category_theory.limits.connected
⟷
Mathlib.CategoryTheory.Limits.Connected
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
@@ -3,11 +3,11 @@ Copyright (c) 2020 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.Equalizers
-import Mathbin.CategoryTheory.Limits.Shapes.WidePullbacks
-import Mathbin.CategoryTheory.IsConnected
-import Mathbin.CategoryTheory.Limits.Preserves.Basic
+import CategoryTheory.Limits.Shapes.BinaryProducts
+import CategoryTheory.Limits.Shapes.Equalizers
+import CategoryTheory.Limits.Shapes.WidePullbacks
+import CategoryTheory.IsConnected
+import CategoryTheory.Limits.Preserves.Basic
#align_import category_theory.limits.connected from "leanprover-community/mathlib"@"10bf4f825ad729c5653adc039dafa3622e7f93c9"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,11 +2,6 @@
Copyright (c) 2020 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.connected
-! leanprover-community/mathlib commit 10bf4f825ad729c5653adc039dafa3622e7f93c9
-! 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.Equalizers
@@ -14,6 +9,8 @@ import Mathbin.CategoryTheory.Limits.Shapes.WidePullbacks
import Mathbin.CategoryTheory.IsConnected
import Mathbin.CategoryTheory.Limits.Preserves.Basic
+#align_import category_theory.limits.connected from "leanprover-community/mathlib"@"10bf4f825ad729c5653adc039dafa3622e7f93c9"
+
/-!
# Connected limits
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -89,17 +89,22 @@ variable {J : Type v₂} [SmallCategory J]
namespace ProdPreservesConnectedLimits
+#print CategoryTheory.ProdPreservesConnectedLimits.γ₂ /-
/-- (Impl). The obvious natural transformation from (X × K -) to K. -/
@[simps]
def γ₂ {K : J ⥤ C} (X : C) : K ⋙ prod.functor.obj X ⟶ K where app Y := Limits.prod.snd
#align category_theory.prod_preserves_connected_limits.γ₂ CategoryTheory.ProdPreservesConnectedLimits.γ₂
+-/
+#print CategoryTheory.ProdPreservesConnectedLimits.γ₁ /-
/-- (Impl). The obvious natural transformation from (X × K -) to X -/
@[simps]
def γ₁ {K : J ⥤ C} (X : C) : K ⋙ prod.functor.obj X ⟶ (Functor.const J).obj X
where app Y := Limits.prod.fst
#align category_theory.prod_preserves_connected_limits.γ₁ CategoryTheory.ProdPreservesConnectedLimits.γ₁
+-/
+#print CategoryTheory.ProdPreservesConnectedLimits.forgetCone /-
/-- (Impl).
Given a cone for (X × K -), produce a cone for K using the natural transformation `γ₂` -/
@[simps]
@@ -108,11 +113,13 @@ def forgetCone {X : C} {K : J ⥤ C} (s : Cone (K ⋙ prod.functor.obj X)) : Con
pt := s.pt
π := s.π ≫ γ₂ X
#align category_theory.prod_preserves_connected_limits.forget_cone CategoryTheory.ProdPreservesConnectedLimits.forgetCone
+-/
end ProdPreservesConnectedLimits
open ProdPreservesConnectedLimits
+#print CategoryTheory.prodPreservesConnectedLimits /-
/-- The functor `(X × -)` preserves any connected limit.
Note that this functor does not preserve the two most obvious disconnected limits - that is,
`(X × -)` does not preserve products or terminal object, eg `(X ⨯ A) ⨯ (X ⨯ B)` is not isomorphic to
@@ -139,6 +146,7 @@ noncomputable def prodPreservesConnectedLimits [IsConnected J] (X : C) :
intro j
simp [← L j] } }
#align category_theory.prod_preserves_connected_limits CategoryTheory.prodPreservesConnectedLimits
+-/
end CategoryTheory
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -89,35 +89,17 @@ variable {J : Type v₂} [SmallCategory J]
namespace ProdPreservesConnectedLimits
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/-- (Impl). The obvious natural transformation from (X × K -) to K. -/
@[simps]
def γ₂ {K : J ⥤ C} (X : C) : K ⋙ prod.functor.obj X ⟶ K where app Y := Limits.prod.snd
#align category_theory.prod_preserves_connected_limits.γ₂ CategoryTheory.ProdPreservesConnectedLimits.γ₂
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/-- (Impl). The obvious natural transformation from (X × K -) to X -/
@[simps]
def γ₁ {K : J ⥤ C} (X : C) : K ⋙ prod.functor.obj X ⟶ (Functor.const J).obj X
where app Y := Limits.prod.fst
#align category_theory.prod_preserves_connected_limits.γ₁ CategoryTheory.ProdPreservesConnectedLimits.γ₁
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/-- (Impl).
Given a cone for (X × K -), produce a cone for K using the natural transformation `γ₂` -/
@[simps]
@@ -131,12 +113,6 @@ end ProdPreservesConnectedLimits
open ProdPreservesConnectedLimits
-/- warning: category_theory.prod_preserves_connected_limits -> CategoryTheory.prodPreservesConnectedLimits is a dubious translation:
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/-- The functor `(X × -)` preserves any connected limit.
Note that this functor does not preserve the two most obvious disconnected limits - that is,
`(X × -)` does not preserve products or terminal object, eg `(X ⨯ A) ⨯ (X ⨯ B)` is not isomorphic to
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce7e9d53d4bbc38065db3b595cd5bd73c323bc1d
@@ -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.connected
-! leanprover-community/mathlib commit d6814c584384ddf2825ff038e868451a7c956f31
+! leanprover-community/mathlib commit 10bf4f825ad729c5653adc039dafa3622e7f93c9
! 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.Limits.Preserves.Basic
/-!
# Connected limits
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
A connected limit is a limit whose shape is a connected category.
We give examples of connected categories, and prove that the functor given
mathlib commit https://github.com/leanprover-community/mathlib/commit/2af0836443b4cfb5feda0df0051acdb398304931
@@ -35,6 +35,7 @@ namespace CategoryTheory
section Examples
+#print CategoryTheory.widePullbackShape_connected /-
instance widePullbackShape_connected (J : Type v₁) : IsConnected (WidePullbackShape J) :=
by
apply is_connected.of_induct
@@ -43,7 +44,9 @@ instance widePullbackShape_connected (J : Type v₁) : IsConnected (WidePullback
· exact hp
· rwa [t (wide_pullback_shape.hom.term j)]
#align category_theory.wide_pullback_shape_connected CategoryTheory.widePullbackShape_connected
+-/
+#print CategoryTheory.widePushoutShape_connected /-
instance widePushoutShape_connected (J : Type v₁) : IsConnected (WidePushoutShape J) :=
by
apply is_connected.of_induct
@@ -52,11 +55,15 @@ instance widePushoutShape_connected (J : Type v₁) : IsConnected (WidePushoutSh
· exact hp
· rwa [← t (wide_pushout_shape.hom.init j)]
#align category_theory.wide_pushout_shape_connected CategoryTheory.widePushoutShape_connected
+-/
+#print CategoryTheory.parallelPairInhabited /-
instance parallelPairInhabited : Inhabited WalkingParallelPair :=
⟨WalkingParallelPair.one⟩
#align category_theory.parallel_pair_inhabited CategoryTheory.parallelPairInhabited
+-/
+#print CategoryTheory.parallel_pair_connected /-
instance parallel_pair_connected : IsConnected WalkingParallelPair :=
by
apply is_connected.of_induct
@@ -65,6 +72,7 @@ instance parallel_pair_connected : IsConnected WalkingParallelPair :=
· rwa [t walking_parallel_pair_hom.left]
· assumption
#align category_theory.parallel_pair_connected CategoryTheory.parallel_pair_connected
+-/
end Examples
@@ -78,17 +86,35 @@ variable {J : Type v₂} [SmallCategory J]
namespace ProdPreservesConnectedLimits
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+Case conversion may be inaccurate. Consider using '#align category_theory.prod_preserves_connected_limits.γ₂ CategoryTheory.ProdPreservesConnectedLimits.γ₂ₓ'. -/
/-- (Impl). The obvious natural transformation from (X × K -) to K. -/
@[simps]
def γ₂ {K : J ⥤ C} (X : C) : K ⋙ prod.functor.obj X ⟶ K where app Y := Limits.prod.snd
#align category_theory.prod_preserves_connected_limits.γ₂ CategoryTheory.ProdPreservesConnectedLimits.γ₂
+/- warning: category_theory.prod_preserves_connected_limits.γ₁ -> CategoryTheory.ProdPreservesConnectedLimits.γ₁ is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align category_theory.prod_preserves_connected_limits.γ₁ CategoryTheory.ProdPreservesConnectedLimits.γ₁ₓ'. -/
/-- (Impl). The obvious natural transformation from (X × K -) to X -/
@[simps]
def γ₁ {K : J ⥤ C} (X : C) : K ⋙ prod.functor.obj X ⟶ (Functor.const J).obj X
where app Y := Limits.prod.fst
#align category_theory.prod_preserves_connected_limits.γ₁ CategoryTheory.ProdPreservesConnectedLimits.γ₁
+/- warning: category_theory.prod_preserves_connected_limits.forget_cone -> CategoryTheory.ProdPreservesConnectedLimits.forgetCone is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align category_theory.prod_preserves_connected_limits.forget_cone CategoryTheory.ProdPreservesConnectedLimits.forgetConeₓ'. -/
/-- (Impl).
Given a cone for (X × K -), produce a cone for K using the natural transformation `γ₂` -/
@[simps]
@@ -102,6 +128,12 @@ end ProdPreservesConnectedLimits
open ProdPreservesConnectedLimits
+/- warning: category_theory.prod_preserves_connected_limits -> CategoryTheory.prodPreservesConnectedLimits is a dubious translation:
+lean 3 declaration is
+ forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Limits.HasBinaryProducts.{u1, u2} C _inst_1] {J : Type.{u1}} [_inst_3 : CategoryTheory.SmallCategory.{u1} J] [_inst_4 : CategoryTheory.IsConnected.{u1, u1} J _inst_3] (X : C), CategoryTheory.Limits.PreservesLimitsOfShape.{u1, u1, u1, u1, u2, u2} C _inst_1 C _inst_1 J _inst_3 (CategoryTheory.Functor.obj.{u1, max u2 u1, u2, max u1 u2} C _inst_1 (CategoryTheory.Functor.{u1, u1, u2, u2} C _inst_1 C _inst_1) (CategoryTheory.Functor.category.{u1, u1, u2, u2} C _inst_1 C _inst_1) (CategoryTheory.Limits.prod.functor.{u1, u2} C _inst_1 _inst_2) X)
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+Case conversion may be inaccurate. Consider using '#align category_theory.prod_preserves_connected_limits CategoryTheory.prodPreservesConnectedLimitsₓ'. -/
/-- The functor `(X × -)` preserves any connected limit.
Note that this functor does not preserve the two most obvious disconnected limits - that is,
`(X × -)` does not preserve products or terminal object, eg `(X ⨯ A) ⨯ (X ⨯ B)` is not isomorphic to
mathlib commit https://github.com/leanprover-community/mathlib/commit/9da1b3534b65d9661eb8f42443598a92bbb49211
@@ -94,7 +94,7 @@ Given a cone for (X × K -), produce a cone for K using the natural transformati
@[simps]
def forgetCone {X : C} {K : J ⥤ C} (s : Cone (K ⋙ prod.functor.obj X)) : Cone K
where
- x := s.x
+ pt := s.pt
π := s.π ≫ γ₂ X
#align category_theory.prod_preserves_connected_limits.forget_cone CategoryTheory.ProdPreservesConnectedLimits.forgetCone
mathlib commit https://github.com/leanprover-community/mathlib/commit/eb0cb4511aaef0da2462207b67358a0e1fe1e2ee
@@ -114,12 +114,12 @@ noncomputable def prodPreservesConnectedLimits [IsConnected J] (X : C) :
preserves := fun c l =>
{ lift := fun s =>
prod.lift (s.π.app (Classical.arbitrary _) ≫ Limits.prod.fst) (l.lift (forgetCone s))
- fac' := fun s j => by
+ fac := fun s j => by
apply prod.hom_ext
· erw [assoc, lim_map_π, comp_id, limit.lift_π]
exact (nat_trans_from_is_connected (s.π ≫ γ₁ X) j (Classical.arbitrary _)).symm
· simp [← l.fac (forget_cone s) j]
- uniq' := fun s m L => by
+ uniq := fun s m L => by
apply prod.hom_ext
· erw [limit.lift_π, ← L (Classical.arbitrary J), assoc, lim_map_π, comp_id]
rfl
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
@@ -34,18 +34,18 @@ section Examples
instance widePullbackShape_connected (J : Type v₁) : IsConnected (WidePullbackShape J) := by
apply IsConnected.of_induct
- introv hp t
- cases j
- · exact hp
- · rwa [t (WidePullbackShape.Hom.term _)]
+ · introv hp t
+ cases j
+ · exact hp
+ · rwa [t (WidePullbackShape.Hom.term _)]
#align category_theory.wide_pullback_shape_connected CategoryTheory.widePullbackShape_connected
instance widePushoutShape_connected (J : Type v₁) : IsConnected (WidePushoutShape J) := by
apply IsConnected.of_induct
- introv hp t
- cases j
- · exact hp
- · rwa [← t (WidePushoutShape.Hom.init _)]
+ · introv hp t
+ cases j
+ · exact hp
+ · rwa [← t (WidePushoutShape.Hom.init _)]
#align category_theory.wide_pushout_shape_connected CategoryTheory.widePushoutShape_connected
instance parallelPairInhabited : Inhabited WalkingParallelPair :=
@@ -54,10 +54,10 @@ instance parallelPairInhabited : Inhabited WalkingParallelPair :=
instance parallel_pair_connected : IsConnected WalkingParallelPair := by
apply IsConnected.of_induct
- introv _ t
- cases j
- · rwa [t WalkingParallelPairHom.left]
- · assumption
+ · introv _ t
+ cases j
+ · rwa [t WalkingParallelPairHom.left]
+ · assumption
#align category_theory.parallel_pair_connected CategoryTheory.parallel_pair_connected
end Examples
Empty lines were removed by executing the following Python script twice
import os
import re
# Loop through each file in the repository
for dir_path, dirs, files in os.walk('.'):
for filename in files:
if filename.endswith('.lean'):
file_path = os.path.join(dir_path, filename)
# Open the file and read its contents
with open(file_path, 'r') as file:
content = file.read()
# Use a regular expression to replace sequences of "variable" lines separated by empty lines
# with sequences without empty lines
modified_content = re.sub(r'(variable.*\n)\n(variable(?! .* in))', r'\1\2', content)
# Write the modified content back to the file
with open(file_path, 'w') as file:
file.write(modified_content)
@@ -63,9 +63,7 @@ instance parallel_pair_connected : IsConnected WalkingParallelPair := by
end Examples
variable {C : Type u₂} [Category.{v₂} C]
-
variable [HasBinaryProducts C]
-
variable {J : Type v₂} [SmallCategory J]
namespace ProdPreservesConnectedLimits
@@ -77,8 +77,8 @@ def γ₂ {K : J ⥤ C} (X : C) : K ⋙ prod.functor.obj X ⟶ K where app Y :=
/-- (Impl). The obvious natural transformation from (X × K -) to X -/
@[simps]
-def γ₁ {K : J ⥤ C} (X : C) : K ⋙ prod.functor.obj X ⟶ (Functor.const J).obj X
- where app Y := Limits.prod.fst
+def γ₁ {K : J ⥤ C} (X : C) : K ⋙ prod.functor.obj X ⟶ (Functor.const J).obj X where
+ app Y := Limits.prod.fst
#align category_theory.prod_preserves_connected_limits.γ₁ CategoryTheory.ProdPreservesConnectedLimits.γ₁
/-- (Impl).
@@ -2,11 +2,6 @@
Copyright (c) 2020 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.connected
-! leanprover-community/mathlib commit d6814c584384ddf2825ff038e868451a7c956f31
-! 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.Equalizers
@@ -14,6 +9,8 @@ import Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks
import Mathlib.CategoryTheory.IsConnected
import Mathlib.CategoryTheory.Limits.Preserves.Basic
+#align_import category_theory.limits.connected from "leanprover-community/mathlib"@"d6814c584384ddf2825ff038e868451a7c956f31"
+
/-!
# Connected limits
The unported dependencies are