category_theory.limits.shapes.strict_initial

Changes since the initial port

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

Changes in mathlib3

70fd9563

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

f4758115

bump to nightly-2024-04-06-08

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

e34029c9

Diff

@@ -248,7 +248,7 @@ theorem IsTerminal.subsingleton_to (hI : IsTerminal I) {A : C} : Subsingleton (I
 
 variable {J : Type v} [SmallCategory J]
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (j «expr ≠ » i) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (j «expr ≠ » i) -/
 #print CategoryTheory.Limits.limit_π_isIso_of_is_strict_terminal /-
 /-- If all but one object in a diagram is strict terminal, the the limit is isomorphic to the
 said object via `limit.π`. -/

f4758115

bump to nightly-2024-02-01-06

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

5433bded

Diff

@@ -255,6 +255,24 @@ said object via `limit.π`. -/
 theorem limit_π_isIso_of_is_strict_terminal (F : J ⥤ C) [HasLimit F] (i : J)
     (H : ∀ (j) (_ : j ≠ i), IsTerminal (F.obj j)) [Subsingleton (i ⟶ i)] : IsIso (limit.π F i) := by
   classical
+  refine' ⟨⟨limit.lift _ ⟨_, ⟨_, _⟩⟩, _, _⟩⟩
+  · exact fun j => dite (j = i) (fun h => eq_to_hom (by cases h; rfl)) fun h => (H _ h).from _
+  · intro j k f
+    split_ifs
+    · cases h; cases h_1; obtain rfl : f = 𝟙 _ := Subsingleton.elim _ _; simpa
+    · cases h; erw [category.comp_id]
+      haveI : is_iso (F.map f) := (H _ h_1).isIso_from _
+      rw [← is_iso.comp_inv_eq]
+      apply (H _ h_1).hom_ext
+    · cases h_1; apply (H _ h).hom_ext
+    · apply (H _ h).hom_ext
+  · ext
+    rw [assoc, limit.lift_π]
+    dsimp only
+    split_ifs
+    · cases h; rw [id_comp, eq_to_hom_refl]; exact comp_id _
+    · apply (H _ h).hom_ext
+  · rw [limit.lift_π]; simpa
 #align category_theory.limits.limit_π_is_iso_of_is_strict_terminal CategoryTheory.Limits.limit_π_isIso_of_is_strict_terminal
 -/

f4758115

bump to nightly-2024-01-31-06

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

61100fe9

Diff

@@ -255,24 +255,6 @@ said object via `limit.π`. -/
 theorem limit_π_isIso_of_is_strict_terminal (F : J ⥤ C) [HasLimit F] (i : J)
     (H : ∀ (j) (_ : j ≠ i), IsTerminal (F.obj j)) [Subsingleton (i ⟶ i)] : IsIso (limit.π F i) := by
   classical
-  refine' ⟨⟨limit.lift _ ⟨_, ⟨_, _⟩⟩, _, _⟩⟩
-  · exact fun j => dite (j = i) (fun h => eq_to_hom (by cases h; rfl)) fun h => (H _ h).from _
-  · intro j k f
-    split_ifs
-    · cases h; cases h_1; obtain rfl : f = 𝟙 _ := Subsingleton.elim _ _; simpa
-    · cases h; erw [category.comp_id]
-      haveI : is_iso (F.map f) := (H _ h_1).isIso_from _
-      rw [← is_iso.comp_inv_eq]
-      apply (H _ h_1).hom_ext
-    · cases h_1; apply (H _ h).hom_ext
-    · apply (H _ h).hom_ext
-  · ext
-    rw [assoc, limit.lift_π]
-    dsimp only
-    split_ifs
-    · cases h; rw [id_comp, eq_to_hom_refl]; exact comp_id _
-    · apply (H _ h).hom_ext
-  · rw [limit.lift_π]; simpa
 #align category_theory.limits.limit_π_is_iso_of_is_strict_terminal CategoryTheory.Limits.limit_π_isIso_of_is_strict_terminal
 -/

f4758115

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,8 +3,8 @@ Copyright (c) 2021 Bhavik Mehta. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Bhavik Mehta
 -/
-import Mathbin.CategoryTheory.Limits.Shapes.Terminal
-import Mathbin.CategoryTheory.Limits.Shapes.BinaryProducts
+import CategoryTheory.Limits.Shapes.Terminal
+import CategoryTheory.Limits.Shapes.BinaryProducts
 
 #align_import category_theory.limits.shapes.strict_initial from "leanprover-community/mathlib"@"f47581155c818e6361af4e4fda60d27d020c226b"
 
@@ -248,7 +248,7 @@ theorem IsTerminal.subsingleton_to (hI : IsTerminal I) {A : C} : Subsingleton (I
 
 variable {J : Type v} [SmallCategory J]
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (j «expr ≠ » i) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (j «expr ≠ » i) -/
 #print CategoryTheory.Limits.limit_π_isIso_of_is_strict_terminal /-
 /-- If all but one object in a diagram is strict terminal, the the limit is isomorphic to the
 said object via `limit.π`. -/

f4758115

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2021 Bhavik Mehta. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Bhavik Mehta
-
-! This file was ported from Lean 3 source module category_theory.limits.shapes.strict_initial
-! leanprover-community/mathlib commit f47581155c818e6361af4e4fda60d27d020c226b
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.CategoryTheory.Limits.Shapes.Terminal
 import Mathbin.CategoryTheory.Limits.Shapes.BinaryProducts
 
+#align_import category_theory.limits.shapes.strict_initial from "leanprover-community/mathlib"@"f47581155c818e6361af4e4fda60d27d020c226b"
+
 /-!
 # Strict initial objects
 
@@ -251,7 +248,7 @@ theorem IsTerminal.subsingleton_to (hI : IsTerminal I) {A : C} : Subsingleton (I
 
 variable {J : Type v} [SmallCategory J]
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (j «expr ≠ » i) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (j «expr ≠ » i) -/
 #print CategoryTheory.Limits.limit_π_isIso_of_is_strict_terminal /-
 /-- If all but one object in a diagram is strict terminal, the the limit is isomorphic to the
 said object via `limit.π`. -/

f4758115

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -252,6 +252,7 @@ theorem IsTerminal.subsingleton_to (hI : IsTerminal I) {A : C} : Subsingleton (I
 variable {J : Type v} [SmallCategory J]
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (j «expr ≠ » i) -/
+#print CategoryTheory.Limits.limit_π_isIso_of_is_strict_terminal /-
 /-- If all but one object in a diagram is strict terminal, the the limit is isomorphic to the
 said object via `limit.π`. -/
 theorem limit_π_isIso_of_is_strict_terminal (F : J ⥤ C) [HasLimit F] (i : J)
@@ -276,6 +277,7 @@ theorem limit_π_isIso_of_is_strict_terminal (F : J ⥤ C) [HasLimit F] (i : J)
     · apply (H _ h).hom_ext
   · rw [limit.lift_π]; simpa
 #align category_theory.limits.limit_π_is_iso_of_is_strict_terminal CategoryTheory.Limits.limit_π_isIso_of_is_strict_terminal
+-/
 
 variable [HasTerminal C]

f4758115

bump to nightly-2023-06-08-23

mathlib commit https://github.com/leanprover-community/mathlib/commit/31c24aa72e7b3e5ed97a8412470e904f82b81004

d3cfe2e3

Diff

@@ -251,7 +251,7 @@ theorem IsTerminal.subsingleton_to (hI : IsTerminal I) {A : C} : Subsingleton (I
 
 variable {J : Type v} [SmallCategory J]
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (j «expr ≠ » i) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (j «expr ≠ » i) -/
 /-- If all but one object in a diagram is strict terminal, the the limit is isomorphic to the
 said object via `limit.π`. -/
 theorem limit_π_isIso_of_is_strict_terminal (F : J ⥤ C) [HasLimit F] (i : J)

f4758115

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -257,24 +257,24 @@ said object via `limit.π`. -/
 theorem limit_π_isIso_of_is_strict_terminal (F : J ⥤ C) [HasLimit F] (i : J)
     (H : ∀ (j) (_ : j ≠ i), IsTerminal (F.obj j)) [Subsingleton (i ⟶ i)] : IsIso (limit.π F i) := by
   classical
-    refine' ⟨⟨limit.lift _ ⟨_, ⟨_, _⟩⟩, _, _⟩⟩
-    · exact fun j => dite (j = i) (fun h => eq_to_hom (by cases h; rfl)) fun h => (H _ h).from _
-    · intro j k f
-      split_ifs
-      · cases h; cases h_1; obtain rfl : f = 𝟙 _ := Subsingleton.elim _ _; simpa
-      · cases h; erw [category.comp_id]
-        haveI : is_iso (F.map f) := (H _ h_1).isIso_from _
-        rw [← is_iso.comp_inv_eq]
-        apply (H _ h_1).hom_ext
-      · cases h_1; apply (H _ h).hom_ext
-      · apply (H _ h).hom_ext
-    · ext
-      rw [assoc, limit.lift_π]
-      dsimp only
-      split_ifs
-      · cases h; rw [id_comp, eq_to_hom_refl]; exact comp_id _
-      · apply (H _ h).hom_ext
-    · rw [limit.lift_π]; simpa
+  refine' ⟨⟨limit.lift _ ⟨_, ⟨_, _⟩⟩, _, _⟩⟩
+  · exact fun j => dite (j = i) (fun h => eq_to_hom (by cases h; rfl)) fun h => (H _ h).from _
+  · intro j k f
+    split_ifs
+    · cases h; cases h_1; obtain rfl : f = 𝟙 _ := Subsingleton.elim _ _; simpa
+    · cases h; erw [category.comp_id]
+      haveI : is_iso (F.map f) := (H _ h_1).isIso_from _
+      rw [← is_iso.comp_inv_eq]
+      apply (H _ h_1).hom_ext
+    · cases h_1; apply (H _ h).hom_ext
+    · apply (H _ h).hom_ext
+  · ext
+    rw [assoc, limit.lift_π]
+    dsimp only
+    split_ifs
+    · cases h; rw [id_comp, eq_to_hom_refl]; exact comp_id _
+    · apply (H _ h).hom_ext
+  · rw [limit.lift_π]; simpa
 #align category_theory.limits.limit_π_is_iso_of_is_strict_terminal CategoryTheory.Limits.limit_π_isIso_of_is_strict_terminal
 
 variable [HasTerminal C]

f4758115

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -251,12 +251,6 @@ theorem IsTerminal.subsingleton_to (hI : IsTerminal I) {A : C} : Subsingleton (I
 
 variable {J : Type v} [SmallCategory J]
 
-/- warning: category_theory.limits.limit_π_is_iso_of_is_strict_terminal -> CategoryTheory.Limits.limit_π_isIso_of_is_strict_terminal is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Limits.HasStrictTerminalObjects.{u1, u2} C _inst_1] {J : Type.{u1}} [_inst_3 : CategoryTheory.SmallCategory.{u1} J] (F : CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) [_inst_4 : CategoryTheory.Limits.HasLimit.{u1, u1, u1, u2} J _inst_3 C _inst_1 F] (i : J), (forall (j : J), (Ne.{succ u1} J j i) -> (CategoryTheory.Limits.IsTerminal.{u1, u2} C _inst_1 (CategoryTheory.Functor.obj.{u1, u1, u1, u2} J _inst_3 C _inst_1 F j))) -> (forall [_inst_5 : Subsingleton.{succ u1} (Quiver.Hom.{succ u1, u1} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) i i)], CategoryTheory.IsIso.{u1, u2} C _inst_1 (CategoryTheory.Limits.limit.{u1, u1, u1, u2} J _inst_3 C _inst_1 F _inst_4) (CategoryTheory.Functor.obj.{u1, u1, u1, u2} J _inst_3 C _inst_1 F i) (CategoryTheory.Limits.limit.π.{u1, u1, u1, u2} J _inst_3 C _inst_1 F _inst_4 i))
-but is expected to have type
-  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Limits.HasStrictTerminalObjects.{u1, u2} C _inst_1] {J : Type.{u1}} [_inst_3 : CategoryTheory.SmallCategory.{u1} J] (F : CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) [_inst_4 : CategoryTheory.Limits.HasLimit.{u1, u1, u1, u2} J _inst_3 C _inst_1 F] (i : J), (forall (j : J), (Ne.{succ u1} J j i) -> (CategoryTheory.Limits.IsTerminal.{u1, u2} C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) j))) -> (forall [_inst_5 : Subsingleton.{succ u1} (Quiver.Hom.{succ u1, u1} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) i i)], CategoryTheory.IsIso.{u1, u2} C _inst_1 (CategoryTheory.Limits.limit.{u1, u1, u1, u2} J _inst_3 C _inst_1 F _inst_4) (Prefunctor.obj.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) i) (CategoryTheory.Limits.limit.π.{u1, u1, u1, u2} J _inst_3 C _inst_1 F _inst_4 i))
-Case conversion may be inaccurate. Consider using '#align category_theory.limits.limit_π_is_iso_of_is_strict_terminal CategoryTheory.Limits.limit_π_isIso_of_is_strict_terminalₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (j «expr ≠ » i) -/
 /-- If all but one object in a diagram is strict terminal, the the limit is isomorphic to the
 said object via `limit.π`. -/

f4758115

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -264,39 +264,23 @@ theorem limit_π_isIso_of_is_strict_terminal (F : J ⥤ C) [HasLimit F] (i : J)
     (H : ∀ (j) (_ : j ≠ i), IsTerminal (F.obj j)) [Subsingleton (i ⟶ i)] : IsIso (limit.π F i) := by
   classical
     refine' ⟨⟨limit.lift _ ⟨_, ⟨_, _⟩⟩, _, _⟩⟩
-    ·
-      exact fun j =>
-        dite (j = i)
-          (fun h =>
-            eq_to_hom
-              (by
-                cases h
-                rfl))
-          fun h => (H _ h).from _
+    · exact fun j => dite (j = i) (fun h => eq_to_hom (by cases h; rfl)) fun h => (H _ h).from _
     · intro j k f
       split_ifs
-      · cases h
-        cases h_1
-        obtain rfl : f = 𝟙 _ := Subsingleton.elim _ _
-        simpa
-      · cases h
-        erw [category.comp_id]
+      · cases h; cases h_1; obtain rfl : f = 𝟙 _ := Subsingleton.elim _ _; simpa
+      · cases h; erw [category.comp_id]
         haveI : is_iso (F.map f) := (H _ h_1).isIso_from _
         rw [← is_iso.comp_inv_eq]
         apply (H _ h_1).hom_ext
-      · cases h_1
-        apply (H _ h).hom_ext
+      · cases h_1; apply (H _ h).hom_ext
       · apply (H _ h).hom_ext
     · ext
       rw [assoc, limit.lift_π]
       dsimp only
       split_ifs
-      · cases h
-        rw [id_comp, eq_to_hom_refl]
-        exact comp_id _
+      · cases h; rw [id_comp, eq_to_hom_refl]; exact comp_id _
       · apply (H _ h).hom_ext
-    · rw [limit.lift_π]
-      simpa
+    · rw [limit.lift_π]; simpa
 #align category_theory.limits.limit_π_is_iso_of_is_strict_terminal CategoryTheory.Limits.limit_π_isIso_of_is_strict_terminal
 
 variable [HasTerminal C]

f4758115

bump to nightly-2023-03-09-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/21e3562c5e12d846c7def5eff8cdbc520d7d4936

061741a1

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Bhavik Mehta
 
 ! This file was ported from Lean 3 source module category_theory.limits.shapes.strict_initial
-! leanprover-community/mathlib commit 70fd9563a21e7b963887c9360bd29b2393e6225a
+! leanprover-community/mathlib commit f47581155c818e6361af4e4fda60d27d020c226b
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.CategoryTheory.Limits.Shapes.BinaryProducts
 /-!
 # Strict initial objects
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file sets up the basic theory of strict initial objects: initial objects where every morphism
 to it is an isomorphism. This generalises a property of the empty set in the category of sets:
 namely that the only function to the empty set is from itself.

70fd9563

bump to nightly-2023-03-07-20

mathlib commit https://github.com/leanprover-community/mathlib/commit/3b267e70a936eebb21ab546f49a8df34dd300b25

c0bba963

Diff

@@ -54,6 +54,7 @@ variable (C : Type u) [Category.{v} C]
 
 section StrictInitial
 
+#print CategoryTheory.Limits.HasStrictInitialObjects /-
 /-- We say `C` has strict initial objects if every initial object is strict, ie given any morphism
 `f : A ⟶ I` where `I` is initial, then `f` is an isomorphism.
 
@@ -63,6 +64,7 @@ initial objects exist.
 class HasStrictInitialObjects : Prop where
   out : ∀ {I A : C} (f : A ⟶ I), IsInitial I → IsIso f
 #align category_theory.limits.has_strict_initial_objects CategoryTheory.Limits.HasStrictInitialObjects
+-/
 
 variable {C}
 
@@ -70,65 +72,88 @@ section
 
 variable [HasStrictInitialObjects C] {I : C}
 
+#print CategoryTheory.Limits.IsInitial.isIso_to /-
 theorem IsInitial.isIso_to (hI : IsInitial I) {A : C} (f : A ⟶ I) : IsIso f :=
   HasStrictInitialObjects.out f hI
 #align category_theory.limits.is_initial.is_iso_to CategoryTheory.Limits.IsInitial.isIso_to
+-/
 
+#print CategoryTheory.Limits.IsInitial.strict_hom_ext /-
 theorem IsInitial.strict_hom_ext (hI : IsInitial I) {A : C} (f g : A ⟶ I) : f = g :=
   by
   haveI := hI.is_iso_to f
   haveI := hI.is_iso_to g
   exact eq_of_inv_eq_inv (hI.hom_ext (inv f) (inv g))
 #align category_theory.limits.is_initial.strict_hom_ext CategoryTheory.Limits.IsInitial.strict_hom_ext
+-/
 
+#print CategoryTheory.Limits.IsInitial.subsingleton_to /-
 theorem IsInitial.subsingleton_to (hI : IsInitial I) {A : C} : Subsingleton (A ⟶ I) :=
   ⟨hI.strict_hom_ext⟩
 #align category_theory.limits.is_initial.subsingleton_to CategoryTheory.Limits.IsInitial.subsingleton_to
+-/
 
+#print CategoryTheory.Limits.initial_mono_of_strict_initial_objects /-
 instance (priority := 100) initial_mono_of_strict_initial_objects : InitialMonoClass C
     where isInitial_mono_from I A hI :=
     { right_cancellation := fun B g h i => hI.strict_hom_ext _ _ }
 #align category_theory.limits.initial_mono_of_strict_initial_objects CategoryTheory.Limits.initial_mono_of_strict_initial_objects
+-/
 
+#print CategoryTheory.Limits.mulIsInitial /-
 /-- If `I` is initial, then `X ⨯ I` is isomorphic to it. -/
 @[simps Hom]
 noncomputable def mulIsInitial (X : C) [HasBinaryProduct X I] (hI : IsInitial I) : X ⨯ I ≅ I :=
   @asIso _ prod.snd (hI.isIso_to _)
 #align category_theory.limits.mul_is_initial CategoryTheory.Limits.mulIsInitial
+-/
 
+#print CategoryTheory.Limits.mulIsInitial_inv /-
 @[simp]
 theorem mulIsInitial_inv (X : C) [HasBinaryProduct X I] (hI : IsInitial I) :
     (mulIsInitial X hI).inv = hI.to _ :=
   hI.hom_ext _ _
 #align category_theory.limits.mul_is_initial_inv CategoryTheory.Limits.mulIsInitial_inv
+-/
 
+#print CategoryTheory.Limits.isInitialMul /-
 /-- If `I` is initial, then `I ⨯ X` is isomorphic to it. -/
 @[simps Hom]
 noncomputable def isInitialMul (X : C) [HasBinaryProduct I X] (hI : IsInitial I) : I ⨯ X ≅ I :=
   @asIso _ prod.fst (hI.isIso_to _)
 #align category_theory.limits.is_initial_mul CategoryTheory.Limits.isInitialMul
+-/
 
+#print CategoryTheory.Limits.isInitialMul_inv /-
 @[simp]
 theorem isInitialMul_inv (X : C) [HasBinaryProduct I X] (hI : IsInitial I) :
     (isInitialMul X hI).inv = hI.to _ :=
   hI.hom_ext _ _
 #align category_theory.limits.is_initial_mul_inv CategoryTheory.Limits.isInitialMul_inv
+-/
 
 variable [HasInitial C]
 
+#print CategoryTheory.Limits.initial_isIso_to /-
 instance initial_isIso_to {A : C} (f : A ⟶ ⊥_ C) : IsIso f :=
   initialIsInitial.isIso_to _
 #align category_theory.limits.initial_is_iso_to CategoryTheory.Limits.initial_isIso_to
+-/
 
+#print CategoryTheory.Limits.initial.hom_ext /-
 @[ext]
 theorem initial.hom_ext {A : C} (f g : A ⟶ ⊥_ C) : f = g :=
   initialIsInitial.strict_hom_ext _ _
 #align category_theory.limits.initial.hom_ext CategoryTheory.Limits.initial.hom_ext
+-/
 
+#print CategoryTheory.Limits.initial.subsingleton_to /-
 theorem initial.subsingleton_to {A : C} : Subsingleton (A ⟶ ⊥_ C) :=
   initialIsInitial.subsingleton_to
 #align category_theory.limits.initial.subsingleton_to CategoryTheory.Limits.initial.subsingleton_to
+-/
 
+#print CategoryTheory.Limits.mulInitial /-
 /-- The product of `X` with an initial object in a category with strict initial objects is itself
 initial.
 This is the generalisation of the fact that `X × empty ≃ empty` for types (or `n * 0 = 0`).
@@ -137,12 +162,16 @@ This is the generalisation of the fact that `X × empty ≃ empty` for types (or
 noncomputable def mulInitial (X : C) [HasBinaryProduct X (⊥_ C)] : X ⨯ ⊥_ C ≅ ⊥_ C :=
   mulIsInitial _ initialIsInitial
 #align category_theory.limits.mul_initial CategoryTheory.Limits.mulInitial
+-/
 
+#print CategoryTheory.Limits.mulInitial_inv /-
 @[simp]
 theorem mulInitial_inv (X : C) [HasBinaryProduct X (⊥_ C)] : (mulInitial X).inv = initial.to _ :=
   Subsingleton.elim _ _
 #align category_theory.limits.mul_initial_inv CategoryTheory.Limits.mulInitial_inv
+-/
 
+#print CategoryTheory.Limits.initialMul /-
 /-- The product of `X` with an initial object in a category with strict initial objects is itself
 initial.
 This is the generalisation of the fact that `empty × X ≃ empty` for types (or `0 * n = 0`).
@@ -151,14 +180,18 @@ This is the generalisation of the fact that `empty × X ≃ empty` for types (or
 noncomputable def initialMul (X : C) [HasBinaryProduct (⊥_ C) X] : (⊥_ C) ⨯ X ≅ ⊥_ C :=
   isInitialMul _ initialIsInitial
 #align category_theory.limits.initial_mul CategoryTheory.Limits.initialMul
+-/
 
+#print CategoryTheory.Limits.initialMul_inv /-
 @[simp]
 theorem initialMul_inv (X : C) [HasBinaryProduct (⊥_ C) X] : (initialMul X).inv = initial.to _ :=
   Subsingleton.elim _ _
 #align category_theory.limits.initial_mul_inv CategoryTheory.Limits.initialMul_inv
+-/
 
 end
 
+#print CategoryTheory.Limits.hasStrictInitialObjects_of_initial_is_strict /-
 /-- If `C` has an initial object such that every morphism *to* it is an isomorphism, then `C`
 has strict initial objects. -/
 theorem hasStrictInitialObjects_of_initial_is_strict [HasInitial C]
@@ -168,11 +201,13 @@ theorem hasStrictInitialObjects_of_initial_is_strict [HasInitial C]
       haveI := h A (f ≫ hI.to _)
       ⟨⟨hI.to _ ≫ inv (f ≫ hI.to (⊥_ C)), by rw [← assoc, is_iso.hom_inv_id], hI.hom_ext _ _⟩⟩ }
 #align category_theory.limits.has_strict_initial_objects_of_initial_is_strict CategoryTheory.Limits.hasStrictInitialObjects_of_initial_is_strict
+-/
 
 end StrictInitial
 
 section StrictTerminal
 
+#print CategoryTheory.Limits.HasStrictTerminalObjects /-
 /-- We say `C` has strict terminal objects if every terminal object is strict, ie given any morphism
 `f : I ⟶ A` where `I` is terminal, then `f` is an isomorphism.
 
@@ -182,6 +217,7 @@ terminal objects exist.
 class HasStrictTerminalObjects : Prop where
   out : ∀ {I A : C} (f : I ⟶ A), IsTerminal I → IsIso f
 #align category_theory.limits.has_strict_terminal_objects CategoryTheory.Limits.HasStrictTerminalObjects
+-/
 
 variable {C}
 
@@ -189,23 +225,35 @@ section
 
 variable [HasStrictTerminalObjects C] {I : C}
 
+#print CategoryTheory.Limits.IsTerminal.isIso_from /-
 theorem IsTerminal.isIso_from (hI : IsTerminal I) {A : C} (f : I ⟶ A) : IsIso f :=
   HasStrictTerminalObjects.out f hI
 #align category_theory.limits.is_terminal.is_iso_from CategoryTheory.Limits.IsTerminal.isIso_from
+-/
 
+#print CategoryTheory.Limits.IsTerminal.strict_hom_ext /-
 theorem IsTerminal.strict_hom_ext (hI : IsTerminal I) {A : C} (f g : I ⟶ A) : f = g :=
   by
   haveI := hI.is_iso_from f
   haveI := hI.is_iso_from g
   exact eq_of_inv_eq_inv (hI.hom_ext (inv f) (inv g))
 #align category_theory.limits.is_terminal.strict_hom_ext CategoryTheory.Limits.IsTerminal.strict_hom_ext
+-/
 
+#print CategoryTheory.Limits.IsTerminal.subsingleton_to /-
 theorem IsTerminal.subsingleton_to (hI : IsTerminal I) {A : C} : Subsingleton (I ⟶ A) :=
   ⟨hI.strict_hom_ext⟩
 #align category_theory.limits.is_terminal.subsingleton_to CategoryTheory.Limits.IsTerminal.subsingleton_to
+-/
 
 variable {J : Type v} [SmallCategory J]
 
+/- warning: category_theory.limits.limit_π_is_iso_of_is_strict_terminal -> CategoryTheory.Limits.limit_π_isIso_of_is_strict_terminal is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Limits.HasStrictTerminalObjects.{u1, u2} C _inst_1] {J : Type.{u1}} [_inst_3 : CategoryTheory.SmallCategory.{u1} J] (F : CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) [_inst_4 : CategoryTheory.Limits.HasLimit.{u1, u1, u1, u2} J _inst_3 C _inst_1 F] (i : J), (forall (j : J), (Ne.{succ u1} J j i) -> (CategoryTheory.Limits.IsTerminal.{u1, u2} C _inst_1 (CategoryTheory.Functor.obj.{u1, u1, u1, u2} J _inst_3 C _inst_1 F j))) -> (forall [_inst_5 : Subsingleton.{succ u1} (Quiver.Hom.{succ u1, u1} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) i i)], CategoryTheory.IsIso.{u1, u2} C _inst_1 (CategoryTheory.Limits.limit.{u1, u1, u1, u2} J _inst_3 C _inst_1 F _inst_4) (CategoryTheory.Functor.obj.{u1, u1, u1, u2} J _inst_3 C _inst_1 F i) (CategoryTheory.Limits.limit.π.{u1, u1, u1, u2} J _inst_3 C _inst_1 F _inst_4 i))
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Limits.HasStrictTerminalObjects.{u1, u2} C _inst_1] {J : Type.{u1}} [_inst_3 : CategoryTheory.SmallCategory.{u1} J] (F : CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) [_inst_4 : CategoryTheory.Limits.HasLimit.{u1, u1, u1, u2} J _inst_3 C _inst_1 F] (i : J), (forall (j : J), (Ne.{succ u1} J j i) -> (CategoryTheory.Limits.IsTerminal.{u1, u2} C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) j))) -> (forall [_inst_5 : Subsingleton.{succ u1} (Quiver.Hom.{succ u1, u1} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) i i)], CategoryTheory.IsIso.{u1, u2} C _inst_1 (CategoryTheory.Limits.limit.{u1, u1, u1, u2} J _inst_3 C _inst_1 F _inst_4) (Prefunctor.obj.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) i) (CategoryTheory.Limits.limit.π.{u1, u1, u1, u2} J _inst_3 C _inst_1 F _inst_4 i))
+Case conversion may be inaccurate. Consider using '#align category_theory.limits.limit_π_is_iso_of_is_strict_terminal CategoryTheory.Limits.limit_π_isIso_of_is_strict_terminalₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (j «expr ≠ » i) -/
 /-- If all but one object in a diagram is strict terminal, the the limit is isomorphic to the
 said object via `limit.π`. -/
@@ -250,21 +298,28 @@ theorem limit_π_isIso_of_is_strict_terminal (F : J ⥤ C) [HasLimit F] (i : J)
 
 variable [HasTerminal C]
 
+#print CategoryTheory.Limits.terminal_isIso_from /-
 instance terminal_isIso_from {A : C} (f : ⊤_ C ⟶ A) : IsIso f :=
   terminalIsTerminal.isIso_from _
 #align category_theory.limits.terminal_is_iso_from CategoryTheory.Limits.terminal_isIso_from
+-/
 
+#print CategoryTheory.Limits.terminal.hom_ext /-
 @[ext]
 theorem terminal.hom_ext {A : C} (f g : ⊤_ C ⟶ A) : f = g :=
   terminalIsTerminal.strict_hom_ext _ _
 #align category_theory.limits.terminal.hom_ext CategoryTheory.Limits.terminal.hom_ext
+-/
 
+#print CategoryTheory.Limits.terminal.subsingleton_to /-
 theorem terminal.subsingleton_to {A : C} : Subsingleton (⊤_ C ⟶ A) :=
   terminalIsTerminal.subsingleton_to
 #align category_theory.limits.terminal.subsingleton_to CategoryTheory.Limits.terminal.subsingleton_to
+-/
 
 end
 
+#print CategoryTheory.Limits.hasStrictTerminalObjects_of_terminal_is_strict /-
 /-- If `C` has an object such that every morphism *from* it is an isomorphism, then `C`
 has strict terminal objects. -/
 theorem hasStrictTerminalObjects_of_terminal_is_strict (I : C) (h : ∀ (A) (f : I ⟶ A), IsIso f) :
@@ -274,6 +329,7 @@ theorem hasStrictTerminalObjects_of_terminal_is_strict (I : C) (h : ∀ (A) (f :
       haveI := h A (hI'.from _ ≫ f)
       ⟨⟨inv (hI'.from I ≫ f) ≫ hI'.from I, hI'.hom_ext _ _, by rw [assoc, is_iso.inv_hom_id]⟩⟩ }
 #align category_theory.limits.has_strict_terminal_objects_of_terminal_is_strict CategoryTheory.Limits.hasStrictTerminalObjects_of_terminal_is_strict
+-/
 
 end StrictTerminal

70fd9563

bump to nightly-2023-03-01-20

mathlib commit https://github.com/leanprover-community/mathlib/commit/4c586d291f189eecb9d00581aeb3dd998ac34442

20cadee0

Diff

@@ -206,7 +206,7 @@ theorem IsTerminal.subsingleton_to (hI : IsTerminal I) {A : C} : Subsingleton (I
 
 variable {J : Type v} [SmallCategory J]
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (j «expr ≠ » i) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (j «expr ≠ » i) -/
 /-- If all but one object in a diagram is strict terminal, the the limit is isomorphic to the
 said object via `limit.π`. -/
 theorem limit_π_isIso_of_is_strict_terminal (F : J ⥤ C) [HasLimit F] (i : J)

70fd9563

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

70fd9563

chore: banish Type _ and Sort _ (#6499)

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

This has nice performance benefits.

32de3f67

Diff

@@ -30,7 +30,7 @@ The dual notion (strict terminal objects) occurs much less frequently in practic
 
 ## TODO
 
-* Construct examples of this: `Type _`, `TopCat`, `Groupoid`, simplicial types, posets.
+* Construct examples of this: `Type*`, `TopCat`, `Groupoid`, simplicial types, posets.
 * Construct the bottom element of the subobject lattice given strict initials.
 * Show cartesian closed categories have strict initials

70fd9563

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

depends on: #5966

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

89aa3a3b

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2021 Bhavik Mehta. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Bhavik Mehta
-
-! This file was ported from Lean 3 source module category_theory.limits.shapes.strict_initial
-! leanprover-community/mathlib commit 70fd9563a21e7b963887c9360bd29b2393e6225a
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.CategoryTheory.Limits.Shapes.Terminal
 import Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts
 
+#align_import category_theory.limits.shapes.strict_initial from "leanprover-community/mathlib"@"70fd9563a21e7b963887c9360bd29b2393e6225a"
+
 /-!
 # Strict initial objects

70fd9563

chore: fix many typos (#4983)

These are all doc fixes

54b72114

Diff

@@ -204,7 +204,7 @@ theorem IsTerminal.subsingleton_to (hI : IsTerminal I) {A : C} : Subsingleton (I
 
 variable {J : Type v} [SmallCategory J]
 
-/-- If all but one object in a diagram is strict terminal, the the limit is isomorphic to the
+/-- If all but one object in a diagram is strict terminal, then the limit is isomorphic to the
 said object via `limit.π`. -/
 theorem limit_π_isIso_of_is_strict_terminal (F : J ⥤ C) [HasLimit F] (i : J)
     (H : ∀ (j) (_ : j ≠ i), IsTerminal (F.obj j)) [Subsingleton (i ⟶ i)] : IsIso (limit.π F i) := by

70fd9563

chore: fix upper/lowercase in comments (#4360)

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

27d257fc

Diff

@@ -33,7 +33,7 @@ The dual notion (strict terminal objects) occurs much less frequently in practic
 
 ## TODO
 
-* Construct examples of this: `Type*`, `Top`, `Groupoid`, simplicial types, posets.
+* Construct examples of this: `Type _`, `TopCat`, `Groupoid`, simplicial types, posets.
 * Construct the bottom element of the subobject lattice given strict initials.
 * Show cartesian closed categories have strict initials
 
@@ -131,7 +131,7 @@ theorem initial.subsingleton_to {A : C} : Subsingleton (A ⟶ ⊥_ C) :=
 
 /-- The product of `X` with an initial object in a category with strict initial objects is itself
 initial.
-This is the generalisation of the fact that `X × empty ≃ empty` for types (or `n * 0 = 0`).
+This is the generalisation of the fact that `X × Empty ≃ Empty` for types (or `n * 0 = 0`).
 -/
 @[simps! hom]
 noncomputable def mulInitial (X : C) [HasBinaryProduct X (⊥_ C)] : X ⨯ ⊥_ C ≅ ⊥_ C :=
@@ -145,7 +145,7 @@ theorem mulInitial_inv (X : C) [HasBinaryProduct X (⊥_ C)] : (mulInitial X).in
 
 /-- The product of `X` with an initial object in a category with strict initial objects is itself
 initial.
-This is the generalisation of the fact that `empty × X ≃ empty` for types (or `0 * n = 0`).
+This is the generalisation of the fact that `Empty × X ≃ Empty` for types (or `0 * n = 0`).
 -/
 @[simps! hom]
 noncomputable def initialMul (X : C) [HasBinaryProduct (⊥_ C) X] : (⊥_ C) ⨯ X ≅ ⊥_ C :=

70fd9563

chore: tidy various files (#3124)

55209140

Diff

@@ -27,7 +27,7 @@ If the binary product of `X` with a strict initial object exists, it is also ini
 
 To show a category `C` with an initial object has strict initial objects, the most convenient way
 is to show any morphism to the (chosen) initial object is an isomorphism and use
-`has_strict_initial_objects_of_initial_is_strict`.
+`hasStrictInitialObjects_of_initial_is_strict`.
 
 The dual notion (strict terminal objects) occurs much less frequently in practice so is ignored.
 
@@ -84,16 +84,15 @@ theorem IsInitial.subsingleton_to (hI : IsInitial I) {A : C} : Subsingleton (A 
   ⟨hI.strict_hom_ext⟩
 #align category_theory.limits.is_initial.subsingleton_to CategoryTheory.Limits.IsInitial.subsingleton_to
 
-instance (priority := 100) initial_mono_of_strict_initial_objects : InitialMonoClass C
-    where isInitial_mono_from := fun _ hI =>
-    { right_cancellation := fun _ _ _ => hI.strict_hom_ext _ _ }
+instance (priority := 100) initial_mono_of_strict_initial_objects : InitialMonoClass C where
+  isInitial_mono_from := fun _ hI => { right_cancellation := fun _ _ _ => hI.strict_hom_ext _ _ }
 #align category_theory.limits.initial_mono_of_strict_initial_objects CategoryTheory.Limits.initial_mono_of_strict_initial_objects
 
 /-- If `I` is initial, then `X ⨯ I` is isomorphic to it. -/
 @[simps! hom]
 noncomputable def mulIsInitial (X : C) [HasBinaryProduct X I] (hI : IsInitial I) : X ⨯ I ≅ I := by
-   have := hI.isIso_to (prod.snd : X ⨯ I ⟶ I)
-   exact asIso prod.snd
+  have := hI.isIso_to (prod.snd : X ⨯ I ⟶ I)
+  exact asIso prod.snd
 #align category_theory.limits.mul_is_initial CategoryTheory.Limits.mulIsInitial
 
 @[simp]
@@ -164,7 +163,7 @@ end
 has strict initial objects. -/
 theorem hasStrictInitialObjects_of_initial_is_strict [HasInitial C]
     (h : ∀ (A) (f : A ⟶ ⊥_ C), IsIso f) : HasStrictInitialObjects C :=
-  { out := @fun I A f hI =>
+  { out := fun {I A} f hI =>
       haveI := h A (f ≫ hI.to _)
       ⟨⟨hI.to _ ≫ inv (f ≫ hI.to (⊥_ C)), by rw [← assoc, IsIso.hom_inv_id], hI.hom_ext _ _⟩⟩ }
 #align category_theory.limits.has_strict_initial_objects_of_initial_is_strict CategoryTheory.Limits.hasStrictInitialObjects_of_initial_is_strict
@@ -211,14 +210,9 @@ theorem limit_π_isIso_of_is_strict_terminal (F : J ⥤ C) [HasLimit F] (i : J)
     (H : ∀ (j) (_ : j ≠ i), IsTerminal (F.obj j)) [Subsingleton (i ⟶ i)] : IsIso (limit.π F i) := by
   classical
     refine' ⟨⟨limit.lift _ ⟨_, ⟨_, _⟩⟩, _, _⟩⟩
-    ·
-      exact fun j =>
+    · exact fun j =>
         dite (j = i)
-          (fun h =>
-            eqToHom
-              (by
-                cases h
-                rfl))
+          (fun h => eqToHom (by cases h; rfl))
           fun h => (H _ h).from _
     · intro j k f
       split_ifs with h h_1 h_1
@@ -267,7 +261,7 @@ end
 has strict terminal objects. -/
 theorem hasStrictTerminalObjects_of_terminal_is_strict (I : C) (h : ∀ (A) (f : I ⟶ A), IsIso f) :
     HasStrictTerminalObjects C :=
-  { out := @fun I' A f hI' =>
+  { out := fun {I' A} f hI' =>
       haveI := h A (hI'.from _ ≫ f)
       ⟨⟨inv (hI'.from I ≫ f) ≫ hI'.from I, hI'.hom_ext _ _, by rw [assoc, IsIso.inv_hom_id]⟩⟩ }
 #align category_theory.limits.has_strict_terminal_objects_of_terminal_is_strict CategoryTheory.Limits.hasStrictTerminalObjects_of_terminal_is_strict

70fd9563

feat: port CategoryTheory.Limits.Shapes.StrictInitial (#2695)

Co-authored-by: Moritz Firsching <firsching@google.com> Co-authored-by: ChrisHughes24 <chrishughes24@gmail.com>

11a27e2c

`category_theory.limits.shapes.strict_initial` ⟷ `Mathlib.CategoryTheory.Limits.Shapes.StrictInitial`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 108

category_theory.limits.shapes.strict_initial ⟷ Mathlib.CategoryTheory.Limits.Shapes.StrictInitial

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 108

`category_theory.limits.shapes.strict_initial` ⟷ `Mathlib.CategoryTheory.Limits.Shapes.StrictInitial`