -/
 instance (priority := 100) isFiltered_of_directed_le_nonempty (α : Type u) [Preorder α]
     [IsDirected α (· ≤ ·)] [Nonempty α] : IsFiltered α where
 #align category_theory.is_filtered_of_directed_le_nonempty CategoryTheory.isFiltered_of_directed_le_nonempty
--/
 
 -- Sanity checks
 example (α : Type u) [SemilatticeSup α] [OrderBot α] : IsFiltered α := by infer_instance
@@ -563,7 +571,12 @@ instance (priority := 100) isCofiltered_of_semilatticeInf_nonempty (α : Type u)
 #align category_theory.is_cofiltered_of_semilattice_inf_nonempty CategoryTheory.isCofiltered_of_semilatticeInf_nonempty
 -/
 
-#print CategoryTheory.isCofilteredOrEmpty_of_directed_ge /-
+/- warning: category_theory.is_cofiltered_or_empty_of_directed_ge -> CategoryTheory.isCofilteredOrEmpty_of_directed_ge is a dubious translation:
+lean 3 declaration is
+  forall (α : Type.{u1}) [_inst_2 : Preorder.{u1} α] [_inst_3 : IsDirected.{u1} α (GE.ge.{u1} α (Preorder.toHasLe.{u1} α _inst_2))], CategoryTheory.IsCofilteredOrEmpty.{u1, u1} α (Preorder.smallCategory.{u1} α _inst_2)
+but is expected to have type
+  forall (α : Type.{u1}) [_inst_2 : Preorder.{u1} α] [_inst_3 : IsDirected.{u1} α (fun (x._@.Mathlib.CategoryTheory.Filtered._hyg.3767 : α) (x._@.Mathlib.CategoryTheory.Filtered._hyg.3769 : α) => GE.ge.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.CategoryTheory.Filtered._hyg.3767 x._@.Mathlib.CategoryTheory.Filtered._hyg.3769)], CategoryTheory.IsCofilteredOrEmpty.{u1, u1} α (Preorder.smallCategory.{u1} α _inst_2)
+Case conversion may be inaccurate. Consider using '#align category_theory.is_cofiltered_or_empty_of_directed_ge CategoryTheory.isCofilteredOrEmpty_of_directed_geₓ'. -/
 instance (priority := 100) isCofilteredOrEmpty_of_directed_ge (α : Type u) [Preorder α]
     [IsDirected α (· ≥ ·)] : IsCofilteredOrEmpty α
     where
@@ -572,13 +585,16 @@ instance (priority := 100) isCofilteredOrEmpty_of_directed_ge (α : Type u) [Pre
     ⟨Z, homOfLE hX, homOfLE hY, trivial⟩
   cone_maps X Y f g := ⟨X, 𝟙 _, by simp⟩
 #align category_theory.is_cofiltered_or_empty_of_directed_ge CategoryTheory.isCofilteredOrEmpty_of_directed_ge
--/
 
-#print CategoryTheory.isCofiltered_of_directed_ge_nonempty /-
+/- warning: category_theory.is_cofiltered_of_directed_ge_nonempty -> CategoryTheory.isCofiltered_of_directed_ge_nonempty is a dubious translation:
+lean 3 declaration is
+  forall (α : Type.{u1}) [_inst_2 : Preorder.{u1} α] [_inst_3 : IsDirected.{u1} α (GE.ge.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] [_inst_4 : Nonempty.{succ u1} α], CategoryTheory.IsCofiltered.{u1, u1} α (Preorder.smallCategory.{u1} α _inst_2)
+but is expected to have type
+  forall (α : Type.{u1}) [_inst_2 : Preorder.{u1} α] [_inst_3 : IsDirected.{u1} α (fun (x._@.Mathlib.CategoryTheory.Filtered._hyg.3866 : α) (x._@.Mathlib.CategoryTheory.Filtered._hyg.3868 : α) => GE.ge.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.CategoryTheory.Filtered._hyg.3866 x._@.Mathlib.CategoryTheory.Filtered._hyg.3868)] [_inst_4 : Nonempty.{succ u1} α], CategoryTheory.IsCofiltered.{u1, u1} α (Preorder.smallCategory.{u1} α _inst_2)
+Case conversion may be inaccurate. Consider using '#align category_theory.is_cofiltered_of_directed_ge_nonempty CategoryTheory.isCofiltered_of_directed_ge_nonemptyₓ'. -/
 instance (priority := 100) isCofiltered_of_directed_ge_nonempty (α : Type u) [Preorder α]
     [IsDirected α (· ≥ ·)] [Nonempty α] : IsCofiltered α where
 #align category_theory.is_cofiltered_of_directed_ge_nonempty CategoryTheory.isCofiltered_of_directed_ge_nonempty
--/
 
 -- Sanity checks
 example (α : Type u) [SemilatticeInf α] [OrderBot α] : IsCofiltered α := by infer_instance

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

@@ -316,7 +316,7 @@ theorem cocone_nonempty (F : J ⥤ C) : Nonempty (Cocone F) := by
     dsimp
     simp only [category.comp_id]
     apply w
-    simp only [Finset.mem_univ, Finset.mem_bunionᵢ, exists_and_left, exists_prop_of_true,
+    simp only [Finset.mem_univ, Finset.mem_biUnion, exists_and_left, exists_prop_of_true,
       Finset.mem_image]
     exact ⟨j, rfl, j', g, by simp⟩
 #align category_theory.is_filtered.cocone_nonempty CategoryTheory.IsFiltered.cocone_nonempty
@@ -797,7 +797,7 @@ theorem cone_nonempty (F : J ⥤ C) : Nonempty (Cone F) := by
     simp only [category.id_comp]
     symm
     apply w
-    simp only [Finset.mem_univ, Finset.mem_bunionᵢ, exists_and_left, exists_prop_of_true,
+    simp only [Finset.mem_univ, Finset.mem_biUnion, exists_and_left, exists_prop_of_true,
       Finset.mem_image]
     exact ⟨j, rfl, j', g, by simp⟩
 #align category_theory.is_cofiltered.cone_nonempty CategoryTheory.IsCofiltered.cone_nonempty

mathlib commit https://github.com/leanprover-community/mathlib/commit/36b8aa61ea7c05727161f96a0532897bd72aedab

@@ -679,7 +679,7 @@ theorem cospan {i j j' : C} (f : j ⟶ i) (f' : j' ⟶ i) :
 lean 3 declaration is
   forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.IsCofilteredOrEmpty.{u1, u2} C _inst_1] (F : CategoryTheory.Functor.{u1, u3, u2, succ u3} C _inst_1 Type.{u3} CategoryTheory.types.{u3}) (j : C), Directed.{u3, max 1 (succ u2) (succ u1)} (Set.{u3} (CategoryTheory.Functor.obj.{u1, u3, u2, succ u3} C _inst_1 Type.{u3} CategoryTheory.types.{u3} F j)) (PSigma.{succ u2, succ u1} C (fun (i : C) => Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) i j)) (Superset.{u3} (Set.{u3} (CategoryTheory.Functor.obj.{u1, u3, u2, succ u3} C _inst_1 Type.{u3} CategoryTheory.types.{u3} F j)) (Set.hasSubset.{u3} (CategoryTheory.Functor.obj.{u1, u3, u2, succ u3} C _inst_1 Type.{u3} CategoryTheory.types.{u3} F j))) (fun (f : PSigma.{succ u2, succ u1} C (fun (i : C) => Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) i j)) => Set.range.{u3, succ u3} (CategoryTheory.Functor.obj.{u1, u3, u2, succ u3} C _inst_1 Type.{u3} CategoryTheory.types.{u3} F j) (CategoryTheory.Functor.obj.{u1, u3, u2, succ u3} C _inst_1 Type.{u3} CategoryTheory.types.{u3} F (PSigma.fst.{succ u2, succ u1} C (fun (i : C) => Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) i j) f)) (CategoryTheory.Functor.map.{u1, u3, u2, succ u3} C _inst_1 Type.{u3} CategoryTheory.types.{u3} F (PSigma.fst.{succ u2, succ u1} C (fun (i : C) => Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) i j) f) j (PSigma.snd.{succ u2, succ u1} C (fun (i : C) => Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) i j) f)))
 but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] [_inst_2 : CategoryTheory.IsCofilteredOrEmpty.{u2, u3} C _inst_1] (F : CategoryTheory.Functor.{u2, u1, u3, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1}) (j : C), Directed.{u1, max (succ u3) (succ u2)} (Set.{u1} (Prefunctor.obj.{succ u2, succ u1, u3, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u3, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} F) j)) (PSigma.{succ u3, succ u2} C (fun (i : C) => Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) i j)) (fun (x._@.Mathlib.CategoryTheory.Filtered._hyg.4398 : Set.{u1} (Prefunctor.obj.{succ u2, succ u1, u3, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u3, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} F) j)) (x._@.Mathlib.CategoryTheory.Filtered._hyg.4400 : Set.{u1} (Prefunctor.obj.{succ u2, succ u1, u3, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u3, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} F) j)) => Superset.{u1} (Set.{u1} (Prefunctor.obj.{succ u2, succ u1, u3, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u3, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} F) j)) (Set.instHasSubsetSet.{u1} (Prefunctor.obj.{succ u2, succ u1, u3, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u3, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} F) j)) x._@.Mathlib.CategoryTheory.Filtered._hyg.4398 x._@.Mathlib.CategoryTheory.Filtered._hyg.4400) (fun (f : PSigma.{succ u3, succ u2} C (fun (i : C) => Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) i j)) => Set.range.{u1, succ u1} (Prefunctor.obj.{succ u2, succ u1, u3, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u3, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} F) j) (Prefunctor.obj.{succ u2, succ u1, u3, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u3, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} F) (PSigma.fst.{succ u3, succ u2} C (fun (i : C) => Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) i j) f)) (Prefunctor.map.{succ u2, succ u1, u3, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u3, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} F) (PSigma.fst.{succ u3, succ u2} C (fun (i : C) => Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) i j) f) j (PSigma.snd.{succ u3, succ u2} C (fun (i : C) => Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) i j) f)))
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] [_inst_2 : CategoryTheory.IsCofilteredOrEmpty.{u2, u3} C _inst_1] (F : CategoryTheory.Functor.{u2, u1, u3, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1}) (j : C), Directed.{u1, max (succ u3) (succ u2)} (Set.{u1} (Prefunctor.obj.{succ u2, succ u1, u3, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u3, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} F) j)) (PSigma.{succ u3, succ u2} C (fun (i : C) => Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) i j)) (fun (x._@.Mathlib.CategoryTheory.Filtered._hyg.4396 : Set.{u1} (Prefunctor.obj.{succ u2, succ u1, u3, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u3, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} F) j)) (x._@.Mathlib.CategoryTheory.Filtered._hyg.4398 : Set.{u1} (Prefunctor.obj.{succ u2, succ u1, u3, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u3, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} F) j)) => Superset.{u1} (Set.{u1} (Prefunctor.obj.{succ u2, succ u1, u3, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u3, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} F) j)) (Set.instHasSubsetSet.{u1} (Prefunctor.obj.{succ u2, succ u1, u3, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u3, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} F) j)) x._@.Mathlib.CategoryTheory.Filtered._hyg.4396 x._@.Mathlib.CategoryTheory.Filtered._hyg.4398) (fun (f : PSigma.{succ u3, succ u2} C (fun (i : C) => Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) i j)) => Set.range.{u1, succ u1} (Prefunctor.obj.{succ u2, succ u1, u3, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u3, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} F) j) (Prefunctor.obj.{succ u2, succ u1, u3, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u3, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} F) (PSigma.fst.{succ u3, succ u2} C (fun (i : C) => Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) i j) f)) (Prefunctor.map.{succ u2, succ u1, u3, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u3, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} F) (PSigma.fst.{succ u3, succ u2} C (fun (i : C) => Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) i j) f) j (PSigma.snd.{succ u3, succ u2} C (fun (i : C) => Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) i j) f)))
 Case conversion may be inaccurate. Consider using '#align category_theory.functor.ranges_directed CategoryTheory.Functor.ranges_directedₓ'. -/
 theorem CategoryTheory.Functor.ranges_directed (F : C ⥤ Type _) (j : C) :
     Directed (· ⊇ ·) fun f : Σ'i, i ⟶ j => Set.range (F.map f.2) := fun ⟨i, ij⟩ ⟨k, kj⟩ =>

mathlib commit https://github.com/leanprover-community/mathlib/commit/3180fab693e2cee3bff62675571264cb8778b212

@@ -679,7 +679,7 @@ theorem cospan {i j j' : C} (f : j ⟶ i) (f' : j' ⟶ i) :
 lean 3 declaration is
   forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.IsCofilteredOrEmpty.{u1, u2} C _inst_1] (F : CategoryTheory.Functor.{u1, u3, u2, succ u3} C _inst_1 Type.{u3} CategoryTheory.types.{u3}) (j : C), Directed.{u3, max 1 (succ u2) (succ u1)} (Set.{u3} (CategoryTheory.Functor.obj.{u1, u3, u2, succ u3} C _inst_1 Type.{u3} CategoryTheory.types.{u3} F j)) (PSigma.{succ u2, succ u1} C (fun (i : C) => Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) i j)) (Superset.{u3} (Set.{u3} (CategoryTheory.Functor.obj.{u1, u3, u2, succ u3} C _inst_1 Type.{u3} CategoryTheory.types.{u3} F j)) (Set.hasSubset.{u3} (CategoryTheory.Functor.obj.{u1, u3, u2, succ u3} C _inst_1 Type.{u3} CategoryTheory.types.{u3} F j))) (fun (f : PSigma.{succ u2, succ u1} C (fun (i : C) => Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) i j)) => Set.range.{u3, succ u3} (CategoryTheory.Functor.obj.{u1, u3, u2, succ u3} C _inst_1 Type.{u3} CategoryTheory.types.{u3} F j) (CategoryTheory.Functor.obj.{u1, u3, u2, succ u3} C _inst_1 Type.{u3} CategoryTheory.types.{u3} F (PSigma.fst.{succ u2, succ u1} C (fun (i : C) => Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) i j) f)) (CategoryTheory.Functor.map.{u1, u3, u2, succ u3} C _inst_1 Type.{u3} CategoryTheory.types.{u3} F (PSigma.fst.{succ u2, succ u1} C (fun (i : C) => Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) i j) f) j (PSigma.snd.{succ u2, succ u1} C (fun (i : C) => Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) i j) f)))
 but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] [_inst_2 : CategoryTheory.IsCofilteredOrEmpty.{u2, u3} C _inst_1] (F : CategoryTheory.Functor.{u2, u1, u3, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1}) (j : C), Directed.{u1, max (succ u3) (succ u2)} (Set.{u1} (Prefunctor.obj.{succ u2, succ u1, u3, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u3, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} F) j)) (PSigma.{succ u3, succ u2} C (fun (i : C) => Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) i j)) (fun (x._@.Mathlib.CategoryTheory.Filtered._hyg.4393 : Set.{u1} (Prefunctor.obj.{succ u2, succ u1, u3, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u3, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} F) j)) (x._@.Mathlib.CategoryTheory.Filtered._hyg.4395 : Set.{u1} (Prefunctor.obj.{succ u2, succ u1, u3, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u3, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} F) j)) => Superset.{u1} (Set.{u1} (Prefunctor.obj.{succ u2, succ u1, u3, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u3, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} F) j)) (Set.instHasSubsetSet.{u1} (Prefunctor.obj.{succ u2, succ u1, u3, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u3, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} F) j)) x._@.Mathlib.CategoryTheory.Filtered._hyg.4393 x._@.Mathlib.CategoryTheory.Filtered._hyg.4395) (fun (f : 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(CategoryTheory.Functor.toPrefunctor.{u2, u1, u3, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} F) (PSigma.fst.{succ u3, succ u2} C (fun (i : C) => Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) i j) f)) (Prefunctor.map.{succ u2, succ u1, u3, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u3, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} F) (PSigma.fst.{succ u3, succ u2} C (fun (i : C) => Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) i j) f) j (PSigma.snd.{succ u3, succ u2} C (fun (i : C) => Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) i j) f)))
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] [_inst_2 : CategoryTheory.IsCofilteredOrEmpty.{u2, u3} C _inst_1] (F : CategoryTheory.Functor.{u2, u1, u3, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1}) (j : C), Directed.{u1, max (succ u3) (succ u2)} (Set.{u1} (Prefunctor.obj.{succ u2, succ u1, u3, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u3, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} F) j)) (PSigma.{succ u3, succ u2} C (fun (i : C) => Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) i j)) (fun (x._@.Mathlib.CategoryTheory.Filtered._hyg.4398 : Set.{u1} (Prefunctor.obj.{succ u2, succ u1, u3, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u3, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} F) j)) (x._@.Mathlib.CategoryTheory.Filtered._hyg.4400 : Set.{u1} (Prefunctor.obj.{succ u2, succ u1, u3, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u3, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} F) j)) => Superset.{u1} (Set.{u1} (Prefunctor.obj.{succ u2, succ u1, u3, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u3, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} F) j)) (Set.instHasSubsetSet.{u1} (Prefunctor.obj.{succ u2, succ u1, u3, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u3, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} F) j)) x._@.Mathlib.CategoryTheory.Filtered._hyg.4398 x._@.Mathlib.CategoryTheory.Filtered._hyg.4400) (fun (f : PSigma.{succ u3, succ u2} C (fun (i : C) => Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) i j)) => Set.range.{u1, succ u1} (Prefunctor.obj.{succ u2, succ u1, u3, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u3, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} F) j) (Prefunctor.obj.{succ u2, succ u1, u3, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u3, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} F) (PSigma.fst.{succ u3, succ u2} C (fun (i : C) => Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) i j) f)) (Prefunctor.map.{succ u2, succ u1, u3, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u3, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} F) (PSigma.fst.{succ u3, succ u2} C (fun (i : C) => Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) i j) f) j (PSigma.snd.{succ u3, succ u2} C (fun (i : C) => Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) i j) f)))
 Case conversion may be inaccurate. Consider using '#align category_theory.functor.ranges_directed CategoryTheory.Functor.ranges_directedₓ'. -/
 theorem CategoryTheory.Functor.ranges_directed (F : C ⥤ Type _) (j : C) :
     Directed (· ⊇ ·) fun f : Σ'i, i ⟶ j => Set.range (F.map f.2) := fun ⟨i, ij⟩ ⟨k, kj⟩ =>

mathlib commit https://github.com/leanprover-community/mathlib/commit/195fcd60ff2bfe392543bceb0ec2adcdb472db4c

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Reid Barton, Scott Morrison
 
 ! This file was ported from Lean 3 source module category_theory.filtered
-! leanprover-community/mathlib commit 14e80e85cbca5872a329fbfd3d1f3fd64e306934
+! leanprover-community/mathlib commit ee05e9ce1322178f0c12004eb93c00d2c8c00ed2
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -17,6 +17,9 @@ import Mathbin.CategoryTheory.Category.Ulift
 /-!
 # Filtered categories
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 A category is filtered if every finite diagram admits a cocone.
 We give a simple characterisation of this condition as
 1. for every pair of objects there exists another object "to the right",

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

@@ -63,6 +63,7 @@ namespace CategoryTheory
 
 variable (C : Type u) [Category.{v} C]
 
+#print CategoryTheory.IsFilteredOrEmpty /-
 /-- A category `is_filtered_or_empty` if
 1. for every pair of objects there exists another object "to the right", and
 2. for every pair of parallel morphisms there exists a morphism to the right so the compositions
@@ -72,7 +73,9 @@ class IsFilteredOrEmpty : Prop where
   cocone_objs : ∀ X Y : C, ∃ (Z : _)(f : X ⟶ Z)(g : Y ⟶ Z), True
   cocone_maps : ∀ ⦃X Y : C⦄ (f g : X ⟶ Y), ∃ (Z : _)(h : Y ⟶ Z), f ≫ h = g ≫ h
 #align category_theory.is_filtered_or_empty CategoryTheory.IsFilteredOrEmpty
+-/
 
+#print CategoryTheory.IsFiltered /-
 /-- A category `is_filtered` if
 1. for every pair of objects there exists another object "to the right",
 2. for every pair of parallel morphisms there exists a morphism to the right so the compositions
@@ -84,18 +87,24 @@ See <https://stacks.math.columbia.edu/tag/002V>. (They also define a diagram bei
 class IsFiltered extends IsFilteredOrEmpty C : Prop where
   [Nonempty : Nonempty C]
 #align category_theory.is_filtered CategoryTheory.IsFiltered
+-/
 
+#print CategoryTheory.isFilteredOrEmpty_of_semilatticeSup /-
 instance (priority := 100) isFilteredOrEmpty_of_semilatticeSup (α : Type u) [SemilatticeSup α] :
     IsFilteredOrEmpty α
     where
   cocone_objs X Y := ⟨X ⊔ Y, homOfLE le_sup_left, homOfLE le_sup_right, trivial⟩
   cocone_maps X Y f g := ⟨Y, 𝟙 _, by ext⟩
 #align category_theory.is_filtered_or_empty_of_semilattice_sup CategoryTheory.isFilteredOrEmpty_of_semilatticeSup
+-/
 
+#print CategoryTheory.isFiltered_of_semilatticeSup_nonempty /-
 instance (priority := 100) isFiltered_of_semilatticeSup_nonempty (α : Type u) [SemilatticeSup α]
     [Nonempty α] : IsFiltered α where
 #align category_theory.is_filtered_of_semilattice_sup_nonempty CategoryTheory.isFiltered_of_semilatticeSup_nonempty
+-/
 
+#print CategoryTheory.isFilteredOrEmpty_of_directed_le /-
 instance (priority := 100) isFilteredOrEmpty_of_directed_le (α : Type u) [Preorder α]
     [IsDirected α (· ≤ ·)] : IsFilteredOrEmpty α
     where
@@ -104,10 +113,13 @@ instance (priority := 100) isFilteredOrEmpty_of_directed_le (α : Type u) [Preor
     ⟨Z, homOfLE h1, homOfLE h2, trivial⟩
   cocone_maps X Y f g := ⟨Y, 𝟙 _, by simp⟩
 #align category_theory.is_filtered_or_empty_of_directed_le CategoryTheory.isFilteredOrEmpty_of_directed_le
+-/
 
+#print CategoryTheory.isFiltered_of_directed_le_nonempty /-
 instance (priority := 100) isFiltered_of_directed_le_nonempty (α : Type u) [Preorder α]
     [IsDirected α (· ≤ ·)] [Nonempty α] : IsFiltered α where
 #align category_theory.is_filtered_of_directed_le_nonempty CategoryTheory.isFiltered_of_directed_le_nonempty
+-/
 
 -- Sanity checks
 example (α : Type u) [SemilatticeSup α] [OrderBot α] : IsFiltered α := by infer_instance
@@ -134,27 +146,34 @@ theorem cocone_maps : ∀ ⦃X Y : C⦄ (f g : X ⟶ Y), ∃ (Z : _)(h : Y ⟶ Z
   IsFilteredOrEmpty.cocone_maps
 #align category_theory.is_filtered.cocone_maps CategoryTheory.IsFiltered.cocone_maps
 
+#print CategoryTheory.IsFiltered.max /-
 /-- `max j j'` is an arbitrary choice of object to the right of both `j` and `j'`,
 whose existence is ensured by `is_filtered`.
 -/
 noncomputable def max (j j' : C) : C :=
   (cocone_objs j j').some
 #align category_theory.is_filtered.max CategoryTheory.IsFiltered.max
+-/
 
+#print CategoryTheory.IsFiltered.leftToMax /-
 /-- `left_to_max j j'` is an arbitrary choice of morphism from `j` to `max j j'`,
 whose existence is ensured by `is_filtered`.
 -/
 noncomputable def leftToMax (j j' : C) : j ⟶ max j j' :=
   (cocone_objs j j').choose_spec.some
 #align category_theory.is_filtered.left_to_max CategoryTheory.IsFiltered.leftToMax
+-/
 
+#print CategoryTheory.IsFiltered.rightToMax /-
 /-- `right_to_max j j'` is an arbitrary choice of morphism from `j'` to `max j j'`,
 whose existence is ensured by `is_filtered`.
 -/
 noncomputable def rightToMax (j j' : C) : j' ⟶ max j j' :=
   (cocone_objs j j').choose_spec.choose_spec.some
 #align category_theory.is_filtered.right_to_max CategoryTheory.IsFiltered.rightToMax
+-/
 
+#print CategoryTheory.IsFiltered.coeq /-
 /-- `coeq f f'`, for morphisms `f f' : j ⟶ j'`, is an arbitrary choice of object
 which admits a morphism `coeq_hom f f' : j' ⟶ coeq f f'` such that
 `coeq_condition : f ≫ coeq_hom f f' = f' ≫ coeq_hom f f'`.
@@ -163,7 +182,9 @@ Its existence is ensured by `is_filtered`.
 noncomputable def coeq {j j' : C} (f f' : j ⟶ j') : C :=
   (cocone_maps f f').some
 #align category_theory.is_filtered.coeq CategoryTheory.IsFiltered.coeq
+-/
 
+#print CategoryTheory.IsFiltered.coeqHom /-
 /-- `coeq_hom f f'`, for morphisms `f f' : j ⟶ j'`, is an arbitrary choice of morphism
 `coeq_hom f f' : j' ⟶ coeq f f'` such that
 `coeq_condition : f ≫ coeq_hom f f' = f' ≫ coeq_hom f f'`.
@@ -172,7 +193,9 @@ Its existence is ensured by `is_filtered`.
 noncomputable def coeqHom {j j' : C} (f f' : j ⟶ j') : j' ⟶ coeq f f' :=
   (cocone_maps f f').choose_spec.some
 #align category_theory.is_filtered.coeq_hom CategoryTheory.IsFiltered.coeqHom
+-/
 
+#print CategoryTheory.IsFiltered.coeq_condition /-
 /-- `coeq_condition f f'`, for morphisms `f f' : j ⟶ j'`, is the proof that
 `f ≫ coeq_hom f f' = f' ≫ coeq_hom f f'`.
 -/
@@ -180,6 +203,7 @@ noncomputable def coeqHom {j j' : C} (f f' : j ⟶ j') : j' ⟶ coeq f f' :=
 theorem coeq_condition {j j' : C} (f f' : j ⟶ j') : f ≫ coeqHom f f' = f' ≫ coeqHom f f' :=
   (cocone_maps f f').choose_spec.choose_spec
 #align category_theory.is_filtered.coeq_condition CategoryTheory.IsFiltered.coeq_condition
+-/
 
 end AllowEmpty
 
@@ -189,6 +213,7 @@ open CategoryTheory.Limits
 
 variable {C} [IsFiltered C]
 
+#print CategoryTheory.IsFiltered.sup_objs_exists /-
 /-- Any finite collection of objects in a filtered category has an object "to the right".
 -/
 theorem sup_objs_exists (O : Finset C) : ∃ S : C, ∀ {X}, X ∈ O → Nonempty (X ⟶ S) := by
@@ -202,9 +227,11 @@ theorem sup_objs_exists (O : Finset C) : ∃ S : C, ∀ {X}, X ∈ O → Nonempt
       · exact ⟨left_to_max _ _⟩
       · exact ⟨(w' (Finset.mem_of_mem_insert_of_ne mY h)).some ≫ right_to_max _ _⟩
 #align category_theory.is_filtered.sup_objs_exists CategoryTheory.IsFiltered.sup_objs_exists
+-/
 
 variable (O : Finset C) (H : Finset (Σ'(X Y : C)(mX : X ∈ O)(mY : Y ∈ O), X ⟶ Y))
 
+#print CategoryTheory.IsFiltered.sup_exists /-
 /-- Given any `finset` of objects `{X, ...}` and
 indexed collection of `finset`s of morphisms `{f, ...}` in `C`,
 there exists an object `S`, with a morphism `T X : X ⟶ S` from each `X`,
@@ -237,7 +264,9 @@ theorem sup_exists :
         rw [heq_iff_eq, PSigma.mk.inj_iff] at h
         exact ⟨rfl, h.1.symm⟩
 #align category_theory.is_filtered.sup_exists CategoryTheory.IsFiltered.sup_exists
+-/
 
+#print CategoryTheory.IsFiltered.sup /-
 /-- An arbitrary choice of object "to the right"
 of a finite collection of objects `O` and morphisms `H`,
 making all the triangles commute.
@@ -245,13 +274,17 @@ making all the triangles commute.
 noncomputable def sup : C :=
   (sup_exists O H).some
 #align category_theory.is_filtered.sup CategoryTheory.IsFiltered.sup
+-/
 
+#print CategoryTheory.IsFiltered.toSup /-
 /-- The morphisms to `sup O H`.
 -/
 noncomputable def toSup {X : C} (m : X ∈ O) : X ⟶ sup O H :=
   (sup_exists O H).choose_spec.some m
 #align category_theory.is_filtered.to_sup CategoryTheory.IsFiltered.toSup
+-/
 
+#print CategoryTheory.IsFiltered.toSup_commutes /-
 /-- The triangles of consisting of a morphism in `H` and the maps to `sup O H` commute.
 -/
 theorem toSup_commutes {X Y : C} (mX : X ∈ O) (mY : Y ∈ O) {f : X ⟶ Y}
@@ -259,9 +292,11 @@ theorem toSup_commutes {X Y : C} (mX : X ∈ O) (mY : Y ∈ O) {f : X ⟶ Y}
     f ≫ toSup O H mY = toSup O H mX :=
   (sup_exists O H).choose_spec.choose_spec mX mY mf
 #align category_theory.is_filtered.to_sup_commutes CategoryTheory.IsFiltered.toSup_commutes
+-/
 
 variable {J : Type v} [SmallCategory J] [FinCategory J]
 
+#print CategoryTheory.IsFiltered.cocone_nonempty /-
 /-- If we have `is_filtered C`, then for any functor `F : J ⥤ C` with `fin_category J`,
 there exists a cocone over `F`.
 -/
@@ -282,15 +317,19 @@ theorem cocone_nonempty (F : J ⥤ C) : Nonempty (Cocone F) := by
       Finset.mem_image]
     exact ⟨j, rfl, j', g, by simp⟩
 #align category_theory.is_filtered.cocone_nonempty CategoryTheory.IsFiltered.cocone_nonempty
+-/
 
+#print CategoryTheory.IsFiltered.cocone /-
 /-- An arbitrary choice of cocone over `F : J ⥤ C`, for `fin_category J` and `is_filtered C`.
 -/
 noncomputable def cocone (F : J ⥤ C) : Cocone F :=
   (cocone_nonempty F).some
 #align category_theory.is_filtered.cocone CategoryTheory.IsFiltered.cocone
+-/
 
 variable {D : Type u₁} [Category.{v₁} D]
 
+#print CategoryTheory.IsFiltered.of_right_adjoint /-
 /-- If `C` is filtered, and we have a functor `R : C ⥤ D` with a left adjoint, then `D` is filtered.
 -/
 theorem of_right_adjoint {L : D ⥤ C} {R : C ⥤ D} (h : L ⊣ R) : IsFiltered D :=
@@ -301,12 +340,21 @@ theorem of_right_adjoint {L : D ⥤ C} {R : C ⥤ D} (h : L ⊣ R) : IsFiltered
         rw [← h.hom_equiv_naturality_left, ← h.hom_equiv_naturality_left, coeq_condition]⟩
     Nonempty := IsFiltered.nonempty.map R.obj }
 #align category_theory.is_filtered.of_right_adjoint CategoryTheory.IsFiltered.of_right_adjoint
+-/
 
+#print CategoryTheory.IsFiltered.of_isRightAdjoint /-
 /-- If `C` is filtered, and we have a right adjoint functor `R : C ⥤ D`, then `D` is filtered. -/
 theorem of_isRightAdjoint (R : C ⥤ D) [IsRightAdjoint R] : IsFiltered D :=
   of_right_adjoint (Adjunction.ofRightAdjoint R)
 #align category_theory.is_filtered.of_is_right_adjoint CategoryTheory.IsFiltered.of_isRightAdjoint
+-/
 
+/- warning: category_theory.is_filtered.of_equivalence -> CategoryTheory.IsFiltered.of_equivalence is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.IsFiltered.{u1, u3} C _inst_1] {D : Type.{u4}} [_inst_5 : CategoryTheory.Category.{u2, u4} D], (CategoryTheory.Equivalence.{u1, u2, u3, u4} C _inst_1 D _inst_5) -> (CategoryTheory.IsFiltered.{u2, u4} D _inst_5)
+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.IsFiltered.{u1, u3} C _inst_1] {D : Type.{u4}} [_inst_5 : CategoryTheory.Category.{u2, u4} D], (CategoryTheory.Equivalence.{u1, u2, u3, u4} C D _inst_1 _inst_5) -> (CategoryTheory.IsFiltered.{u2, u4} D _inst_5)
+Case conversion may be inaccurate. Consider using '#align category_theory.is_filtered.of_equivalence CategoryTheory.IsFiltered.of_equivalenceₓ'. -/
 /-- Being filtered is preserved by equivalence of categories. -/
 theorem of_equivalence (h : C ≌ D) : IsFiltered D :=
   of_right_adjoint h.symm.toAdjunction
@@ -318,34 +366,43 @@ section SpecialShapes
 
 variable {C} [IsFilteredOrEmpty C]
 
+#print CategoryTheory.IsFiltered.max₃ /-
 /-- `max₃ j₁ j₂ j₃` is an arbitrary choice of object to the right of `j₁`, `j₂` and `j₃`,
 whose existence is ensured by `is_filtered`.
 -/
 noncomputable def max₃ (j₁ j₂ j₃ : C) : C :=
   max (max j₁ j₂) j₃
 #align category_theory.is_filtered.max₃ CategoryTheory.IsFiltered.max₃
+-/
 
+#print CategoryTheory.IsFiltered.firstToMax₃ /-
 /-- `first_to_max₃ j₁ j₂ j₃` is an arbitrary choice of morphism from `j₁` to `max₃ j₁ j₂ j₃`,
 whose existence is ensured by `is_filtered`.
 -/
 noncomputable def firstToMax₃ (j₁ j₂ j₃ : C) : j₁ ⟶ max₃ j₁ j₂ j₃ :=
   leftToMax j₁ j₂ ≫ leftToMax (max j₁ j₂) j₃
 #align category_theory.is_filtered.first_to_max₃ CategoryTheory.IsFiltered.firstToMax₃
+-/
 
+#print CategoryTheory.IsFiltered.secondToMax₃ /-
 /-- `second_to_max₃ j₁ j₂ j₃` is an arbitrary choice of morphism from `j₂` to `max₃ j₁ j₂ j₃`,
 whose existence is ensured by `is_filtered`.
 -/
 noncomputable def secondToMax₃ (j₁ j₂ j₃ : C) : j₂ ⟶ max₃ j₁ j₂ j₃ :=
   rightToMax j₁ j₂ ≫ leftToMax (max j₁ j₂) j₃
 #align category_theory.is_filtered.second_to_max₃ CategoryTheory.IsFiltered.secondToMax₃
+-/
 
+#print CategoryTheory.IsFiltered.thirdToMax₃ /-
 /-- `third_to_max₃ j₁ j₂ j₃` is an arbitrary choice of morphism from `j₃` to `max₃ j₁ j₂ j₃`,
 whose existence is ensured by `is_filtered`.
 -/
 noncomputable def thirdToMax₃ (j₁ j₂ j₃ : C) : j₃ ⟶ max₃ j₁ j₂ j₃ :=
   rightToMax (max j₁ j₂) j₃
 #align category_theory.is_filtered.third_to_max₃ CategoryTheory.IsFiltered.thirdToMax₃
+-/
 
+#print CategoryTheory.IsFiltered.coeq₃ /-
 /-- `coeq₃ f g h`, for morphisms `f g h : j₁ ⟶ j₂`, is an arbitrary choice of object
 which admits a morphism `coeq₃_hom f g h : j₂ ⟶ coeq₃ f g h` such that
 `coeq₃_condition₁`, `coeq₃_condition₂` and `coeq₃_condition₃` are satisfied.
@@ -355,7 +412,9 @@ noncomputable def coeq₃ {j₁ j₂ : C} (f g h : j₁ ⟶ j₂) : C :=
   coeq (coeqHom f g ≫ leftToMax (coeq f g) (coeq g h))
     (coeqHom g h ≫ rightToMax (coeq f g) (coeq g h))
 #align category_theory.is_filtered.coeq₃ CategoryTheory.IsFiltered.coeq₃
+-/
 
+#print CategoryTheory.IsFiltered.coeq₃Hom /-
 /-- `coeq₃_hom f g h`, for morphisms `f g h : j₁ ⟶ j₂`, is an arbitrary choice of morphism
 `j₂ ⟶ coeq₃ f g h` such that `coeq₃_condition₁`, `coeq₃_condition₂` and `coeq₃_condition₃`
 are satisfied. Its existence is ensured by `is_filtered`.
@@ -366,11 +425,15 @@ noncomputable def coeq₃Hom {j₁ j₂ : C} (f g h : j₁ ⟶ j₂) : j₂ ⟶
       coeqHom (coeqHom f g ≫ leftToMax (coeq f g) (coeq g h))
         (coeqHom g h ≫ rightToMax (coeq f g) (coeq g h))
 #align category_theory.is_filtered.coeq₃_hom CategoryTheory.IsFiltered.coeq₃Hom
+-/
 
+#print CategoryTheory.IsFiltered.coeq₃_condition₁ /-
 theorem coeq₃_condition₁ {j₁ j₂ : C} (f g h : j₁ ⟶ j₂) : f ≫ coeq₃Hom f g h = g ≫ coeq₃Hom f g h :=
   by rw [coeq₃_hom, reassoc_of (coeq_condition f g)]
 #align category_theory.is_filtered.coeq₃_condition₁ CategoryTheory.IsFiltered.coeq₃_condition₁
+-/
 
+#print CategoryTheory.IsFiltered.coeq₃_condition₂ /-
 theorem coeq₃_condition₂ {j₁ j₂ : C} (f g h : j₁ ⟶ j₂) : g ≫ coeq₃Hom f g h = h ≫ coeq₃Hom f g h :=
   by
   dsimp [coeq₃_hom]
@@ -379,11 +442,15 @@ theorem coeq₃_condition₂ {j₁ j₂ : C} (f g h : j₁ ⟶ j₂) : g ≫ coe
   slice_lhs 1 3 => rw [← category.assoc, coeq_condition _ _]
   simp only [category.assoc]
 #align category_theory.is_filtered.coeq₃_condition₂ CategoryTheory.IsFiltered.coeq₃_condition₂
+-/
 
+#print CategoryTheory.IsFiltered.coeq₃_condition₃ /-
 theorem coeq₃_condition₃ {j₁ j₂ : C} (f g h : j₁ ⟶ j₂) : f ≫ coeq₃Hom f g h = h ≫ coeq₃Hom f g h :=
   Eq.trans (coeq₃_condition₁ f g h) (coeq₃_condition₂ f g h)
 #align category_theory.is_filtered.coeq₃_condition₃ CategoryTheory.IsFiltered.coeq₃_condition₃
+-/
 
+#print CategoryTheory.IsFiltered.span /-
 /-- For every span `j ⟵ i ⟶ j'`, there
    exists a cocone `j ⟶ k ⟵ j'` such that the square commutes. -/
 theorem span {i j j' : C} (f : i ⟶ j) (f' : i ⟶ j') :
@@ -392,7 +459,9 @@ theorem span {i j j' : C} (f : i ⟶ j) (f' : i ⟶ j') :
   let ⟨k, e, he⟩ := cocone_maps (f ≫ G) (f' ≫ G')
   ⟨k, G ≫ e, G' ≫ e, by simpa only [← category.assoc] ⟩
 #align category_theory.is_filtered.span CategoryTheory.IsFiltered.span
+-/
 
+#print CategoryTheory.IsFiltered.bowtie /-
 /-- Given a "bowtie" of morphisms
 ```
  j₁   j₂
@@ -414,7 +483,9 @@ theorem bowtie {j₁ j₂ k₁ k₂ : C} (f₁ : j₁ ⟶ k₁) (g₁ : j₁ ⟶
   simp_rw [category.assoc] at hs
   exact ⟨s, k₁t ≫ ts, k₂t ≫ ts, by rw [reassoc_of ht], hs⟩
 #align category_theory.is_filtered.bowtie CategoryTheory.IsFiltered.bowtie
+-/
 
+#print CategoryTheory.IsFiltered.tulip /-
 /-- Given a "tulip" of morphisms
 ```
  j₁    j₂    j₃
@@ -442,11 +513,13 @@ theorem tulip {j₁ j₂ j₃ k₁ k₂ l : C} (f₁ : j₁ ⟶ k₁) (f₂ : j
   refine' ⟨s, k₁l ≫ l's, ls, k₂l ≫ l's, _, by rw [reassoc_of hl], _⟩ <;>
     simp only [hs₁, hs₂, category.assoc]
 #align category_theory.is_filtered.tulip CategoryTheory.IsFiltered.tulip
+-/
 
 end SpecialShapes
 
 end IsFiltered
 
+#print CategoryTheory.IsCofilteredOrEmpty /-
 /-- A category `is_cofiltered_or_empty` if
 1. for every pair of objects there exists another object "to the left", and
 2. for every pair of parallel morphisms there exists a morphism to the left so the compositions
@@ -456,7 +529,9 @@ class IsCofilteredOrEmpty : Prop where
   cone_objs : ∀ X Y : C, ∃ (W : _)(f : W ⟶ X)(g : W ⟶ Y), True
   cone_maps : ∀ ⦃X Y : C⦄ (f g : X ⟶ Y), ∃ (W : _)(h : W ⟶ X), h ≫ f = h ≫ g
 #align category_theory.is_cofiltered_or_empty CategoryTheory.IsCofilteredOrEmpty
+-/
 
+#print CategoryTheory.IsCofiltered /-
 /-- A category `is_cofiltered` if
 1. for every pair of objects there exists another object "to the left",
 2. for every pair of parallel morphisms there exists a morphism to the left so the compositions
@@ -468,18 +543,24 @@ See <https://stacks.math.columbia.edu/tag/04AZ>.
 class IsCofiltered extends IsCofilteredOrEmpty C : Prop where
   [Nonempty : Nonempty C]
 #align category_theory.is_cofiltered CategoryTheory.IsCofiltered
+-/
 
+#print CategoryTheory.isCofilteredOrEmpty_of_semilatticeInf /-
 instance (priority := 100) isCofilteredOrEmpty_of_semilatticeInf (α : Type u) [SemilatticeInf α] :
     IsCofilteredOrEmpty α
     where
   cone_objs X Y := ⟨X ⊓ Y, homOfLE inf_le_left, homOfLE inf_le_right, trivial⟩
   cone_maps X Y f g := ⟨X, 𝟙 _, by ext⟩
 #align category_theory.is_cofiltered_or_empty_of_semilattice_inf CategoryTheory.isCofilteredOrEmpty_of_semilatticeInf
+-/
 
+#print CategoryTheory.isCofiltered_of_semilatticeInf_nonempty /-
 instance (priority := 100) isCofiltered_of_semilatticeInf_nonempty (α : Type u) [SemilatticeInf α]
     [Nonempty α] : IsCofiltered α where
 #align category_theory.is_cofiltered_of_semilattice_inf_nonempty CategoryTheory.isCofiltered_of_semilatticeInf_nonempty
+-/
 
+#print CategoryTheory.isCofilteredOrEmpty_of_directed_ge /-
 instance (priority := 100) isCofilteredOrEmpty_of_directed_ge (α : Type u) [Preorder α]
     [IsDirected α (· ≥ ·)] : IsCofilteredOrEmpty α
     where
@@ -488,10 +569,13 @@ instance (priority := 100) isCofilteredOrEmpty_of_directed_ge (α : Type u) [Pre
     ⟨Z, homOfLE hX, homOfLE hY, trivial⟩
   cone_maps X Y f g := ⟨X, 𝟙 _, by simp⟩
 #align category_theory.is_cofiltered_or_empty_of_directed_ge CategoryTheory.isCofilteredOrEmpty_of_directed_ge
+-/
 
+#print CategoryTheory.isCofiltered_of_directed_ge_nonempty /-
 instance (priority := 100) isCofiltered_of_directed_ge_nonempty (α : Type u) [Preorder α]
     [IsDirected α (· ≥ ·)] [Nonempty α] : IsCofiltered α where
 #align category_theory.is_cofiltered_of_directed_ge_nonempty CategoryTheory.isCofiltered_of_directed_ge_nonempty
+-/
 
 -- Sanity checks
 example (α : Type u) [SemilatticeInf α] [OrderBot α] : IsCofiltered α := by infer_instance
@@ -518,27 +602,34 @@ theorem cone_maps : ∀ ⦃X Y : C⦄ (f g : X ⟶ Y), ∃ (W : _)(h : W ⟶ X),
   IsCofilteredOrEmpty.cone_maps
 #align category_theory.is_cofiltered.cone_maps CategoryTheory.IsCofiltered.cone_maps
 
+#print CategoryTheory.IsCofiltered.min /-
 /-- `min j j'` is an arbitrary choice of object to the left of both `j` and `j'`,
 whose existence is ensured by `is_cofiltered`.
 -/
 noncomputable def min (j j' : C) : C :=
   (cone_objs j j').some
 #align category_theory.is_cofiltered.min CategoryTheory.IsCofiltered.min
+-/
 
+#print CategoryTheory.IsCofiltered.minToLeft /-
 /-- `min_to_left j j'` is an arbitrary choice of morphism from `min j j'` to `j`,
 whose existence is ensured by `is_cofiltered`.
 -/
 noncomputable def minToLeft (j j' : C) : min j j' ⟶ j :=
   (cone_objs j j').choose_spec.some
 #align category_theory.is_cofiltered.min_to_left CategoryTheory.IsCofiltered.minToLeft
+-/
 
+#print CategoryTheory.IsCofiltered.minToRight /-
 /-- `min_to_right j j'` is an arbitrary choice of morphism from `min j j'` to `j'`,
 whose existence is ensured by `is_cofiltered`.
 -/
 noncomputable def minToRight (j j' : C) : min j j' ⟶ j' :=
   (cone_objs j j').choose_spec.choose_spec.some
 #align category_theory.is_cofiltered.min_to_right CategoryTheory.IsCofiltered.minToRight
+-/
 
+#print CategoryTheory.IsCofiltered.eq /-
 /-- `eq f f'`, for morphisms `f f' : j ⟶ j'`, is an arbitrary choice of object
 which admits a morphism `eq_hom f f' : eq f f' ⟶ j` such that
 `eq_condition : eq_hom f f' ≫ f = eq_hom f f' ≫ f'`.
@@ -547,7 +638,9 @@ Its existence is ensured by `is_cofiltered`.
 noncomputable def eq {j j' : C} (f f' : j ⟶ j') : C :=
   (cone_maps f f').some
 #align category_theory.is_cofiltered.eq CategoryTheory.IsCofiltered.eq
+-/
 
+#print CategoryTheory.IsCofiltered.eqHom /-
 /-- `eq_hom f f'`, for morphisms `f f' : j ⟶ j'`, is an arbitrary choice of morphism
 `eq_hom f f' : eq f f' ⟶ j` such that
 `eq_condition : eq_hom f f' ≫ f = eq_hom f f' ≫ f'`.
@@ -556,7 +649,9 @@ Its existence is ensured by `is_cofiltered`.
 noncomputable def eqHom {j j' : C} (f f' : j ⟶ j') : eq f f' ⟶ j :=
   (cone_maps f f').choose_spec.some
 #align category_theory.is_cofiltered.eq_hom CategoryTheory.IsCofiltered.eqHom
+-/
 
+#print CategoryTheory.IsCofiltered.eq_condition /-
 /-- `eq_condition f f'`, for morphisms `f f' : j ⟶ j'`, is the proof that
 `eq_hom f f' ≫ f = eq_hom f f' ≫ f'`.
 -/
@@ -564,7 +659,9 @@ noncomputable def eqHom {j j' : C} (f f' : j ⟶ j') : eq f f' ⟶ j :=
 theorem eq_condition {j j' : C} (f f' : j ⟶ j') : eqHom f f' ≫ f = eqHom f f' ≫ f' :=
   (cone_maps f f').choose_spec.choose_spec
 #align category_theory.is_cofiltered.eq_condition CategoryTheory.IsCofiltered.eq_condition
+-/
 
+#print CategoryTheory.IsCofiltered.cospan /-
 /-- For every cospan `j ⟶ i ⟵ j'`,
  there exists a cone `j ⟵ k ⟶ j'` such that the square commutes. -/
 theorem cospan {i j j' : C} (f : j ⟶ i) (f' : j' ⟶ i) :
@@ -573,7 +670,14 @@ theorem cospan {i j j' : C} (f : j ⟶ i) (f' : j' ⟶ i) :
   let ⟨k, e, he⟩ := cone_maps (G ≫ f) (G' ≫ f')
   ⟨k, e ≫ G, e ≫ G', by simpa only [category.assoc] using he⟩
 #align category_theory.is_cofiltered.cospan CategoryTheory.IsCofiltered.cospan
+-/
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.functor.ranges_directed CategoryTheory.Functor.ranges_directedₓ'. -/
 theorem CategoryTheory.Functor.ranges_directed (F : C ⥤ Type _) (j : C) :
     Directed (· ⊇ ·) fun f : Σ'i, i ⟶ j => Set.range (F.map f.2) := fun ⟨i, ij⟩ ⟨k, kj⟩ =>
   by
@@ -589,6 +693,7 @@ open CategoryTheory.Limits
 
 variable {C} [IsCofiltered C]
 
+#print CategoryTheory.IsCofiltered.inf_objs_exists /-
 /-- Any finite collection of objects in a cofiltered category has an object "to the left".
 -/
 theorem inf_objs_exists (O : Finset C) : ∃ S : C, ∀ {X}, X ∈ O → Nonempty (S ⟶ X) := by
@@ -602,9 +707,11 @@ theorem inf_objs_exists (O : Finset C) : ∃ S : C, ∀ {X}, X ∈ O → Nonempt
       · exact ⟨min_to_left _ _⟩
       · exact ⟨min_to_right _ _ ≫ (w' (Finset.mem_of_mem_insert_of_ne mY h)).some⟩
 #align category_theory.is_cofiltered.inf_objs_exists CategoryTheory.IsCofiltered.inf_objs_exists
+-/
 
 variable (O : Finset C) (H : Finset (Σ'(X Y : C)(mX : X ∈ O)(mY : Y ∈ O), X ⟶ Y))
 
+#print CategoryTheory.IsCofiltered.inf_exists /-
 /-- Given any `finset` of objects `{X, ...}` and
 indexed collection of `finset`s of morphisms `{f, ...}` in `C`,
 there exists an object `S`, with a morphism `T X : S ⟶ X` from each `X`,
@@ -637,7 +744,9 @@ theorem inf_exists :
         rw [heq_iff_eq, PSigma.mk.inj_iff] at h
         exact ⟨rfl, h.1.symm⟩
 #align category_theory.is_cofiltered.inf_exists CategoryTheory.IsCofiltered.inf_exists
+-/
 
+#print CategoryTheory.IsCofiltered.inf /-
 /-- An arbitrary choice of object "to the left"
 of a finite collection of objects `O` and morphisms `H`,
 making all the triangles commute.
@@ -645,13 +754,17 @@ making all the triangles commute.
 noncomputable def inf : C :=
   (inf_exists O H).some
 #align category_theory.is_cofiltered.inf CategoryTheory.IsCofiltered.inf
+-/
 
+#print CategoryTheory.IsCofiltered.infTo /-
 /-- The morphisms from `inf O H`.
 -/
 noncomputable def infTo {X : C} (m : X ∈ O) : inf O H ⟶ X :=
   (inf_exists O H).choose_spec.some m
 #align category_theory.is_cofiltered.inf_to CategoryTheory.IsCofiltered.infTo
+-/
 
+#print CategoryTheory.IsCofiltered.infTo_commutes /-
 /-- The triangles consisting of a morphism in `H` and the maps from `inf O H` commute.
 -/
 theorem infTo_commutes {X Y : C} (mX : X ∈ O) (mY : Y ∈ O) {f : X ⟶ Y}
@@ -659,9 +772,11 @@ theorem infTo_commutes {X Y : C} (mX : X ∈ O) (mY : Y ∈ O) {f : X ⟶ Y}
     infTo O H mX ≫ f = infTo O H mY :=
   (inf_exists O H).choose_spec.choose_spec mX mY mf
 #align category_theory.is_cofiltered.inf_to_commutes CategoryTheory.IsCofiltered.infTo_commutes
+-/
 
 variable {J : Type w} [SmallCategory J] [FinCategory J]
 
+#print CategoryTheory.IsCofiltered.cone_nonempty /-
 /-- If we have `is_cofiltered C`, then for any functor `F : J ⥤ C` with `fin_category J`,
 there exists a cone over `F`.
 -/
@@ -683,15 +798,19 @@ theorem cone_nonempty (F : J ⥤ C) : Nonempty (Cone F) := by
       Finset.mem_image]
     exact ⟨j, rfl, j', g, by simp⟩
 #align category_theory.is_cofiltered.cone_nonempty CategoryTheory.IsCofiltered.cone_nonempty
+-/
 
+#print CategoryTheory.IsCofiltered.cone /-
 /-- An arbitrary choice of cone over `F : J ⥤ C`, for `fin_category J` and `is_cofiltered C`.
 -/
 noncomputable def cone (F : J ⥤ C) : Cone F :=
   (cone_nonempty F).some
 #align category_theory.is_cofiltered.cone CategoryTheory.IsCofiltered.cone
+-/
 
 variable {D : Type u₁} [Category.{v₁} D]
 
+#print CategoryTheory.IsCofiltered.of_left_adjoint /-
 /-- If `C` is cofiltered, and we have a functor `L : C ⥤ D` with a right adjoint,
 then `D` is cofiltered.
 -/
@@ -704,12 +823,21 @@ theorem of_left_adjoint {L : C ⥤ D} {R : D ⥤ C} (h : L ⊣ R) : IsCofiltered
         rw [← h.hom_equiv_naturality_right_symm, ← h.hom_equiv_naturality_right_symm, eq_condition]⟩
     Nonempty := IsCofiltered.nonempty.map L.obj }
 #align category_theory.is_cofiltered.of_left_adjoint CategoryTheory.IsCofiltered.of_left_adjoint
+-/
 
+#print CategoryTheory.IsCofiltered.of_isLeftAdjoint /-
 /-- If `C` is cofiltered, and we have a left adjoint functor `L : C ⥤ D`, then `D` is cofiltered. -/
 theorem of_isLeftAdjoint (L : C ⥤ D) [IsLeftAdjoint L] : IsCofiltered D :=
   of_left_adjoint (Adjunction.ofLeftAdjoint L)
 #align category_theory.is_cofiltered.of_is_left_adjoint CategoryTheory.IsCofiltered.of_isLeftAdjoint
+-/
 
+/- warning: category_theory.is_cofiltered.of_equivalence -> CategoryTheory.IsCofiltered.of_equivalence is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.IsCofiltered.{u1, u3} C _inst_1] {D : Type.{u4}} [_inst_5 : CategoryTheory.Category.{u2, u4} D], (CategoryTheory.Equivalence.{u1, u2, u3, u4} C _inst_1 D _inst_5) -> (CategoryTheory.IsCofiltered.{u2, u4} D _inst_5)
+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.IsCofiltered.{u1, u3} C _inst_1] {D : Type.{u4}} [_inst_5 : CategoryTheory.Category.{u2, u4} D], (CategoryTheory.Equivalence.{u1, u2, u3, u4} C D _inst_1 _inst_5) -> (CategoryTheory.IsCofiltered.{u2, u4} D _inst_5)
+Case conversion may be inaccurate. Consider using '#align category_theory.is_cofiltered.of_equivalence CategoryTheory.IsCofiltered.of_equivalenceₓ'. -/
 /-- Being cofiltered is preserved by equivalence of categories. -/
 theorem of_equivalence (h : C ≌ D) : IsCofiltered D :=
   of_left_adjoint h.toAdjunction
@@ -723,6 +851,7 @@ section Opposite
 
 open Opposite
 
+#print CategoryTheory.isCofiltered_op_of_isFiltered /-
 instance isCofiltered_op_of_isFiltered [IsFiltered C] : IsCofiltered Cᵒᵖ
     where
   cone_objs X Y :=
@@ -736,7 +865,9 @@ instance isCofiltered_op_of_isFiltered [IsFiltered C] : IsCofiltered Cᵒᵖ
       exact is_filtered.coeq_condition f.unop g.unop⟩
   Nonempty := ⟨op IsFiltered.nonempty.some⟩
 #align category_theory.is_cofiltered_op_of_is_filtered CategoryTheory.isCofiltered_op_of_isFiltered
+-/
 
+#print CategoryTheory.isFiltered_op_of_isCofiltered /-
 instance isFiltered_op_of_isCofiltered [IsCofiltered C] : IsFiltered Cᵒᵖ
     where
   cocone_objs X Y :=
@@ -750,6 +881,7 @@ instance isFiltered_op_of_isCofiltered [IsCofiltered C] : IsFiltered Cᵒᵖ
       exact is_cofiltered.eq_condition f.unop g.unop⟩
   Nonempty := ⟨op IsCofiltered.nonempty.some⟩
 #align category_theory.is_filtered_op_of_is_cofiltered CategoryTheory.isFiltered_op_of_isCofiltered
+-/
 
 end Opposite
 

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

@@ -391,6 +391,12 @@ theorem of_cocone_nonempty (h : ∀ {J : Type w} [SmallCategory J] [FinCategory
 theorem of_hasFiniteColimits [HasFiniteColimits C] : IsFiltered C :=
   of_cocone_nonempty.{v} C fun F => ⟨colimit.cocone F⟩
 
+theorem of_isTerminal {X : C} (h : IsTerminal X) : IsFiltered C :=
+  of_cocone_nonempty.{v} _ fun {_} _ _ _ => ⟨⟨X, ⟨fun _ => h.from _, fun _ _ _ => h.hom_ext _ _⟩⟩⟩
+
+instance (priority := 100) of_hasTerminal [HasTerminal C] : IsFiltered C :=
+  of_isTerminal _ terminalIsTerminal
+
 /-- For every universe `w`, `C` is filtered if and only if every finite diagram in `C` with shape
     in `w` admits a cocone. -/
 theorem iff_cocone_nonempty : IsFiltered C ↔
@@ -873,6 +879,12 @@ theorem of_hasFiniteLimits [HasFiniteLimits C] : IsCofiltered C :=
   of_cone_nonempty.{v} C fun F => ⟨limit.cone F⟩
 #align category_theory.cofiltered_of_has_finite_limits CategoryTheory.IsCofiltered.of_hasFiniteLimits
 
+theorem of_isInitial {X : C} (h : IsInitial X) : IsCofiltered C :=
+  of_cone_nonempty.{v} _ fun {_} _ _ _ => ⟨⟨X, ⟨fun _ => h.to _, fun _ _ _ => h.hom_ext _ _⟩⟩⟩
+
+instance (priority := 100) of_hasInitial [HasInitial C] : IsCofiltered C :=
+  of_isInitial _ initialIsInitial
+
 @[deprecated] -- 2024-03-11
 alias _root_.CategoryTheory.cofiltered_of_hasFiniteLimits := of_hasFiniteLimits
 

@@ -388,6 +388,9 @@ theorem of_cocone_nonempty (h : ∀ {J : Type w} [SmallCategory J] [FinCategory
       simp_all
   apply IsFiltered.mk
 
+theorem of_hasFiniteColimits [HasFiniteColimits C] : IsFiltered C :=
+  of_cocone_nonempty.{v} C fun F => ⟨colimit.cocone F⟩
+
 /-- For every universe `w`, `C` is filtered if and only if every finite diagram in `C` with shape
     in `w` admits a cocone. -/
 theorem iff_cocone_nonempty : IsFiltered C ↔
@@ -866,6 +869,13 @@ theorem of_cone_nonempty (h : ∀ {J : Type w} [SmallCategory J] [FinCategory J]
       simp_all
   apply IsCofiltered.mk
 
+theorem of_hasFiniteLimits [HasFiniteLimits C] : IsCofiltered C :=
+  of_cone_nonempty.{v} C fun F => ⟨limit.cone F⟩
+#align category_theory.cofiltered_of_has_finite_limits CategoryTheory.IsCofiltered.of_hasFiniteLimits
+
+@[deprecated] -- 2024-03-11
+alias _root_.CategoryTheory.cofiltered_of_hasFiniteLimits := of_hasFiniteLimits
+
 /-- For every universe `w`, `C` is filtered if and only if every finite diagram in `C` with shape
     in `w` admits a cocone. -/
 theorem iff_cone_nonempty : IsCofiltered C ↔

Minor clean up of imports, getting ready to minimize the heartbeats variation observed/reduced in #9732.

This has the effect of slightly (although not enough) delaying the import of positivity (which in turn imports the kitchen sink) into the category theory development.

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

@@ -3,7 +3,7 @@ Copyright (c) 2019 Reid Barton. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Reid Barton, Scott Morrison
 -/
-import Mathlib.CategoryTheory.FinCategory
+import Mathlib.CategoryTheory.FinCategory.Basic
 import Mathlib.CategoryTheory.Limits.Cones
 import Mathlib.CategoryTheory.Limits.Shapes.FiniteLimits
 import Mathlib.CategoryTheory.Adjunction.Basic

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".

@@ -139,7 +139,7 @@ section AllowEmpty
 variable {C}
 variable [IsFilteredOrEmpty C]
 
--- porting note: the following definitions were removed because the names are invalid,
+-- Porting note: the following definitions were removed because the names are invalid,
 -- direct references to `IsFilteredOrEmpty` have been added instead
 --
 -- theorem cocone_objs : ∀ X Y : C, ∃ (Z : _) (f : X ⟶ Z) (g : Y ⟶ Z), True :=
@@ -189,7 +189,7 @@ noncomputable def coeqHom {j j' : C} (f f' : j ⟶ j') : j' ⟶ coeq f f' :=
   (IsFilteredOrEmpty.cocone_maps f f').choose_spec.choose
 #align category_theory.is_filtered.coeq_hom CategoryTheory.IsFiltered.coeqHom
 
--- porting note: the simp tag has been removed as the linter complained
+-- Porting note: the simp tag has been removed as the linter complained
 /-- `coeq_condition f f'`, for morphisms `f f' : j ⟶ j'`, is the proof that
 `f ≫ coeqHom f f' = f' ≫ coeqHom f f'`.
 -/
@@ -598,7 +598,7 @@ section AllowEmpty
 variable {C}
 variable [IsCofilteredOrEmpty C]
 
--- porting note: the following definitions were removed because the names are invalid,
+-- Porting note: the following definitions were removed because the names are invalid,
 -- direct references to `IsCofilteredOrEmpty` have been added instead
 --
 --theorem cone_objs : ∀ X Y : C, ∃ (W : _) (f : W ⟶ X) (g : W ⟶ Y), True :=
@@ -648,7 +648,7 @@ noncomputable def eqHom {j j' : C} (f f' : j ⟶ j') : eq f f' ⟶ j :=
   (IsCofilteredOrEmpty.cone_maps f f').choose_spec.choose
 #align category_theory.is_cofiltered.eq_hom CategoryTheory.IsCofiltered.eqHom
 
--- porting note: the simp tag has been removed as the linter complained
+-- Porting note: the simp tag has been removed as the linter complained
 /-- `eq_condition f f'`, for morphisms `f f' : j ⟶ j'`, is the proof that
 `eqHom f f' ≫ f = eqHom f f' ≫ f'`.
 -/

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

@@ -325,14 +325,14 @@ theorem cocone_nonempty (F : J ⥤ C) : Nonempty (Cocone F) := by
   let H : Finset (Σ' (X Y : C) (_ : X ∈ O) (_ : Y ∈ O), X ⟶ Y) :=
     Finset.univ.biUnion   fun X : J =>
       Finset.univ.biUnion fun Y : J =>
-        Finset.univ.image fun f : X ⟶ Y => ⟨F.obj X, F.obj Y, by simp, by simp, F.map f⟩
+        Finset.univ.image fun f : X ⟶ Y => ⟨F.obj X, F.obj Y, by simp [O], by simp [O], F.map f⟩
   obtain ⟨Z, f, w⟩ := sup_exists O H
-  refine' ⟨⟨Z, ⟨fun X => f (by simp), _⟩⟩⟩
+  refine' ⟨⟨Z, ⟨fun X => f (by simp [O]), _⟩⟩⟩
   intro j j' g
   dsimp
   simp only [Category.comp_id]
   apply w
-  simp only [Finset.mem_biUnion, Finset.mem_univ, Finset.mem_image, PSigma.mk.injEq,
+  simp only [O, H, Finset.mem_biUnion, Finset.mem_univ, Finset.mem_image, PSigma.mk.injEq,
     true_and, exists_and_left]
   exact ⟨j, rfl, j', g, by simp⟩
 #align category_theory.is_filtered.cocone_nonempty CategoryTheory.IsFiltered.cocone_nonempty
@@ -800,15 +800,15 @@ theorem cone_nonempty (F : J ⥤ C) : Nonempty (Cone F) := by
   let H : Finset (Σ' (X Y : C) (_ : X ∈ O) (_ : Y ∈ O), X ⟶ Y) :=
     Finset.univ.biUnion fun X : J =>
       Finset.univ.biUnion fun Y : J =>
-        Finset.univ.image fun f : X ⟶ Y => ⟨F.obj X, F.obj Y, by simp, by simp, F.map f⟩
+        Finset.univ.image fun f : X ⟶ Y => ⟨F.obj X, F.obj Y, by simp [O], by simp [O], F.map f⟩
   obtain ⟨Z, f, w⟩ := inf_exists O H
-  refine' ⟨⟨Z, ⟨fun X => f (by simp), _⟩⟩⟩
+  refine' ⟨⟨Z, ⟨fun X => f (by simp [O]), _⟩⟩⟩
   intro j j' g
   dsimp
   simp only [Category.id_comp]
   symm
   apply w
-  simp only [Finset.mem_biUnion, Finset.mem_univ, Finset.mem_image,
+  simp only [O, H, Finset.mem_biUnion, Finset.mem_univ, Finset.mem_image,
     PSigma.mk.injEq, true_and, exists_and_left]
   exact ⟨j, rfl, j', g, by simp⟩
 #align category_theory.is_cofiltered.cone_nonempty CategoryTheory.IsCofiltered.cone_nonempty

@@ -52,6 +52,10 @@ categories.
 In `CategoryTheory.Limits.FilteredColimitCommutesFiniteLimit` we show that filtered colimits
 commute with finite limits.
 
+There is another characterization of filtered categories, namely that whenever `F : J ⥤ C` is a
+functor from a finite category, there is `X : C` such that `Nonempty (limit (F.op ⋙ yoneda.obj X))`.
+This is shown in `CategoryTheory.Limits.Filtered`.
+
 -/
 
 

I replaced a few "terminal" refine/refine's with exact.

The strategy was very simple-minded: essentially any refine whose following line had smaller indentation got replaced by exact and then I cleaned up the mess.

This PR certainly leaves some further terminal refines, but maybe the current change is beneficial.

@@ -264,7 +264,7 @@ theorem sup_exists :
   classical
   induction' H using Finset.induction with h' H' nmf h''
   · obtain ⟨S, f⟩ := sup_objs_exists O
-    refine' ⟨S, fun mX => (f mX).some, by rintro - - - - - ⟨⟩⟩
+    exact ⟨S, fun mX => (f mX).some, by rintro - - - - - ⟨⟩⟩
   · obtain ⟨X, Y, mX, mY, f⟩ := h'
     obtain ⟨S', T', w'⟩ := h''
     refine' ⟨coeq (f ≫ T' mY) (T' mX), fun mZ => T' mZ ≫ coeqHom (f ≫ T' mY) (T' mX), _⟩
@@ -739,7 +739,7 @@ theorem inf_exists :
   classical
   induction' H using Finset.induction with h' H' nmf h''
   · obtain ⟨S, f⟩ := inf_objs_exists O
-    refine' ⟨S, fun mX => (f mX).some, by rintro - - - - - ⟨⟩⟩
+    exact ⟨S, fun mX => (f mX).some, by rintro - - - - - ⟨⟩⟩
   · obtain ⟨X, Y, mX, mY, f⟩ := h'
     obtain ⟨S', T', w'⟩ := h''
     refine' ⟨eq (T' mX ≫ f) (T' mY), fun mZ => eqHom (T' mX ≫ f) (T' mY) ≫ T' mZ, _⟩

@@ -5,9 +5,11 @@ Authors: Reid Barton, Scott Morrison
 -/
 import Mathlib.CategoryTheory.FinCategory
 import Mathlib.CategoryTheory.Limits.Cones
+import Mathlib.CategoryTheory.Limits.Shapes.FiniteLimits
 import Mathlib.CategoryTheory.Adjunction.Basic
 import Mathlib.CategoryTheory.Category.Preorder
 import Mathlib.CategoryTheory.Category.ULift
+import Mathlib.CategoryTheory.PEmpty
 
 #align_import category_theory.filtered from "leanprover-community/mathlib"@"14e80e85cbca5872a329fbfd3d1f3fd64e306934"
 
@@ -37,6 +39,8 @@ This formulation is often more useful in practice and is available via `sup_exis
 which takes a finset of objects, and an indexed family (indexed by source and target)
 of finsets of morphisms.
 
+We also prove the converse of `cocone_nonempty` as `of_cocone_nonempty`.
+
 Furthermore, we give special support for two diagram categories: The `bowtie` and the `tulip`.
 This is because these shapes show up in the proofs that forgetful functors of algebraic categories
 (e.g. `MonCat`, `CommRingCat`, ...) preserve filtered colimits.
@@ -306,7 +310,7 @@ theorem toSup_commutes {X Y : C} (mX : X ∈ O) (mY : Y ∈ O) {f : X ⟶ Y}
   (sup_exists O H).choose_spec.choose_spec mX mY mf
 #align category_theory.is_filtered.to_sup_commutes CategoryTheory.IsFiltered.toSup_commutes
 
-variable {J : Type v} [SmallCategory J] [FinCategory J]
+variable {J : Type w} [SmallCategory J] [FinCategory J]
 
 /-- If we have `IsFiltered C`, then for any functor `F : J ⥤ C` with `FinCategory J`,
 there exists a cocone over `F`.
@@ -356,6 +360,38 @@ theorem of_equivalence (h : C ≌ D) : IsFiltered D :=
 
 end Nonempty
 
+section OfCocone
+
+open CategoryTheory.Limits
+
+/-- If every finite diagram in `C` admits a cocone, then `C` is filtered. It is sufficient to verify
+    this for diagrams whose shape lives in any one fixed universe. -/
+theorem of_cocone_nonempty (h : ∀ {J : Type w} [SmallCategory J] [FinCategory J] (F : J ⥤ C),
+    Nonempty (Cocone F)) : IsFiltered C := by
+  have : Nonempty C := by
+    obtain ⟨c⟩ := h (Functor.empty _)
+    exact ⟨c.pt⟩
+  have : IsFilteredOrEmpty C := by
+    refine ⟨?_, ?_⟩
+    · intros X Y
+      obtain ⟨c⟩ := h (ULiftHom.down ⋙ ULift.downFunctor ⋙ pair X Y)
+      exact ⟨c.pt, c.ι.app ⟨⟨WalkingPair.left⟩⟩, c.ι.app ⟨⟨WalkingPair.right⟩⟩, trivial⟩
+    · intros X Y f g
+      obtain ⟨c⟩ := h (ULiftHom.down ⋙ ULift.downFunctor ⋙ parallelPair f g)
+      refine ⟨c.pt, c.ι.app ⟨WalkingParallelPair.one⟩, ?_⟩
+      have h₁ := c.ι.naturality ⟨WalkingParallelPairHom.left⟩
+      have h₂ := c.ι.naturality ⟨WalkingParallelPairHom.right⟩
+      simp_all
+  apply IsFiltered.mk
+
+/-- For every universe `w`, `C` is filtered if and only if every finite diagram in `C` with shape
+    in `w` admits a cocone. -/
+theorem iff_cocone_nonempty : IsFiltered C ↔
+    ∀ {J : Type w} [SmallCategory J] [FinCategory J] (F : J ⥤ C), Nonempty (Cocone F) :=
+  ⟨fun _ _ _ _ F => cocone_nonempty F, of_cocone_nonempty C⟩
+
+end OfCocone
+
 section SpecialShapes
 
 variable {C}
@@ -801,6 +837,39 @@ theorem of_equivalence (h : C ≌ D) : IsCofiltered D :=
 
 end Nonempty
 
+
+section OfCone
+
+open CategoryTheory.Limits
+
+/-- If every finite diagram in `C` admits a cone, then `C` is cofiltered. It is sufficient to
+    verify this for diagrams whose shape lives in any one fixed universe. -/
+theorem of_cone_nonempty (h : ∀ {J : Type w} [SmallCategory J] [FinCategory J] (F : J ⥤ C),
+    Nonempty (Cone F)) : IsCofiltered C := by
+  have : Nonempty C := by
+    obtain ⟨c⟩ := h (Functor.empty _)
+    exact ⟨c.pt⟩
+  have : IsCofilteredOrEmpty C := by
+    refine ⟨?_, ?_⟩
+    · intros X Y
+      obtain ⟨c⟩ := h (ULiftHom.down ⋙ ULift.downFunctor ⋙ pair X Y)
+      exact ⟨c.pt, c.π.app ⟨⟨WalkingPair.left⟩⟩, c.π.app ⟨⟨WalkingPair.right⟩⟩, trivial⟩
+    · intros X Y f g
+      obtain ⟨c⟩ := h (ULiftHom.down ⋙ ULift.downFunctor ⋙ parallelPair f g)
+      refine ⟨c.pt, c.π.app ⟨WalkingParallelPair.zero⟩, ?_⟩
+      have h₁ := c.π.naturality ⟨WalkingParallelPairHom.left⟩
+      have h₂ := c.π.naturality ⟨WalkingParallelPairHom.right⟩
+      simp_all
+  apply IsCofiltered.mk
+
+/-- For every universe `w`, `C` is filtered if and only if every finite diagram in `C` with shape
+    in `w` admits a cocone. -/
+theorem iff_cone_nonempty : IsCofiltered C ↔
+    ∀ {J : Type w} [SmallCategory J] [FinCategory J] (F : J ⥤ C), Nonempty (Cone F) :=
+  ⟨fun _ _ _ _ F => cone_nonempty F, of_cone_nonempty C⟩
+
+end OfCone
+
 end IsCofiltered
 
 section Opposite

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

@@ -454,7 +454,7 @@ theorem bowtie {j₁ j₂ k₁ k₂ : C} (f₁ : j₁ ⟶ k₁) (g₁ : j₁ ⟶
   obtain ⟨t, k₁t, k₂t, ht⟩ := span f₁ g₁
   obtain ⟨s, ts, hs⟩ := IsFilteredOrEmpty.cocone_maps (f₂ ≫ k₁t) (g₂ ≫ k₂t)
   simp_rw [Category.assoc] at hs
-  exact ⟨s, k₁t ≫ ts, k₂t ≫ ts, by simp only [←Category.assoc, ht], hs⟩
+  exact ⟨s, k₁t ≫ ts, k₂t ≫ ts, by simp only [← Category.assoc, ht], hs⟩
 #align category_theory.is_filtered.bowtie CategoryTheory.IsFiltered.bowtie
 
 /-- Given a "tulip" of morphisms
@@ -480,7 +480,7 @@ theorem tulip {j₁ j₂ j₃ k₁ k₂ l : C} (f₁ : j₁ ⟶ k₁) (f₂ : j
       f₁ ≫ α = g₁ ≫ β ∧ f₂ ≫ α = f₃ ≫ γ ∧ f₄ ≫ γ = g₂ ≫ β := by
   obtain ⟨l', k₁l, k₂l, hl⟩ := span f₂ f₃
   obtain ⟨s, ls, l's, hs₁, hs₂⟩ := bowtie g₁ (f₁ ≫ k₁l) g₂ (f₄ ≫ k₂l)
-  refine' ⟨s, k₁l ≫ l's, ls, k₂l ≫ l's, _, by simp only [←Category.assoc, hl], _⟩ <;>
+  refine' ⟨s, k₁l ≫ l's, ls, k₂l ≫ l's, _, by simp only [← Category.assoc, hl], _⟩ <;>
     simp only [hs₁, hs₂, Category.assoc]
 #align category_theory.is_filtered.tulip CategoryTheory.IsFiltered.tulip
 

Only Prop-values fields should be capitalized, not P-valued fields where P is Prop-valued.

Rather than fixing Nonempty := in constructors, I just deleted the line as the instance can almost always be found automatically.

@@ -83,7 +83,7 @@ See <https://stacks.math.columbia.edu/tag/002V>. (They also define a diagram bei
 -/
 class IsFiltered extends IsFilteredOrEmpty C : Prop where
   /-- a filtered category must be non empty -/
-  [Nonempty : Nonempty C]
+  [nonempty : Nonempty C]
 #align category_theory.is_filtered CategoryTheory.IsFiltered
 
 instance (priority := 100) isFilteredOrEmpty_of_semilatticeSup (α : Type u) [SemilatticeSup α] :
@@ -123,7 +123,6 @@ instance : IsFiltered (Discrete PUnit) where
   cocone_maps X Y f g := ⟨⟨PUnit.unit⟩, ⟨⟨by trivial⟩⟩, by
     apply ULift.ext
     apply Subsingleton.elim⟩
-  Nonempty := ⟨⟨PUnit.unit⟩⟩
 
 namespace IsFiltered
 
@@ -234,10 +233,10 @@ variable [IsFiltered C]
 
 /-- Any finite collection of objects in a filtered category has an object "to the right".
 -/
-theorem sup_objs_exists (O : Finset C) : ∃ S : C, ∀ {X}, X ∈ O → _root_.Nonempty (X ⟶ S) := by
+theorem sup_objs_exists (O : Finset C) : ∃ S : C, ∀ {X}, X ∈ O → Nonempty (X ⟶ S) := by
   classical
   induction' O using Finset.induction with X O' nm h
-  · exact ⟨Classical.choice IsFiltered.Nonempty, by intro; simp⟩
+  · exact ⟨Classical.choice IsFiltered.nonempty, by intro; simp⟩
   · obtain ⟨S', w'⟩ := h
     use max X S'
     rintro Y mY
@@ -312,7 +311,7 @@ variable {J : Type v} [SmallCategory J] [FinCategory J]
 /-- If we have `IsFiltered C`, then for any functor `F : J ⥤ C` with `FinCategory J`,
 there exists a cocone over `F`.
 -/
-theorem cocone_nonempty (F : J ⥤ C) : _root_.Nonempty (Cocone F) := by
+theorem cocone_nonempty (F : J ⥤ C) : Nonempty (Cocone F) := by
   classical
   let O := Finset.univ.image F.obj
   let H : Finset (Σ' (X Y : C) (_ : X ∈ O) (_ : Y ∈ O), X ⟶ Y) :=
@@ -342,7 +341,7 @@ variable {D : Type u₁} [Category.{v₁} D]
 -/
 theorem of_right_adjoint {L : D ⥤ C} {R : C ⥤ D} (h : L ⊣ R) : IsFiltered D :=
   { IsFilteredOrEmpty.of_right_adjoint h with
-    Nonempty := IsFiltered.Nonempty.map R.obj }
+    nonempty := IsFiltered.nonempty.map R.obj }
 #align category_theory.is_filtered.of_right_adjoint CategoryTheory.IsFiltered.of_right_adjoint
 
 /-- If `C` is filtered, and we have a right adjoint functor `R : C ⥤ D`, then `D` is filtered. -/
@@ -512,7 +511,7 @@ See <https://stacks.math.columbia.edu/tag/04AZ>.
 -/
 class IsCofiltered extends IsCofilteredOrEmpty C : Prop where
   /-- a cofiltered category must be non empty -/
-  [Nonempty : Nonempty C]
+  [nonempty : Nonempty C]
 #align category_theory.is_cofiltered CategoryTheory.IsCofiltered
 
 instance (priority := 100) isCofilteredOrEmpty_of_semilatticeInf (α : Type u) [SemilatticeInf α] :
@@ -551,7 +550,6 @@ instance : IsCofiltered (Discrete PUnit) where
   cone_maps X Y f g := ⟨⟨PUnit.unit⟩, ⟨⟨by trivial⟩⟩, by
     apply ULift.ext
     apply Subsingleton.elim⟩
-  Nonempty := ⟨⟨PUnit.unit⟩⟩
 
 namespace IsCofiltered
 
@@ -678,10 +676,10 @@ variable [IsCofiltered C]
 
 /-- Any finite collection of objects in a cofiltered category has an object "to the left".
 -/
-theorem inf_objs_exists (O : Finset C) : ∃ S : C, ∀ {X}, X ∈ O → _root_.Nonempty (S ⟶ X) := by
+theorem inf_objs_exists (O : Finset C) : ∃ S : C, ∀ {X}, X ∈ O → Nonempty (S ⟶ X) := by
   classical
   induction' O using Finset.induction with X O' nm h
-  · exact ⟨Classical.choice IsCofiltered.Nonempty, by intro; simp⟩
+  · exact ⟨Classical.choice IsCofiltered.nonempty, by intro; simp⟩
   · obtain ⟨S', w'⟩ := h
     use min X S'
     rintro Y mY
@@ -756,7 +754,7 @@ variable {J : Type w} [SmallCategory J] [FinCategory J]
 /-- If we have `IsCofiltered C`, then for any functor `F : J ⥤ C` with `FinCategory J`,
 there exists a cone over `F`.
 -/
-theorem cone_nonempty (F : J ⥤ C) : _root_.Nonempty (Cone F) := by
+theorem cone_nonempty (F : J ⥤ C) : Nonempty (Cone F) := by
   classical
   let O := Finset.univ.image F.obj
   let H : Finset (Σ' (X Y : C) (_ : X ∈ O) (_ : Y ∈ O), X ⟶ Y) :=
@@ -788,7 +786,7 @@ then `D` is cofiltered.
 -/
 theorem of_left_adjoint {L : C ⥤ D} {R : D ⥤ C} (h : L ⊣ R) : IsCofiltered D :=
   { IsCofilteredOrEmpty.of_left_adjoint h with
-    Nonempty := IsCofiltered.Nonempty.map L.obj }
+    nonempty := IsCofiltered.nonempty.map L.obj }
 #align category_theory.is_cofiltered.of_left_adjoint CategoryTheory.IsCofiltered.of_left_adjoint
 
 /-- If `C` is cofiltered, and we have a left adjoint functor `L : C ⥤ D`, then `D` is cofiltered. -/
@@ -821,7 +819,7 @@ instance isCofilteredOrEmpty_op_of_isFilteredOrEmpty [IsFilteredOrEmpty C] :
       exact IsFiltered.coeq_condition f.unop g.unop⟩
 
 instance isCofiltered_op_of_isFiltered [IsFiltered C] : IsCofiltered Cᵒᵖ where
-  Nonempty := ⟨op IsFiltered.Nonempty.some⟩
+  nonempty := letI : Nonempty C := IsFiltered.nonempty; inferInstance
 #align category_theory.is_cofiltered_op_of_is_filtered CategoryTheory.isCofiltered_op_of_isFiltered
 
 instance isFilteredOrEmpty_op_of_isCofilteredOrEmpty [IsCofilteredOrEmpty C] :
@@ -836,7 +834,7 @@ instance isFilteredOrEmpty_op_of_isCofilteredOrEmpty [IsCofilteredOrEmpty C] :
       exact IsCofiltered.eq_condition f.unop g.unop⟩
 
 instance isFiltered_op_of_isCofiltered [IsCofiltered C] : IsFiltered Cᵒᵖ where
-  Nonempty := ⟨op IsCofiltered.Nonempty.some⟩
+  nonempty := letI : Nonempty C := IsCofiltered.nonempty; inferInstance
 #align category_theory.is_filtered_op_of_is_cofiltered CategoryTheory.isFiltered_op_of_isCofiltered
 
 /-- If Cᵒᵖ is filtered or empty, then C is cofiltered or empty. -/

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

This has nice performance benefits.

@@ -628,7 +628,7 @@ theorem cospan {i j j' : C} (f : j ⟶ i) (f' : j' ⟶ i) :
   ⟨k, e ≫ G, e ≫ G', by simpa only [Category.assoc] using he⟩
 #align category_theory.is_cofiltered.cospan CategoryTheory.IsCofiltered.cospan
 
-theorem _root_.CategoryTheory.Functor.ranges_directed (F : C ⥤ Type _) (j : C) :
+theorem _root_.CategoryTheory.Functor.ranges_directed (F : C ⥤ Type*) (j : C) :
     Directed (· ⊇ ·) fun f : Σ'i, i ⟶ j => Set.range (F.map f.2) := fun ⟨i, ij⟩ ⟨k, kj⟩ => by
   let ⟨l, li, lk, e⟩ := cospan ij kj
   refine' ⟨⟨l, lk ≫ kj⟩, e ▸ _, _⟩ <;> simp_rw [F.map_comp] <;> apply Set.range_comp_subset_range

• depends on: #5966

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

@@ -2,11 +2,6 @@
 Copyright (c) 2019 Reid Barton. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Reid Barton, Scott Morrison
-
-! This file was ported from Lean 3 source module category_theory.filtered
-! leanprover-community/mathlib commit 14e80e85cbca5872a329fbfd3d1f3fd64e306934
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.CategoryTheory.FinCategory
 import Mathlib.CategoryTheory.Limits.Cones
@@ -14,6 +9,8 @@ import Mathlib.CategoryTheory.Adjunction.Basic
 import Mathlib.CategoryTheory.Category.Preorder
 import Mathlib.CategoryTheory.Category.ULift
 
+#align_import category_theory.filtered from "leanprover-community/mathlib"@"14e80e85cbca5872a329fbfd3d1f3fd64e306934"
+
 /-!
 # Filtered categories
 

This PR is the result of running

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

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

@@ -240,8 +240,8 @@ variable [IsFiltered C]
 theorem sup_objs_exists (O : Finset C) : ∃ S : C, ∀ {X}, X ∈ O → _root_.Nonempty (X ⟶ S) := by
   classical
   induction' O using Finset.induction with X O' nm h
-  . exact ⟨Classical.choice IsFiltered.Nonempty, by intro; simp⟩
-  . obtain ⟨S', w'⟩ := h
+  · exact ⟨Classical.choice IsFiltered.Nonempty, by intro; simp⟩
+  · obtain ⟨S', w'⟩ := h
     use max X S'
     rintro Y mY
     obtain rfl | h := eq_or_ne Y X
@@ -278,9 +278,9 @@ theorem sup_exists :
       · rw [@w' _ _ mX mY f']
         simp only [Finset.mem_insert, PSigma.mk.injEq, heq_eq_eq, true_and] at mf'
         rcases mf' with mf' | mf'
-        . exfalso
+        · exfalso
           exact hf mf'.symm
-        . exact mf'
+        · exact mf'
     · rw [@w' _ _ mX' mY' f' _]
       apply Finset.mem_of_mem_insert_of_ne mf'
       contrapose! h
@@ -684,8 +684,8 @@ variable [IsCofiltered C]
 theorem inf_objs_exists (O : Finset C) : ∃ S : C, ∀ {X}, X ∈ O → _root_.Nonempty (S ⟶ X) := by
   classical
   induction' O using Finset.induction with X O' nm h
-  . exact ⟨Classical.choice IsCofiltered.Nonempty, by intro; simp⟩
-  . obtain ⟨S', w'⟩ := h
+  · exact ⟨Classical.choice IsCofiltered.Nonempty, by intro; simp⟩
+  · obtain ⟨S', w'⟩ := h
     use min X S'
     rintro Y mY
     obtain rfl | h := eq_or_ne Y X
@@ -722,9 +722,9 @@ theorem inf_exists :
       · rw [@w' _ _ mX mY f']
         simp only [Finset.mem_insert, PSigma.mk.injEq, heq_eq_eq, true_and] at mf'
         rcases mf' with mf' | mf'
-        . exfalso
+        · exfalso
           exact hf mf'.symm
-        . exact mf'
+        · exact mf'
     · rw [@w' _ _ mX' mY' f' _]
       apply Finset.mem_of_mem_insert_of_ne mf'
       contrapose! h

Also generalize some facts about IsFiltered to IsFilteredOrEmpty.

@@ -196,6 +196,38 @@ theorem coeq_condition {j j' : C} (f f' : j ⟶ j') : f ≫ coeqHom f f' = f' 
 
 end AllowEmpty
 
+end IsFiltered
+
+namespace IsFilteredOrEmpty
+open IsFiltered
+
+variable {C}
+variable [IsFilteredOrEmpty C]
+variable {D : Type u₁} [Category.{v₁} D]
+
+/-- If `C` is filtered or emtpy, and we have a functor `R : C ⥤ D` with a left adjoint, then `D` is
+filtered or empty.
+-/
+theorem of_right_adjoint {L : D ⥤ C} {R : C ⥤ D} (h : L ⊣ R) : IsFilteredOrEmpty D :=
+  { cocone_objs := fun X Y =>
+      ⟨_, h.homEquiv _ _ (leftToMax _ _), h.homEquiv _ _ (rightToMax _ _), ⟨⟩⟩
+    cocone_maps := fun X Y f g =>
+      ⟨_, h.homEquiv _ _ (coeqHom _ _), by
+        rw [← h.homEquiv_naturality_left, ← h.homEquiv_naturality_left, coeq_condition]⟩ }
+
+/-- If `C` is filtered or empty, and we have a right adjoint functor `R : C ⥤ D`, then `D` is
+filtered or empty. -/
+theorem of_isRightAdjoint (R : C ⥤ D) [IsRightAdjoint R] : IsFilteredOrEmpty D :=
+  of_right_adjoint (Adjunction.ofRightAdjoint R)
+
+/-- Being filtered or empty is preserved by equivalence of categories. -/
+theorem of_equivalence (h : C ≌ D) : IsFilteredOrEmpty D :=
+  of_right_adjoint h.symm.toAdjunction
+
+end IsFilteredOrEmpty
+
+namespace IsFiltered
+
 section Nonempty
 
 open CategoryTheory.Limits
@@ -312,11 +344,7 @@ variable {D : Type u₁} [Category.{v₁} D]
 /-- If `C` is filtered, and we have a functor `R : C ⥤ D` with a left adjoint, then `D` is filtered.
 -/
 theorem of_right_adjoint {L : D ⥤ C} {R : C ⥤ D} (h : L ⊣ R) : IsFiltered D :=
-  { cocone_objs := fun X Y =>
-      ⟨_, h.homEquiv _ _ (leftToMax _ _), h.homEquiv _ _ (rightToMax _ _), ⟨⟩⟩
-    cocone_maps := fun X Y f g =>
-      ⟨_, h.homEquiv _ _ (coeqHom _ _), by
-        rw [← h.homEquiv_naturality_left, ← h.homEquiv_naturality_left, coeq_condition]⟩
+  { IsFilteredOrEmpty.of_right_adjoint h with
     Nonempty := IsFiltered.Nonempty.map R.obj }
 #align category_theory.is_filtered.of_right_adjoint CategoryTheory.IsFiltered.of_right_adjoint
 
@@ -611,6 +639,39 @@ theorem _root_.CategoryTheory.Functor.ranges_directed (F : C ⥤ Type _) (j : C)
 
 end AllowEmpty
 
+end IsCofiltered
+
+namespace IsCofilteredOrEmpty
+open IsCofiltered
+
+variable {C}
+variable [IsCofilteredOrEmpty C]
+variable {D : Type u₁} [Category.{v₁} D]
+
+/-- If `C` is cofiltered or empty, and we have a functor `L : C ⥤ D` with a right adjoint,
+then `D` is cofiltered or empty.
+-/
+theorem of_left_adjoint {L : C ⥤ D} {R : D ⥤ C} (h : L ⊣ R) : IsCofilteredOrEmpty D :=
+  { cone_objs := fun X Y =>
+      ⟨L.obj (min (R.obj X) (R.obj Y)), (h.homEquiv _ X).symm (minToLeft _ _),
+        (h.homEquiv _ Y).symm (minToRight _ _), ⟨⟩⟩
+    cone_maps := fun X Y f g =>
+      ⟨L.obj (eq (R.map f) (R.map g)), (h.homEquiv _ _).symm (eqHom _ _), by
+        rw [← h.homEquiv_naturality_right_symm, ← h.homEquiv_naturality_right_symm, eq_condition]⟩ }
+
+/-- If `C` is cofiltered or empty, and we have a left adjoint functor `L : C ⥤ D`, then `D` is
+cofiltered or empty. -/
+theorem of_isLeftAdjoint (L : C ⥤ D) [IsLeftAdjoint L] : IsCofilteredOrEmpty D :=
+  of_left_adjoint (Adjunction.ofLeftAdjoint L)
+
+/-- Being cofiltered or empty is preserved by equivalence of categories. -/
+theorem of_equivalence (h : C ≌ D) : IsCofilteredOrEmpty D :=
+  of_left_adjoint h.toAdjunction
+
+end IsCofilteredOrEmpty
+
+namespace IsCofiltered
+
 section Nonempty
 
 open CategoryTheory.Limits
@@ -729,12 +790,7 @@ variable {D : Type u₁} [Category.{v₁} D]
 then `D` is cofiltered.
 -/
 theorem of_left_adjoint {L : C ⥤ D} {R : D ⥤ C} (h : L ⊣ R) : IsCofiltered D :=
-  { cone_objs := fun X Y =>
-      ⟨L.obj (min (R.obj X) (R.obj Y)), (h.homEquiv _ X).symm (minToLeft _ _),
-        (h.homEquiv _ Y).symm (minToRight _ _), ⟨⟩⟩
-    cone_maps := fun X Y f g =>
-      ⟨L.obj (eq (R.map f) (R.map g)), (h.homEquiv _ _).symm (eqHom _ _), by
-        rw [← h.homEquiv_naturality_right_symm, ← h.homEquiv_naturality_right_symm, eq_condition]⟩
+  { IsCofilteredOrEmpty.of_left_adjoint h with
     Nonempty := IsCofiltered.Nonempty.map L.obj }
 #align category_theory.is_cofiltered.of_left_adjoint CategoryTheory.IsCofiltered.of_left_adjoint
 
@@ -756,7 +812,8 @@ section Opposite
 
 open Opposite
 
-instance isCofiltered_op_of_isFiltered [IsFiltered C] : IsCofiltered Cᵒᵖ where
+instance isCofilteredOrEmpty_op_of_isFilteredOrEmpty [IsFilteredOrEmpty C] :
+    IsCofilteredOrEmpty Cᵒᵖ where
   cone_objs X Y :=
     ⟨op (IsFiltered.max X.unop Y.unop), (IsFiltered.leftToMax _ _).op,
       (IsFiltered.rightToMax _ _).op, trivial⟩
@@ -765,10 +822,13 @@ instance isCofiltered_op_of_isFiltered [IsFiltered C] : IsCofiltered Cᵒᵖ whe
       rw [show f = f.unop.op by simp, show g = g.unop.op by simp, ← op_comp, ← op_comp]
       congr 1
       exact IsFiltered.coeq_condition f.unop g.unop⟩
+
+instance isCofiltered_op_of_isFiltered [IsFiltered C] : IsCofiltered Cᵒᵖ where
   Nonempty := ⟨op IsFiltered.Nonempty.some⟩
 #align category_theory.is_cofiltered_op_of_is_filtered CategoryTheory.isCofiltered_op_of_isFiltered
 
-instance isFiltered_op_of_isCofiltered [IsCofiltered C] : IsFiltered Cᵒᵖ where
+instance isFilteredOrEmpty_op_of_isCofilteredOrEmpty [IsCofilteredOrEmpty C] :
+    IsFilteredOrEmpty Cᵒᵖ where
   cocone_objs X Y :=
     ⟨op (IsCofiltered.min X.unop Y.unop), (IsCofiltered.minToLeft X.unop Y.unop).op,
       (IsCofiltered.minToRight X.unop Y.unop).op, trivial⟩
@@ -777,9 +837,27 @@ instance isFiltered_op_of_isCofiltered [IsCofiltered C] : IsFiltered Cᵒᵖ whe
       rw [show f = f.unop.op by simp, show g = g.unop.op by simp, ← op_comp, ← op_comp]
       congr 1
       exact IsCofiltered.eq_condition f.unop g.unop⟩
+
+instance isFiltered_op_of_isCofiltered [IsCofiltered C] : IsFiltered Cᵒᵖ where
   Nonempty := ⟨op IsCofiltered.Nonempty.some⟩
 #align category_theory.is_filtered_op_of_is_cofiltered CategoryTheory.isFiltered_op_of_isCofiltered
 
+/-- If Cᵒᵖ is filtered or empty, then C is cofiltered or empty. -/
+lemma isCofilteredOrEmpty_of_isFilteredOrEmpty_op [IsFilteredOrEmpty Cᵒᵖ] : IsCofilteredOrEmpty C :=
+  IsCofilteredOrEmpty.of_equivalence (opOpEquivalence _)
+
+/-- If Cᵒᵖ is cofiltered or empty, then C is filtered or empty. -/
+lemma isFilteredOrEmpty_of_isCofilteredOrEmpty_op [IsCofilteredOrEmpty Cᵒᵖ] : IsFilteredOrEmpty C :=
+  IsFilteredOrEmpty.of_equivalence (opOpEquivalence _)
+
+/-- If Cᵒᵖ is filtered, then C is cofiltered. -/
+lemma isCofiltered_of_isFiltered_op [IsFiltered Cᵒᵖ] : IsCofiltered C :=
+  IsCofiltered.of_equivalence (opOpEquivalence _)
+
+/-- If Cᵒᵖ is cofiltered, then C is filtered. -/
+lemma isFiltered_of_isCofiltered_op [IsCofiltered Cᵒᵖ] : IsFiltered C :=
+  IsFiltered.of_equivalence (opOpEquivalence _)
+
 end Opposite
 
 section ULift

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

@@ -70,10 +70,10 @@ variable (C : Type u) [Category.{v} C]
 -/
 class IsFilteredOrEmpty : Prop where
   /-- for every pair of objects there exists another object "to the right" -/
-  cocone_objs : ∀ X Y : C, ∃ (Z : _)(_ : X ⟶ Z)(_ : Y ⟶ Z), True
+  cocone_objs : ∀ X Y : C, ∃ (Z : _) (_ : X ⟶ Z) (_ : Y ⟶ Z), True
   /-- for every pair of parallel morphisms there exists a morphism to the right
     so the compositions are equal -/
-  cocone_maps : ∀ ⦃X Y : C⦄ (f g : X ⟶ Y), ∃ (Z : _)(h : Y ⟶ Z), f ≫ h = g ≫ h
+  cocone_maps : ∀ ⦃X Y : C⦄ (f g : X ⟶ Y), ∃ (Z : _) (h : Y ⟶ Z), f ≫ h = g ≫ h
 #align category_theory.is_filtered_or_empty CategoryTheory.IsFilteredOrEmpty
 
 /-- A category `IsFiltered` if
@@ -138,11 +138,11 @@ variable [IsFilteredOrEmpty C]
 -- porting note: the following definitions were removed because the names are invalid,
 -- direct references to `IsFilteredOrEmpty` have been added instead
 --
--- theorem cocone_objs : ∀ X Y : C, ∃ (Z : _)(f : X ⟶ Z)(g : Y ⟶ Z), True :=
+-- theorem cocone_objs : ∀ X Y : C, ∃ (Z : _) (f : X ⟶ Z) (g : Y ⟶ Z), True :=
 --  IsFilteredOrEmpty.cocone_objs
 -- #align category_theory.is_filtered.cocone_objs CategoryTheory.IsFiltered.cocone_objs
 --
---theorem cocone_maps : ∀ ⦃X Y : C⦄ (f g : X ⟶ Y), ∃ (Z : _)(h : Y ⟶ Z), f ≫ h = g ≫ h :=
+--theorem cocone_maps : ∀ ⦃X Y : C⦄ (f g : X ⟶ Y), ∃ (Z : _) (h : Y ⟶ Z), f ≫ h = g ≫ h :=
 --  IsFilteredOrEmpty.cocone_maps
 --#align category_theory.is_filtered.cocone_maps CategoryTheory.IsFiltered.cocone_maps
 
@@ -217,7 +217,7 @@ theorem sup_objs_exists (O : Finset C) : ∃ S : C, ∀ {X}, X ∈ O → _root_.
     · exact ⟨(w' (Finset.mem_of_mem_insert_of_ne mY h)).some ≫ rightToMax _ _⟩
 #align category_theory.is_filtered.sup_objs_exists CategoryTheory.IsFiltered.sup_objs_exists
 
-variable (O : Finset C) (H : Finset (Σ'(X Y : C)(_ : X ∈ O)(_ : Y ∈ O), X ⟶ Y))
+variable (O : Finset C) (H : Finset (Σ' (X Y : C) (_ : X ∈ O) (_ : Y ∈ O), X ⟶ Y))
 
 /-- Given any `Finset` of objects `{X, ...}` and
 indexed collection of `Finset`s of morphisms `{f, ...}` in `C`,
@@ -225,9 +225,10 @@ there exists an object `S`, with a morphism `T X : X ⟶ S` from each `X`,
 such that the triangles commute: `f ≫ T Y = T X`, for `f : X ⟶ Y` in the `Finset`.
 -/
 theorem sup_exists :
-    ∃ (S : C)(T : ∀ {X : C}, X ∈ O → (X ⟶ S)),
+    ∃ (S : C) (T : ∀ {X : C}, X ∈ O → (X ⟶ S)),
       ∀ {X Y : C} (mX : X ∈ O) (mY : Y ∈ O) {f : X ⟶ Y},
-        (⟨X, Y, mX, mY, f⟩ : Σ'(X Y : C)(_ : X ∈ O)(_ : Y ∈ O), X ⟶ Y) ∈ H → f ≫ T mY = T mX := by
+        (⟨X, Y, mX, mY, f⟩ : Σ' (X Y : C) (_ : X ∈ O) (_ : Y ∈ O), X ⟶ Y) ∈ H →
+          f ≫ T mY = T mX := by
   classical
   induction' H using Finset.induction with h' H' nmf h''
   · obtain ⟨S, f⟩ := sup_objs_exists O
@@ -272,7 +273,7 @@ noncomputable def toSup {X : C} (m : X ∈ O) : X ⟶ sup O H :=
 /-- The triangles of consisting of a morphism in `H` and the maps to `sup O H` commute.
 -/
 theorem toSup_commutes {X Y : C} (mX : X ∈ O) (mY : Y ∈ O) {f : X ⟶ Y}
-    (mf : (⟨X, Y, mX, mY, f⟩ : Σ'(X Y : C)(_ : X ∈ O)(_ : Y ∈ O), X ⟶ Y) ∈ H) :
+    (mf : (⟨X, Y, mX, mY, f⟩ : Σ' (X Y : C) (_ : X ∈ O) (_ : Y ∈ O), X ⟶ Y) ∈ H) :
     f ≫ toSup O H mY = toSup O H mX :=
   (sup_exists O H).choose_spec.choose_spec mX mY mf
 #align category_theory.is_filtered.to_sup_commutes CategoryTheory.IsFiltered.toSup_commutes
@@ -285,7 +286,7 @@ there exists a cocone over `F`.
 theorem cocone_nonempty (F : J ⥤ C) : _root_.Nonempty (Cocone F) := by
   classical
   let O := Finset.univ.image F.obj
-  let H : Finset (Σ'(X Y : C)(_ : X ∈ O)(_ : Y ∈ O), X ⟶ Y) :=
+  let H : Finset (Σ' (X Y : C) (_ : X ∈ O) (_ : Y ∈ O), X ⟶ Y) :=
     Finset.univ.biUnion   fun X : J =>
       Finset.univ.biUnion fun Y : J =>
         Finset.univ.image fun f : X ⟶ Y => ⟨F.obj X, F.obj Y, by simp, by simp, F.map f⟩
@@ -405,7 +406,7 @@ theorem coeq₃_condition₃ {j₁ j₂ : C} (f g h : j₁ ⟶ j₂) : f ≫ coe
 /-- For every span `j ⟵ i ⟶ j'`, there
    exists a cocone `j ⟶ k ⟵ j'` such that the square commutes. -/
 theorem span {i j j' : C} (f : i ⟶ j) (f' : i ⟶ j') :
-    ∃ (k : C)(g : j ⟶ k)(g' : j' ⟶ k), f ≫ g = f' ≫ g' :=
+    ∃ (k : C) (g : j ⟶ k) (g' : j' ⟶ k), f ≫ g = f' ≫ g' :=
   let ⟨K, G, G', _⟩ := IsFilteredOrEmpty.cocone_objs j j'
   let ⟨k, e, he⟩ := IsFilteredOrEmpty.cocone_maps (f ≫ G) (f' ≫ G')
   ⟨k, G ≫ e, G' ≫ e, by simpa only [← Category.assoc] ⟩
@@ -425,7 +426,7 @@ in a filtered category, we can construct an object `s` and two morphisms from `k
 making the resulting squares commute.
 -/
 theorem bowtie {j₁ j₂ k₁ k₂ : C} (f₁ : j₁ ⟶ k₁) (g₁ : j₁ ⟶ k₂) (f₂ : j₂ ⟶ k₁) (g₂ : j₂ ⟶ k₂) :
-    ∃ (s : C)(α : k₁ ⟶ s)(β : k₂ ⟶ s), f₁ ≫ α = g₁ ≫ β ∧ f₂ ≫ α = g₂ ≫ β := by
+    ∃ (s : C) (α : k₁ ⟶ s) (β : k₂ ⟶ s), f₁ ≫ α = g₁ ≫ β ∧ f₂ ≫ α = g₂ ≫ β := by
   obtain ⟨t, k₁t, k₂t, ht⟩ := span f₁ g₁
   obtain ⟨s, ts, hs⟩ := IsFilteredOrEmpty.cocone_maps (f₂ ≫ k₁t) (g₂ ≫ k₂t)
   simp_rw [Category.assoc] at hs
@@ -451,7 +452,7 @@ to `s`, making the resulting squares commute.
 -/
 theorem tulip {j₁ j₂ j₃ k₁ k₂ l : C} (f₁ : j₁ ⟶ k₁) (f₂ : j₂ ⟶ k₁) (f₃ : j₂ ⟶ k₂) (f₄ : j₃ ⟶ k₂)
     (g₁ : j₁ ⟶ l) (g₂ : j₃ ⟶ l) :
-    ∃ (s : C)(α : k₁ ⟶ s)(β : l ⟶ s)(γ : k₂ ⟶ s),
+    ∃ (s : C) (α : k₁ ⟶ s) (β : l ⟶ s) (γ : k₂ ⟶ s),
       f₁ ≫ α = g₁ ≫ β ∧ f₂ ≫ α = f₃ ≫ γ ∧ f₄ ≫ γ = g₂ ≫ β := by
   obtain ⟨l', k₁l, k₂l, hl⟩ := span f₂ f₃
   obtain ⟨s, ls, l's, hs₁, hs₂⟩ := bowtie g₁ (f₁ ≫ k₁l) g₂ (f₄ ≫ k₂l)
@@ -470,10 +471,10 @@ end IsFiltered
 -/
 class IsCofilteredOrEmpty : Prop where
   /-- for every pair of objects there exists another object "to the left" -/
-  cone_objs : ∀ X Y : C, ∃ (W : _)(_ : W ⟶ X)(_ : W ⟶ Y), True
+  cone_objs : ∀ X Y : C, ∃ (W : _) (_ : W ⟶ X) (_ : W ⟶ Y), True
   /-- for every pair of parallel morphisms there exists a morphism to the left
     so the compositions are equal -/
-  cone_maps : ∀ ⦃X Y : C⦄ (f g : X ⟶ Y), ∃ (W : _)(h : W ⟶ X), h ≫ f = h ≫ g
+  cone_maps : ∀ ⦃X Y : C⦄ (f g : X ⟶ Y), ∃ (W : _) (h : W ⟶ X), h ≫ f = h ≫ g
 #align category_theory.is_cofiltered_or_empty CategoryTheory.IsCofilteredOrEmpty
 
 /-- A category `IsCofiltered` if
@@ -537,11 +538,11 @@ variable [IsCofilteredOrEmpty C]
 -- porting note: the following definitions were removed because the names are invalid,
 -- direct references to `IsCofilteredOrEmpty` have been added instead
 --
---theorem cone_objs : ∀ X Y : C, ∃ (W : _)(f : W ⟶ X)(g : W ⟶ Y), True :=
+--theorem cone_objs : ∀ X Y : C, ∃ (W : _) (f : W ⟶ X) (g : W ⟶ Y), True :=
 --  IsCofilteredOrEmpty.cone_objs
 --#align category_theory.is_cofiltered.cone_objs CategoryTheory.IsCofiltered.cone_objs
 --
---theorem cone_maps : ∀ ⦃X Y : C⦄ (f g : X ⟶ Y), ∃ (W : _)(h : W ⟶ X), h ≫ f = h ≫ g :=
+--theorem cone_maps : ∀ ⦃X Y : C⦄ (f g : X ⟶ Y), ∃ (W : _) (h : W ⟶ X), h ≫ f = h ≫ g :=
 --  IsCofilteredOrEmpty.cone_maps
 --#align category_theory.is_cofiltered.cone_maps CategoryTheory.IsCofiltered.cone_maps
 
@@ -596,7 +597,7 @@ theorem eq_condition {j j' : C} (f f' : j ⟶ j') : eqHom f f' ≫ f = eqHom f f
 /-- For every cospan `j ⟶ i ⟵ j'`,
  there exists a cone `j ⟵ k ⟶ j'` such that the square commutes. -/
 theorem cospan {i j j' : C} (f : j ⟶ i) (f' : j' ⟶ i) :
-    ∃ (k : C)(g : k ⟶ j)(g' : k ⟶ j'), g ≫ f = g' ≫ f' :=
+    ∃ (k : C) (g : k ⟶ j) (g' : k ⟶ j'), g ≫ f = g' ≫ f' :=
   let ⟨K, G, G', _⟩ := IsCofilteredOrEmpty.cone_objs j j'
   let ⟨k, e, he⟩ := IsCofilteredOrEmpty.cone_maps (G ≫ f) (G' ≫ f')
   ⟨k, e ≫ G, e ≫ G', by simpa only [Category.assoc] using he⟩
@@ -631,7 +632,7 @@ theorem inf_objs_exists (O : Finset C) : ∃ S : C, ∀ {X}, X ∈ O → _root_.
     · exact ⟨minToRight _ _ ≫ (w' (Finset.mem_of_mem_insert_of_ne mY h)).some⟩
 #align category_theory.is_cofiltered.inf_objs_exists CategoryTheory.IsCofiltered.inf_objs_exists
 
-variable (O : Finset C) (H : Finset (Σ'(X Y : C)(_ : X ∈ O)(_ : Y ∈ O), X ⟶ Y))
+variable (O : Finset C) (H : Finset (Σ' (X Y : C) (_ : X ∈ O) (_ : Y ∈ O), X ⟶ Y))
 
 /-- Given any `Finset` of objects `{X, ...}` and
 indexed collection of `Finset`s of morphisms `{f, ...}` in `C`,
@@ -639,9 +640,10 @@ there exists an object `S`, with a morphism `T X : S ⟶ X` from each `X`,
 such that the triangles commute: `T X ≫ f = T Y`, for `f : X ⟶ Y` in the `Finset`.
 -/
 theorem inf_exists :
-    ∃ (S : C)(T : ∀ {X : C}, X ∈ O → (S ⟶ X)),
+    ∃ (S : C) (T : ∀ {X : C}, X ∈ O → (S ⟶ X)),
       ∀ {X Y : C} (mX : X ∈ O) (mY : Y ∈ O) {f : X ⟶ Y},
-        (⟨X, Y, mX, mY, f⟩ : Σ'(X Y : C)(_ : X ∈ O)(_ : Y ∈ O), X ⟶ Y) ∈ H → T mX ≫ f = T mY := by
+        (⟨X, Y, mX, mY, f⟩ : Σ' (X Y : C) (_ : X ∈ O) (_ : Y ∈ O), X ⟶ Y) ∈ H →
+          T mX ≫ f = T mY := by
   classical
   induction' H using Finset.induction with h' H' nmf h''
   · obtain ⟨S, f⟩ := inf_objs_exists O
@@ -686,7 +688,7 @@ noncomputable def infTo {X : C} (m : X ∈ O) : inf O H ⟶ X :=
 /-- The triangles consisting of a morphism in `H` and the maps from `inf O H` commute.
 -/
 theorem infTo_commutes {X Y : C} (mX : X ∈ O) (mY : Y ∈ O) {f : X ⟶ Y}
-    (mf : (⟨X, Y, mX, mY, f⟩ : Σ'(X Y : C)(_ : X ∈ O)(_ : Y ∈ O), X ⟶ Y) ∈ H) :
+    (mf : (⟨X, Y, mX, mY, f⟩ : Σ' (X Y : C) (_ : X ∈ O) (_ : Y ∈ O), X ⟶ Y) ∈ H) :
     infTo O H mX ≫ f = infTo O H mY :=
   (inf_exists O H).choose_spec.choose_spec mX mY mf
 #align category_theory.is_cofiltered.inf_to_commutes CategoryTheory.IsCofiltered.infTo_commutes
@@ -699,7 +701,7 @@ there exists a cone over `F`.
 theorem cone_nonempty (F : J ⥤ C) : _root_.Nonempty (Cone F) := by
   classical
   let O := Finset.univ.image F.obj
-  let H : Finset (Σ'(X Y : C)(_ : X ∈ O)(_ : Y ∈ O), X ⟶ Y) :=
+  let H : Finset (Σ' (X Y : C) (_ : X ∈ O) (_ : Y ∈ O), X ⟶ Y) :=
     Finset.univ.biUnion fun X : J =>
       Finset.univ.biUnion fun Y : J =>
         Finset.univ.image fun f : X ⟶ Y => ⟨F.obj X, F.obj Y, by simp, by simp, F.map f⟩

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

@@ -42,7 +42,7 @@ of finsets of morphisms.
 
 Furthermore, we give special support for two diagram categories: The `bowtie` and the `tulip`.
 This is because these shapes show up in the proofs that forgetful functors of algebraic categories
-(e.g. `Mon`, `CommRing`, ...) preserve filtered colimits.
+(e.g. `MonCat`, `CommRingCat`, ...) preserve filtered colimits.
 
 All of the above API, except for the `bowtie` and the `tulip`, is also provided for cofiltered
 categories.

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>

@@ -286,8 +286,8 @@ theorem cocone_nonempty (F : J ⥤ C) : _root_.Nonempty (Cocone F) := by
   classical
   let O := Finset.univ.image F.obj
   let H : Finset (Σ'(X Y : C)(_ : X ∈ O)(_ : Y ∈ O), X ⟶ Y) :=
-    Finset.univ.bunionᵢ   fun X : J =>
-      Finset.univ.bunionᵢ fun Y : J =>
+    Finset.univ.biUnion   fun X : J =>
+      Finset.univ.biUnion fun Y : J =>
         Finset.univ.image fun f : X ⟶ Y => ⟨F.obj X, F.obj Y, by simp, by simp, F.map f⟩
   obtain ⟨Z, f, w⟩ := sup_exists O H
   refine' ⟨⟨Z, ⟨fun X => f (by simp), _⟩⟩⟩
@@ -295,7 +295,7 @@ theorem cocone_nonempty (F : J ⥤ C) : _root_.Nonempty (Cocone F) := by
   dsimp
   simp only [Category.comp_id]
   apply w
-  simp only [Finset.mem_bunionᵢ, Finset.mem_univ, Finset.mem_image, PSigma.mk.injEq,
+  simp only [Finset.mem_biUnion, Finset.mem_univ, Finset.mem_image, PSigma.mk.injEq,
     true_and, exists_and_left]
   exact ⟨j, rfl, j', g, by simp⟩
 #align category_theory.is_filtered.cocone_nonempty CategoryTheory.IsFiltered.cocone_nonempty
@@ -700,8 +700,8 @@ theorem cone_nonempty (F : J ⥤ C) : _root_.Nonempty (Cone F) := by
   classical
   let O := Finset.univ.image F.obj
   let H : Finset (Σ'(X Y : C)(_ : X ∈ O)(_ : Y ∈ O), X ⟶ Y) :=
-    Finset.univ.bunionᵢ fun X : J =>
-      Finset.univ.bunionᵢ fun Y : J =>
+    Finset.univ.biUnion fun X : J =>
+      Finset.univ.biUnion fun Y : J =>
         Finset.univ.image fun f : X ⟶ Y => ⟨F.obj X, F.obj Y, by simp, by simp, F.map f⟩
   obtain ⟨Z, f, w⟩ := inf_exists O H
   refine' ⟨⟨Z, ⟨fun X => f (by simp), _⟩⟩⟩
@@ -710,7 +710,7 @@ theorem cone_nonempty (F : J ⥤ C) : _root_.Nonempty (Cone F) := by
   simp only [Category.id_comp]
   symm
   apply w
-  simp only [Finset.mem_bunionᵢ, Finset.mem_univ, Finset.mem_image,
+  simp only [Finset.mem_biUnion, Finset.mem_univ, Finset.mem_image,
     PSigma.mk.injEq, true_and, exists_and_left]
   exact ⟨j, rfl, j', g, by simp⟩
 #align category_theory.is_cofiltered.cone_nonempty CategoryTheory.IsCofiltered.cone_nonempty

Co-authored-by: Kevin Buzzard <k.buzzard@imperial.ac.uk> Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Parcly Taxel <reddeloostw@gmail.com> Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>

@@ -552,14 +552,14 @@ noncomputable def min (j j' : C) : C :=
   (IsCofilteredOrEmpty.cone_objs j j').choose
 #align category_theory.is_cofiltered.min CategoryTheory.IsCofiltered.min
 
-/-- `min_to_left j j'` is an arbitrary choice of morphism from `min j j'` to `j`,
+/-- `minToLeft j j'` is an arbitrary choice of morphism from `min j j'` to `j`,
 whose existence is ensured by `IsCofiltered`.
 -/
 noncomputable def minToLeft (j j' : C) : min j j' ⟶ j :=
   (IsCofilteredOrEmpty.cone_objs j j').choose_spec.choose
 #align category_theory.is_cofiltered.min_to_left CategoryTheory.IsCofiltered.minToLeft
 
-/-- `min_to_right j j'` is an arbitrary choice of morphism from `min j j'` to `j'`,
+/-- `minToRight j j'` is an arbitrary choice of morphism from `min j j'` to `j'`,
 whose existence is ensured by `IsCofiltered`.
 -/
 noncomputable def minToRight (j j' : C) : min j j' ⟶ j' :=

This PR puts, with one exception, every single remaining by that lies all by itself on its own line to the previous line, thus matching the current behaviour of start-port.sh. The exception is when the by begins the second or later argument to a tuple or anonymous constructor; see https://github.com/leanprover-community/mathlib4/pull/3825#discussion_r1186702599.

Essentially this is s/\n *by$/ by/g, but with manual editing to satisfy the linter's max-100-char-line requirement. The Python style linter is also modified to catch these "isolated bys".

@@ -389,8 +389,8 @@ theorem coeq₃_condition₁ {j₁ j₂ : C} (f g h : j₁ ⟶ j₂) : f ≫ coe
   by simp only [coeq₃Hom, ← Category.assoc, coeq_condition f g]
 #align category_theory.is_filtered.coeq₃_condition₁ CategoryTheory.IsFiltered.coeq₃_condition₁
 
-theorem coeq₃_condition₂ {j₁ j₂ : C} (f g h : j₁ ⟶ j₂) : g ≫ coeq₃Hom f g h = h ≫ coeq₃Hom f g h :=
-  by
+theorem coeq₃_condition₂ {j₁ j₂ : C} (f g h : j₁ ⟶ j₂) :
+    g ≫ coeq₃Hom f g h = h ≫ coeq₃Hom f g h := by
   dsimp [coeq₃Hom]
   slice_lhs 2 4 => rw [← Category.assoc, coeq_condition _ _]
   slice_rhs 2 4 => rw [← Category.assoc, coeq_condition _ _]

@@ -103,8 +103,7 @@ instance (priority := 100) isFiltered_of_semilatticeSup_nonempty (α : Type u) [
 #align category_theory.is_filtered_of_semilattice_sup_nonempty CategoryTheory.isFiltered_of_semilatticeSup_nonempty
 
 instance (priority := 100) isFilteredOrEmpty_of_directed_le (α : Type u) [Preorder α]
-    [IsDirected α (· ≤ ·)] : IsFilteredOrEmpty α
-    where
+    [IsDirected α (· ≤ ·)] : IsFilteredOrEmpty α where
   cocone_objs X Y :=
     let ⟨Z, h1, h2⟩ := exists_ge_ge X Y
     ⟨Z, homOfLE h1, homOfLE h2, trivial⟩
@@ -154,33 +153,33 @@ noncomputable def max (j j' : C) : C :=
   (IsFilteredOrEmpty.cocone_objs j j').choose
 #align category_theory.is_filtered.max CategoryTheory.IsFiltered.max
 
-/-- `left_to_max j j'` is an arbitrary choice of morphism from `j` to `max j j'`,
-whose existence is ensured by `is_filtered`.
+/-- `leftToMax j j'` is an arbitrary choice of morphism from `j` to `max j j'`,
+whose existence is ensured by `IsFiltered`.
 -/
 noncomputable def leftToMax (j j' : C) : j ⟶ max j j' :=
   (IsFilteredOrEmpty.cocone_objs j j').choose_spec.choose
 #align category_theory.is_filtered.left_to_max CategoryTheory.IsFiltered.leftToMax
 
-/-- `right_to_max j j'` is an arbitrary choice of morphism from `j'` to `max j j'`,
-whose existence is ensured by `is_filtered`.
+/-- `rightToMax j j'` is an arbitrary choice of morphism from `j'` to `max j j'`,
+whose existence is ensured by `IsFiltered`.
 -/
 noncomputable def rightToMax (j j' : C) : j' ⟶ max j j' :=
   (IsFilteredOrEmpty.cocone_objs j j').choose_spec.choose_spec.choose
 #align category_theory.is_filtered.right_to_max CategoryTheory.IsFiltered.rightToMax
 
 /-- `coeq f f'`, for morphisms `f f' : j ⟶ j'`, is an arbitrary choice of object
-which admits a morphism `coeq_hom f f' : j' ⟶ coeq f f'` such that
-`coeq_condition : f ≫ coeq_hom f f' = f' ≫ coeq_hom f f'`.
-Its existence is ensured by `is_filtered`.
+which admits a morphism `coeqHom f f' : j' ⟶ coeq f f'` such that
+`coeq_condition : f ≫ coeqHom f f' = f' ≫ coeqHom f f'`.
+Its existence is ensured by `IsFiltered`.
 -/
 noncomputable def coeq {j j' : C} (f f' : j ⟶ j') : C :=
   (IsFilteredOrEmpty.cocone_maps f f').choose
 #align category_theory.is_filtered.coeq CategoryTheory.IsFiltered.coeq
 
-/-- `coeq_hom f f'`, for morphisms `f f' : j ⟶ j'`, is an arbitrary choice of morphism
-`coeq_hom f f' : j' ⟶ coeq f f'` such that
-`coeq_condition : f ≫ coeq_hom f f' = f' ≫ coeq_hom f f'`.
-Its existence is ensured by `is_filtered`.
+/-- `coeqHom f f'`, for morphisms `f f' : j ⟶ j'`, is an arbitrary choice of morphism
+`coeqHom f f' : j' ⟶ coeq f f'` such that
+`coeq_condition : f ≫ coeqHom f f' = f' ≫ coeqHom f f'`.
+Its existence is ensured by `IsFiltered`.
 -/
 noncomputable def coeqHom {j j' : C} (f f' : j ⟶ j') : j' ⟶ coeq f f' :=
   (IsFilteredOrEmpty.cocone_maps f f').choose_spec.choose
@@ -188,7 +187,7 @@ noncomputable def coeqHom {j j' : C} (f f' : j ⟶ j') : j' ⟶ coeq f f' :=
 
 -- porting note: the simp tag has been removed as the linter complained
 /-- `coeq_condition f f'`, for morphisms `f f' : j ⟶ j'`, is the proof that
-`f ≫ coeq_hom f f' = f' ≫ coeq_hom f f'`.
+`f ≫ coeqHom f f' = f' ≫ coeqHom f f'`.
 -/
 @[reassoc]
 theorem coeq_condition {j j' : C} (f f' : j ⟶ j') : f ≫ coeqHom f f' = f' ≫ coeqHom f f' :=
@@ -280,7 +279,7 @@ theorem toSup_commutes {X Y : C} (mX : X ∈ O) (mY : Y ∈ O) {f : X ⟶ Y}
 
 variable {J : Type v} [SmallCategory J] [FinCategory J]
 
-/-- If we have `is_filtered C`, then for any functor `F : J ⥤ C` with `fin_category J`,
+/-- If we have `IsFiltered C`, then for any functor `F : J ⥤ C` with `FinCategory J`,
 there exists a cocone over `F`.
 -/
 theorem cocone_nonempty (F : J ⥤ C) : _root_.Nonempty (Cocone F) := by
@@ -301,7 +300,7 @@ theorem cocone_nonempty (F : J ⥤ C) : _root_.Nonempty (Cocone F) := by
   exact ⟨j, rfl, j', g, by simp⟩
 #align category_theory.is_filtered.cocone_nonempty CategoryTheory.IsFiltered.cocone_nonempty
 
-/-- An arbitrary choice of cocone over `F : J ⥤ C`, for `fin_category J` and `is_filtered C`.
+/-- An arbitrary choice of cocone over `F : J ⥤ C`, for `FinCategory J` and `IsFiltered C`.
 -/
 noncomputable def cocone (F : J ⥤ C) : Cocone F :=
   (cocone_nonempty F).some
@@ -338,46 +337,46 @@ variable {C}
 variable [IsFilteredOrEmpty C]
 
 /-- `max₃ j₁ j₂ j₃` is an arbitrary choice of object to the right of `j₁`, `j₂` and `j₃`,
-whose existence is ensured by `is_filtered`.
+whose existence is ensured by `IsFiltered`.
 -/
 noncomputable def max₃ (j₁ j₂ j₃ : C) : C :=
   max (max j₁ j₂) j₃
 #align category_theory.is_filtered.max₃ CategoryTheory.IsFiltered.max₃
 
-/-- `first_to_max₃ j₁ j₂ j₃` is an arbitrary choice of morphism from `j₁` to `max₃ j₁ j₂ j₃`,
-whose existence is ensured by `is_filtered`.
+/-- `firstToMax₃ j₁ j₂ j₃` is an arbitrary choice of morphism from `j₁` to `max₃ j₁ j₂ j₃`,
+whose existence is ensured by `IsFiltered`.
 -/
 noncomputable def firstToMax₃ (j₁ j₂ j₃ : C) : j₁ ⟶ max₃ j₁ j₂ j₃ :=
   leftToMax j₁ j₂ ≫ leftToMax (max j₁ j₂) j₃
 #align category_theory.is_filtered.first_to_max₃ CategoryTheory.IsFiltered.firstToMax₃
 
-/-- `second_to_max₃ j₁ j₂ j₃` is an arbitrary choice of morphism from `j₂` to `max₃ j₁ j₂ j₃`,
-whose existence is ensured by `is_filtered`.
+/-- `secondToMax₃ j₁ j₂ j₃` is an arbitrary choice of morphism from `j₂` to `max₃ j₁ j₂ j₃`,
+whose existence is ensured by `IsFiltered`.
 -/
 noncomputable def secondToMax₃ (j₁ j₂ j₃ : C) : j₂ ⟶ max₃ j₁ j₂ j₃ :=
   rightToMax j₁ j₂ ≫ leftToMax (max j₁ j₂) j₃
 #align category_theory.is_filtered.second_to_max₃ CategoryTheory.IsFiltered.secondToMax₃
 
-/-- `third_to_max₃ j₁ j₂ j₃` is an arbitrary choice of morphism from `j₃` to `max₃ j₁ j₂ j₃`,
-whose existence is ensured by `is_filtered`.
+/-- `thirdToMax₃ j₁ j₂ j₃` is an arbitrary choice of morphism from `j₃` to `max₃ j₁ j₂ j₃`,
+whose existence is ensured by `IsFiltered`.
 -/
 noncomputable def thirdToMax₃ (j₁ j₂ j₃ : C) : j₃ ⟶ max₃ j₁ j₂ j₃ :=
   rightToMax (max j₁ j₂) j₃
 #align category_theory.is_filtered.third_to_max₃ CategoryTheory.IsFiltered.thirdToMax₃
 
 /-- `coeq₃ f g h`, for morphisms `f g h : j₁ ⟶ j₂`, is an arbitrary choice of object
-which admits a morphism `coeq₃_hom f g h : j₂ ⟶ coeq₃ f g h` such that
+which admits a morphism `coeq₃Hom f g h : j₂ ⟶ coeq₃ f g h` such that
 `coeq₃_condition₁`, `coeq₃_condition₂` and `coeq₃_condition₃` are satisfied.
-Its existence is ensured by `is_filtered`.
+Its existence is ensured by `IsFiltered`.
 -/
 noncomputable def coeq₃ {j₁ j₂ : C} (f g h : j₁ ⟶ j₂) : C :=
   coeq (coeqHom f g ≫ leftToMax (coeq f g) (coeq g h))
     (coeqHom g h ≫ rightToMax (coeq f g) (coeq g h))
 #align category_theory.is_filtered.coeq₃ CategoryTheory.IsFiltered.coeq₃
 
-/-- `coeq₃_hom f g h`, for morphisms `f g h : j₁ ⟶ j₂`, is an arbitrary choice of morphism
+/-- `coeq₃Hom f g h`, for morphisms `f g h : j₁ ⟶ j₂`, is an arbitrary choice of morphism
 `j₂ ⟶ coeq₃ f g h` such that `coeq₃_condition₁`, `coeq₃_condition₂` and `coeq₃_condition₃`
-are satisfied. Its existence is ensured by `is_filtered`.
+are satisfied. Its existence is ensured by `IsFiltered`.
 -/
 noncomputable def coeq₃Hom {j₁ j₂ : C} (f g h : j₁ ⟶ j₂) : j₂ ⟶ coeq₃ f g h :=
   coeqHom f g ≫
@@ -464,7 +463,7 @@ end SpecialShapes
 
 end IsFiltered
 
-/-- A category `is_cofiltered_or_empty` if
+/-- A category `IsCofilteredOrEmpty` if
 1. for every pair of objects there exists another object "to the left", and
 2. for every pair of parallel morphisms there exists a morphism to the left so the compositions
    are equal.
@@ -477,7 +476,7 @@ class IsCofilteredOrEmpty : Prop where
   cone_maps : ∀ ⦃X Y : C⦄ (f g : X ⟶ Y), ∃ (W : _)(h : W ⟶ X), h ≫ f = h ≫ g
 #align category_theory.is_cofiltered_or_empty CategoryTheory.IsCofilteredOrEmpty
 
-/-- A category `is_cofiltered` if
+/-- A category `IsCofiltered` if
 1. for every pair of objects there exists another object "to the left",
 2. for every pair of parallel morphisms there exists a morphism to the left so the compositions
    are equal, and
@@ -491,8 +490,7 @@ class IsCofiltered extends IsCofilteredOrEmpty C : Prop where
 #align category_theory.is_cofiltered CategoryTheory.IsCofiltered
 
 instance (priority := 100) isCofilteredOrEmpty_of_semilatticeInf (α : Type u) [SemilatticeInf α] :
-    IsCofilteredOrEmpty α
-    where
+    IsCofilteredOrEmpty α where
   cone_objs X Y := ⟨X ⊓ Y, homOfLE inf_le_left, homOfLE inf_le_right, trivial⟩
   cone_maps X Y f g := ⟨X, 𝟙 _, by
     apply ULift.ext
@@ -504,8 +502,7 @@ instance (priority := 100) isCofiltered_of_semilatticeInf_nonempty (α : Type u)
 #align category_theory.is_cofiltered_of_semilattice_inf_nonempty CategoryTheory.isCofiltered_of_semilatticeInf_nonempty
 
 instance (priority := 100) isCofilteredOrEmpty_of_directed_ge (α : Type u) [Preorder α]
-    [IsDirected α (· ≥ ·)] : IsCofilteredOrEmpty α
-    where
+    [IsDirected α (· ≥ ·)] : IsCofilteredOrEmpty α where
   cone_objs X Y :=
     let ⟨Z, hX, hY⟩ := exists_le_le X Y
     ⟨Z, homOfLE hX, homOfLE hY, trivial⟩
@@ -523,8 +520,7 @@ example (α : Type u) [SemilatticeInf α] [OrderBot α] : IsCofiltered α := by
 
 example (α : Type u) [SemilatticeInf α] [OrderTop α] : IsCofiltered α := by infer_instance
 
-instance : IsCofiltered (Discrete PUnit)
-    where
+instance : IsCofiltered (Discrete PUnit) where
   cone_objs X Y := ⟨⟨PUnit.unit⟩, ⟨⟨by trivial⟩⟩, ⟨⟨Subsingleton.elim _ _⟩⟩, trivial⟩
   cone_maps X Y f g := ⟨⟨PUnit.unit⟩, ⟨⟨by trivial⟩⟩, by
     apply ULift.ext
@@ -550,39 +546,39 @@ variable [IsCofilteredOrEmpty C]
 --#align category_theory.is_cofiltered.cone_maps CategoryTheory.IsCofiltered.cone_maps
 
 /-- `min j j'` is an arbitrary choice of object to the left of both `j` and `j'`,
-whose existence is ensured by `is_cofiltered`.
+whose existence is ensured by `IsCofiltered`.
 -/
 noncomputable def min (j j' : C) : C :=
   (IsCofilteredOrEmpty.cone_objs j j').choose
 #align category_theory.is_cofiltered.min CategoryTheory.IsCofiltered.min
 
 /-- `min_to_left j j'` is an arbitrary choice of morphism from `min j j'` to `j`,
-whose existence is ensured by `is_cofiltered`.
+whose existence is ensured by `IsCofiltered`.
 -/
 noncomputable def minToLeft (j j' : C) : min j j' ⟶ j :=
   (IsCofilteredOrEmpty.cone_objs j j').choose_spec.choose
 #align category_theory.is_cofiltered.min_to_left CategoryTheory.IsCofiltered.minToLeft
 
 /-- `min_to_right j j'` is an arbitrary choice of morphism from `min j j'` to `j'`,
-whose existence is ensured by `is_cofiltered`.
+whose existence is ensured by `IsCofiltered`.
 -/
 noncomputable def minToRight (j j' : C) : min j j' ⟶ j' :=
   (IsCofilteredOrEmpty.cone_objs j j').choose_spec.choose_spec.choose
 #align category_theory.is_cofiltered.min_to_right CategoryTheory.IsCofiltered.minToRight
 
 /-- `eq f f'`, for morphisms `f f' : j ⟶ j'`, is an arbitrary choice of object
-which admits a morphism `eq_hom f f' : eq f f' ⟶ j` such that
-`eq_condition : eq_hom f f' ≫ f = eq_hom f f' ≫ f'`.
-Its existence is ensured by `is_cofiltered`.
+which admits a morphism `eqHom f f' : eq f f' ⟶ j` such that
+`eq_condition : eqHom f f' ≫ f = eqHom f f' ≫ f'`.
+Its existence is ensured by `IsCofiltered`.
 -/
 noncomputable def eq {j j' : C} (f f' : j ⟶ j') : C :=
   (IsCofilteredOrEmpty.cone_maps f f').choose
 #align category_theory.is_cofiltered.eq CategoryTheory.IsCofiltered.eq
 
-/-- `eq_hom f f'`, for morphisms `f f' : j ⟶ j'`, is an arbitrary choice of morphism
-`eq_hom f f' : eq f f' ⟶ j` such that
-`eq_condition : eq_hom f f' ≫ f = eq_hom f f' ≫ f'`.
-Its existence is ensured by `is_cofiltered`.
+/-- `eqHom f f'`, for morphisms `f f' : j ⟶ j'`, is an arbitrary choice of morphism
+`eqHom f f' : eq f f' ⟶ j` such that
+`eq_condition : eqHom f f' ≫ f = eqHom f f' ≫ f'`.
+Its existence is ensured by `IsCofiltered`.
 -/
 noncomputable def eqHom {j j' : C} (f f' : j ⟶ j') : eq f f' ⟶ j :=
   (IsCofilteredOrEmpty.cone_maps f f').choose_spec.choose
@@ -590,7 +586,7 @@ noncomputable def eqHom {j j' : C} (f f' : j ⟶ j') : eq f f' ⟶ j :=
 
 -- porting note: the simp tag has been removed as the linter complained
 /-- `eq_condition f f'`, for morphisms `f f' : j ⟶ j'`, is the proof that
-`eq_hom f f' ≫ f = eq_hom f f' ≫ f'`.
+`eqHom f f' ≫ f = eqHom f f' ≫ f'`.
 -/
 @[reassoc]
 theorem eq_condition {j j' : C} (f f' : j ⟶ j') : eqHom f f' ≫ f = eqHom f f' ≫ f' :=
@@ -697,7 +693,7 @@ theorem infTo_commutes {X Y : C} (mX : X ∈ O) (mY : Y ∈ O) {f : X ⟶ Y}
 
 variable {J : Type w} [SmallCategory J] [FinCategory J]
 
-/-- If we have `is_cofiltered C`, then for any functor `F : J ⥤ C` with `fin_category J`,
+/-- If we have `IsCofiltered C`, then for any functor `F : J ⥤ C` with `FinCategory J`,
 there exists a cone over `F`.
 -/
 theorem cone_nonempty (F : J ⥤ C) : _root_.Nonempty (Cone F) := by
@@ -719,7 +715,7 @@ theorem cone_nonempty (F : J ⥤ C) : _root_.Nonempty (Cone F) := by
   exact ⟨j, rfl, j', g, by simp⟩
 #align category_theory.is_cofiltered.cone_nonempty CategoryTheory.IsCofiltered.cone_nonempty
 
-/-- An arbitrary choice of cone over `F : J ⥤ C`, for `fin_category J` and `is_cofiltered C`.
+/-- An arbitrary choice of cone over `F : J ⥤ C`, for `FinCategory J` and `IsCofiltered C`.
 -/
 noncomputable def cone (F : J ⥤ C) : Cone F :=
   (cone_nonempty F).some
@@ -758,28 +754,24 @@ section Opposite
 
 open Opposite
 
-instance isCofiltered_op_of_isFiltered [IsFiltered C] : IsCofiltered Cᵒᵖ
-    where
+instance isCofiltered_op_of_isFiltered [IsFiltered C] : IsCofiltered Cᵒᵖ where
   cone_objs X Y :=
     ⟨op (IsFiltered.max X.unop Y.unop), (IsFiltered.leftToMax _ _).op,
       (IsFiltered.rightToMax _ _).op, trivial⟩
   cone_maps X Y f g :=
-    ⟨op (IsFiltered.coeq f.unop g.unop), (IsFiltered.coeqHom _ _).op,
-      by
+    ⟨op (IsFiltered.coeq f.unop g.unop), (IsFiltered.coeqHom _ _).op, by
       rw [show f = f.unop.op by simp, show g = g.unop.op by simp, ← op_comp, ← op_comp]
       congr 1
       exact IsFiltered.coeq_condition f.unop g.unop⟩
   Nonempty := ⟨op IsFiltered.Nonempty.some⟩
 #align category_theory.is_cofiltered_op_of_is_filtered CategoryTheory.isCofiltered_op_of_isFiltered
 
-instance isFiltered_op_of_isCofiltered [IsCofiltered C] : IsFiltered Cᵒᵖ
-    where
+instance isFiltered_op_of_isCofiltered [IsCofiltered C] : IsFiltered Cᵒᵖ where
   cocone_objs X Y :=
     ⟨op (IsCofiltered.min X.unop Y.unop), (IsCofiltered.minToLeft X.unop Y.unop).op,
       (IsCofiltered.minToRight X.unop Y.unop).op, trivial⟩
   cocone_maps X Y f g :=
-    ⟨op (IsCofiltered.eq f.unop g.unop), (IsCofiltered.eqHom f.unop g.unop).op,
-      by
+    ⟨op (IsCofiltered.eq f.unop g.unop), (IsCofiltered.eqHom f.unop g.unop).op, by
       rw [show f = f.unop.op by simp, show g = g.unop.op by simp, ← op_comp, ← op_comp]
       congr 1
       exact IsCofiltered.eq_condition f.unop g.unop⟩

Co-authored-by: ChrisHughes24 <chrishughes24@gmail.com>