category_theory.limits.shapes.disjoint_coproduct
⟷
Mathlib.CategoryTheory.Limits.Shapes.DisjointCoproduct
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.
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mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -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.BinaryProducts
-import Mathbin.CategoryTheory.Limits.Shapes.Pullbacks
+import CategoryTheory.Limits.Shapes.BinaryProducts
+import CategoryTheory.Limits.Shapes.Pullbacks
#align_import category_theory.limits.shapes.disjoint_coproduct from "leanprover-community/mathlib"@"f47581155c818e6361af4e4fda60d27d020c226b"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -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.disjoint_coproduct
-! 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.BinaryProducts
import Mathbin.CategoryTheory.Limits.Shapes.Pullbacks
+#align_import category_theory.limits.shapes.disjoint_coproduct from "leanprover-community/mathlib"@"f47581155c818e6361af4e4fda60d27d020c226b"
+
/-!
# Disjoint coproducts
mathlib commit https://github.com/leanprover-community/mathlib/commit/09079525fd01b3dda35e96adaa08d2f943e1648c
@@ -135,7 +135,7 @@ class CoproductsDisjoint (C : Type u) [Category.{v} C] where
#align category_theory.limits.coproducts_disjoint CategoryTheory.Limits.CoproductsDisjoint
-/
-attribute [instance] coproducts_disjoint.coproduct_disjoint
+attribute [instance 999] coproducts_disjoint.coproduct_disjoint
#print CategoryTheory.Limits.initialMonoClass_of_disjoint_coproducts /-
/-- If `C` has disjoint coproducts, any morphism out of initial is mono. Note it isn't true in
mathlib commit https://github.com/leanprover-community/mathlib/commit/21e3562c5e12d846c7def5eff8cdbc520d7d4936
@@ -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.disjoint_coproduct
-! leanprover-community/mathlib commit c9c9fa15fec7ca18e9ec97306fb8764bfe988a7e
+! 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.Pullbacks
/-!
# Disjoint coproducts
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
Defines disjoint coproducts: coproducts where the intersection is initial and the coprojections
are monic.
Shows that a category with disjoint coproducts is `initial_mono_class`.
mathlib commit https://github.com/leanprover-community/mathlib/commit/3b267e70a936eebb21ab546f49a8df34dd300b25
@@ -38,6 +38,7 @@ open Category
variable {C : Type u} [Category.{v} C]
+#print CategoryTheory.Limits.CoproductDisjoint /-
/-- Given any pullback diagram of the form
Z ⟶ X₁
@@ -55,7 +56,9 @@ class CoproductDisjoint (X₁ X₂ : C) where
mono_inl : ∀ (X) (X₁ : X₁ ⟶ X) (X₂ : X₂ ⟶ X) (cX : IsColimit (BinaryCofan.mk X₁ X₂)), Mono X₁
mono_inr : ∀ (X) (X₁ : X₁ ⟶ X) (X₂ : X₂ ⟶ X) (cX : IsColimit (BinaryCofan.mk X₁ X₂)), Mono X₂
#align category_theory.limits.coproduct_disjoint CategoryTheory.Limits.CoproductDisjoint
+-/
+#print CategoryTheory.Limits.isInitialOfIsPullbackOfIsCoproduct /-
/-- If the coproduct of `X₁` and `X₂` is disjoint, then given any pullback square
Z ⟶ X₁
@@ -69,7 +72,9 @@ def isInitialOfIsPullbackOfIsCoproduct {Z X₁ X₂ X : C} [CoproductDisjoint X
{comm : f ≫ pX₁ = g ≫ pX₂} (cZ : IsLimit (PullbackCone.mk _ _ comm)) : IsInitial Z :=
CoproductDisjoint.isInitialOfIsPullbackOfIsCoproduct cX cZ
#align category_theory.limits.is_initial_of_is_pullback_of_is_coproduct CategoryTheory.Limits.isInitialOfIsPullbackOfIsCoproduct
+-/
+#print CategoryTheory.Limits.isInitialOfIsPullbackOfCoproduct /-
/-- If the coproduct of `X₁` and `X₂` is disjoint, then given any pullback square
Z ⟶ X₁
@@ -84,7 +89,9 @@ noncomputable def isInitialOfIsPullbackOfCoproduct {Z X₁ X₂ : C} [HasBinaryC
(cZ : IsLimit (PullbackCone.mk _ _ comm)) : IsInitial Z :=
CoproductDisjoint.isInitialOfIsPullbackOfIsCoproduct (coprodIsCoprod _ _) cZ
#align category_theory.limits.is_initial_of_is_pullback_of_coproduct CategoryTheory.Limits.isInitialOfIsPullbackOfCoproduct
+-/
+#print CategoryTheory.Limits.isInitialOfPullbackOfIsCoproduct /-
/-- If the coproduct of `X₁` and `X₂` is disjoint, then provided `X₁ ⟶ X ← X₂` is a coproduct the
pullback is an initial object:
@@ -97,7 +104,9 @@ noncomputable def isInitialOfPullbackOfIsCoproduct {X X₁ X₂ : C} [CoproductD
IsInitial (pullback pX₁ pX₂) :=
CoproductDisjoint.isInitialOfIsPullbackOfIsCoproduct cX (pullbackIsPullback _ _)
#align category_theory.limits.is_initial_of_pullback_of_is_coproduct CategoryTheory.Limits.isInitialOfPullbackOfIsCoproduct
+-/
+#print CategoryTheory.Limits.isInitialOfPullbackOfCoproduct /-
/-- If the coproduct of `X₁` and `X₂` is disjoint, the pullback of `X₁ ⟶ X₁ ⨿ X₂` and `X₂ ⟶ X₁ ⨿ X₂`
is initial.
-/
@@ -106,6 +115,7 @@ noncomputable def isInitialOfPullbackOfCoproduct {X₁ X₂ : C} [HasBinaryCopro
IsInitial (pullback (coprod.inl : X₁ ⟶ _ ⨿ X₂) coprod.inr) :=
isInitialOfIsPullbackOfCoproduct (pullbackIsPullback _ _)
#align category_theory.limits.is_initial_of_pullback_of_coproduct CategoryTheory.Limits.isInitialOfPullbackOfCoproduct
+-/
instance {X₁ X₂ : C} [HasBinaryCoproduct X₁ X₂] [CoproductDisjoint X₁ X₂] :
Mono (coprod.inl : X₁ ⟶ X₁ ⨿ X₂) :=
@@ -115,13 +125,16 @@ instance {X₁ X₂ : C} [HasBinaryCoproduct X₁ X₂] [CoproductDisjoint X₁
Mono (coprod.inr : X₂ ⟶ X₁ ⨿ X₂) :=
CoproductDisjoint.mono_inr _ _ _ (coprodIsCoprod _ _)
+#print CategoryTheory.Limits.CoproductsDisjoint /-
/-- `C` has disjoint coproducts if every coproduct is disjoint. -/
class CoproductsDisjoint (C : Type u) [Category.{v} C] where
CoproductDisjoint : ∀ X Y : C, CoproductDisjoint X Y
#align category_theory.limits.coproducts_disjoint CategoryTheory.Limits.CoproductsDisjoint
+-/
attribute [instance] coproducts_disjoint.coproduct_disjoint
+#print CategoryTheory.Limits.initialMonoClass_of_disjoint_coproducts /-
/-- If `C` has disjoint coproducts, any morphism out of initial is mono. Note it isn't true in
general that `C` has strict initial objects, for instance consider the category of types and
partial functions. -/
@@ -135,6 +148,7 @@ theorem initialMonoClass_of_disjoint_coproducts [CoproductsDisjoint C] : Initial
uniq := fun (s : BinaryCofan _ _) m w =>
(id_comp _).symm.trans (w ⟨WalkingPair.right⟩) } }
#align category_theory.limits.initial_mono_class_of_disjoint_coproducts CategoryTheory.Limits.initialMonoClass_of_disjoint_coproducts
+-/
end Limits
mathlib commit https://github.com/leanprover-community/mathlib/commit/eb0cb4511aaef0da2462207b67358a0e1fe1e2ee
@@ -130,9 +130,9 @@ theorem initialMonoClass_of_disjoint_coproducts [CoproductsDisjoint C] : Initial
isInitial_mono_from := fun I X hI =>
CoproductDisjoint.mono_inl _ _ (𝟙 X)
{ desc := fun s : BinaryCofan _ _ => s.inr
- fac' := fun s j =>
+ fac := fun s j =>
Discrete.casesOn j fun j => WalkingPair.casesOn j (hI.hom_ext _ _) (id_comp _)
- uniq' := fun (s : BinaryCofan _ _) m w =>
+ uniq := fun (s : BinaryCofan _ _) m w =>
(id_comp _).symm.trans (w ⟨WalkingPair.right⟩) } }
#align category_theory.limits.initial_mono_class_of_disjoint_coproducts CategoryTheory.Limits.initialMonoClass_of_disjoint_coproducts
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
@@ -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.disjoint_coproduct
-! leanprover-community/mathlib commit c9c9fa15fec7ca18e9ec97306fb8764bfe988a7e
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts
import Mathlib.CategoryTheory.Limits.Shapes.Pullbacks
+#align_import category_theory.limits.shapes.disjoint_coproduct from "leanprover-community/mathlib"@"c9c9fa15fec7ca18e9ec97306fb8764bfe988a7e"
+
/-!
# Disjoint coproducts
@@ -40,9 +40,9 @@ variable {C : Type u} [Category.{v} C]
/-- Given any pullback diagram of the form
-Z ⟶ X₁
+Z ⟶ X₁
↓ ↓
-X₂ ⟶ X
+X₂ ⟶ X
where `X₁ ⟶ X ← X₂` is a coproduct diagram, then `Z` is initial, and both `X₁ ⟶ X` and `X₂ ⟶ X`
are mono.
@@ -58,9 +58,9 @@ class CoproductDisjoint (X₁ X₂ : C) where
/-- If the coproduct of `X₁` and `X₂` is disjoint, then given any pullback square
-Z ⟶ X₁
+Z ⟶ X₁
↓ ↓
-X₂ ⟶ X
+X₂ ⟶ X
where `X₁ ⟶ X ← X₂` is a coproduct, then `Z` is initial.
-/
@@ -72,9 +72,9 @@ def isInitialOfIsPullbackOfIsCoproduct {Z X₁ X₂ X : C} [CoproductDisjoint X
/-- If the coproduct of `X₁` and `X₂` is disjoint, then given any pullback square
-Z ⟶ X₁
+Z ⟶ X₁
↓ ↓
-X₂ ⟶ X₁ ⨿ X₂
+X₂ ⟶ X₁ ⨿ X₂
`Z` is initial.
-/
@@ -90,7 +90,7 @@ pullback is an initial object:
X₁
↓
-X₂ ⟶ X
+X₂ ⟶ X
-/
noncomputable def isInitialOfPullbackOfIsCoproduct {X X₁ X₂ : C} [CoproductDisjoint X₁ X₂]
{pX₁ : X₁ ⟶ X} {pX₂ : X₂ ⟶ X} [HasPullback pX₁ pX₂] (cX : IsColimit (BinaryCofan.mk pX₁ pX₂)) :
See discussion at https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/mathport.20drops.20priorities.20in.20.60attribute.20.5Binstance.5D.60. mathport
has been dropping the priorities on instances when using the attribute
command.
This PR adds back all the priorities, except for local attribute
, and instances involving coercions, which I didn't want to mess with.
Co-authored-by: Scott Morrison <scott.morrison@gmail.com>
@@ -120,7 +120,7 @@ class CoproductsDisjoint (C : Type u) [Category.{v} C] where
CoproductDisjoint : ∀ X Y : C, CoproductDisjoint X Y
#align category_theory.limits.coproducts_disjoint CategoryTheory.Limits.CoproductsDisjoint
-attribute [instance] CoproductsDisjoint.CoproductDisjoint
+attribute [instance 999] CoproductsDisjoint.CoproductDisjoint
/-- If `C` has disjoint coproducts, any morphism out of initial is mono. Note it isn't true in
general that `C` has strict initial objects, for instance consider the category of types and
@@ -125,14 +125,14 @@ attribute [instance] CoproductsDisjoint.CoproductDisjoint
/-- If `C` has disjoint coproducts, any morphism out of initial is mono. Note it isn't true in
general that `C` has strict initial objects, for instance consider the category of types and
partial functions. -/
-theorem initialMonoClass_of_disjoint_coproducts [CoproductsDisjoint C] : InitialMonoClass C :=
- { isInitial_mono_from := @fun _I X hI =>
- CoproductDisjoint.mono_inl X (IsInitial.to hI X) (CategoryTheory.CategoryStruct.id X)
- { desc := fun s : BinaryCofan _ _ => s.inr
- fac := fun _s j =>
- Discrete.casesOn j fun j => WalkingPair.casesOn j (hI.hom_ext _ _) (id_comp _)
- uniq := fun (_s : BinaryCofan _ _) _m w =>
- (id_comp _).symm.trans (w ⟨WalkingPair.right⟩) } }
+theorem initialMonoClass_of_disjoint_coproducts [CoproductsDisjoint C] : InitialMonoClass C where
+ isInitial_mono_from X hI :=
+ CoproductDisjoint.mono_inl X (IsInitial.to hI X) (CategoryTheory.CategoryStruct.id X)
+ { desc := fun s : BinaryCofan _ _ => s.inr
+ fac := fun _s j =>
+ Discrete.casesOn j fun j => WalkingPair.casesOn j (hI.hom_ext _ _) (id_comp _)
+ uniq := fun (_s : BinaryCofan _ _) _m w =>
+ (id_comp _).symm.trans (w ⟨WalkingPair.right⟩) }
#align category_theory.limits.initial_mono_class_of_disjoint_coproducts CategoryTheory.Limits.initialMonoClass_of_disjoint_coproducts
end Limits
All dependencies are ported!