category_theory.limits.pi
⟷
Mathlib.CategoryTheory.Limits.Pi
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) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
-import Mathbin.CategoryTheory.Pi.Basic
-import Mathbin.CategoryTheory.Limits.HasLimits
+import CategoryTheory.Pi.Basic
+import CategoryTheory.Limits.HasLimits
#align_import category_theory.limits.pi from "leanprover-community/mathlib"@"10bf4f825ad729c5653adc039dafa3622e7f93c9"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,15 +2,12 @@
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-
-! This file was ported from Lean 3 source module category_theory.limits.pi
-! 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.Pi.Basic
import Mathbin.CategoryTheory.Limits.HasLimits
+#align_import category_theory.limits.pi from "leanprover-community/mathlib"@"10bf4f825ad729c5653adc039dafa3622e7f93c9"
+
/-!
# Limits in the category of indexed families of objects.
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -73,9 +73,7 @@ def coneOfConeCompEval (c : ∀ i, Cone (F ⋙ Pi.eval C i)) : Cone F
pt i := (c i).pt
π :=
{ app := fun j i => (c i).π.app j
- naturality' := fun j j' f => by
- ext i
- exact (c i).π.naturality f }
+ naturality' := fun j j' f => by ext i; exact (c i).π.naturality f }
#align category_theory.pi.cone_of_cone_comp_eval CategoryTheory.pi.coneOfConeCompEval
-/
@@ -88,9 +86,7 @@ def coconeOfCoconeCompEval (c : ∀ i, Cocone (F ⋙ Pi.eval C i)) : Cocone F
pt i := (c i).pt
ι :=
{ app := fun j i => (c i).ι.app j
- naturality' := fun j j' f => by
- ext i
- exact (c i).ι.naturality f }
+ naturality' := fun j j' f => by ext i; exact (c i).ι.naturality f }
#align category_theory.pi.cocone_of_cocone_comp_eval CategoryTheory.pi.coconeOfCoconeCompEval
-/
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: Scott Morrison
! This file was ported from Lean 3 source module category_theory.limits.pi
-! leanprover-community/mathlib commit 744d59af0b28d0c42f631038627df9b85ae1d1ce
+! leanprover-community/mathlib commit 10bf4f825ad729c5653adc039dafa3622e7f93c9
! 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.HasLimits
/-!
# Limits in the category of indexed families of objects.
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
Given a functor `F : J ⥤ Π i, C i` into a category of indexed families,
1. we can assemble a collection of cones over `F ⋙ pi.eval C i` into a cone over `F`
2. if all those cones are limit cones, the assembled cone is a limit cone, and
mathlib commit https://github.com/leanprover-community/mathlib/commit/2196ab363eb097c008d4497125e0dde23fb36db2
@@ -36,6 +36,7 @@ variable {J : Type v₁} [SmallCategory J]
variable {F : J ⥤ ∀ i, C i}
+#print CategoryTheory.pi.coneCompEval /-
/-- A cone over `F : J ⥤ Π i, C i` has as its components cones over each of the `F ⋙ pi.eval C i`.
-/
def coneCompEval (c : Cone F) (i : I) : Cone (F ⋙ Pi.eval C i)
@@ -45,7 +46,9 @@ def coneCompEval (c : Cone F) (i : I) : Cone (F ⋙ Pi.eval C i)
{ app := fun j => c.π.app j i
naturality' := fun j j' f => congr_fun (c.π.naturality f) i }
#align category_theory.pi.cone_comp_eval CategoryTheory.pi.coneCompEval
+-/
+#print CategoryTheory.pi.coconeCompEval /-
/--
A cocone over `F : J ⥤ Π i, C i` has as its components cocones over each of the `F ⋙ pi.eval C i`.
-/
@@ -56,7 +59,9 @@ def coconeCompEval (c : Cocone F) (i : I) : Cocone (F ⋙ Pi.eval C i)
{ app := fun j => c.ι.app j i
naturality' := fun j j' f => congr_fun (c.ι.naturality f) i }
#align category_theory.pi.cocone_comp_eval CategoryTheory.pi.coconeCompEval
+-/
+#print CategoryTheory.pi.coneOfConeCompEval /-
/--
Given a family of cones over the `F ⋙ pi.eval C i`, we can assemble these together as a `cone F`.
-/
@@ -69,7 +74,9 @@ def coneOfConeCompEval (c : ∀ i, Cone (F ⋙ Pi.eval C i)) : Cone F
ext i
exact (c i).π.naturality f }
#align category_theory.pi.cone_of_cone_comp_eval CategoryTheory.pi.coneOfConeCompEval
+-/
+#print CategoryTheory.pi.coconeOfCoconeCompEval /-
/-- Given a family of cocones over the `F ⋙ pi.eval C i`,
we can assemble these together as a `cocone F`.
-/
@@ -82,7 +89,9 @@ def coconeOfCoconeCompEval (c : ∀ i, Cocone (F ⋙ Pi.eval C i)) : Cocone F
ext i
exact (c i).ι.naturality f }
#align category_theory.pi.cocone_of_cocone_comp_eval CategoryTheory.pi.coconeOfCoconeCompEval
+-/
+#print CategoryTheory.pi.coneOfConeEvalIsLimit /-
/-- Given a family of limit cones over the `F ⋙ pi.eval C i`,
assembling them together as a `cone F` produces a limit cone.
-/
@@ -97,7 +106,9 @@ def coneOfConeEvalIsLimit {c : ∀ i, Cone (F ⋙ Pi.eval C i)} (P : ∀ i, IsLi
ext i
exact (P i).uniq (cone_comp_eval s i) (m i) fun j => congr_fun (w j) i
#align category_theory.pi.cone_of_cone_eval_is_limit CategoryTheory.pi.coneOfConeEvalIsLimit
+-/
+#print CategoryTheory.pi.coconeOfCoconeEvalIsColimit /-
/-- Given a family of colimit cocones over the `F ⋙ pi.eval C i`,
assembling them together as a `cocone F` produces a colimit cocone.
-/
@@ -112,11 +123,13 @@ def coconeOfCoconeEvalIsColimit {c : ∀ i, Cocone (F ⋙ Pi.eval C i)} (P : ∀
ext i
exact (P i).uniq (cocone_comp_eval s i) (m i) fun j => congr_fun (w j) i
#align category_theory.pi.cocone_of_cocone_eval_is_colimit CategoryTheory.pi.coconeOfCoconeEvalIsColimit
+-/
section
variable [∀ i, HasLimit (F ⋙ Pi.eval C i)]
+#print CategoryTheory.pi.hasLimit_of_hasLimit_comp_eval /-
/-- If we have a functor `F : J ⥤ Π i, C i` into a category of indexed families,
and we have limits for each of the `F ⋙ pi.eval C i`,
then `F` has a limit.
@@ -126,6 +139,7 @@ theorem hasLimit_of_hasLimit_comp_eval : HasLimit F :=
{ Cone := coneOfConeCompEval fun i => limit.cone _
IsLimit := coneOfConeEvalIsLimit fun i => limit.isLimit _ }
#align category_theory.pi.has_limit_of_has_limit_comp_eval CategoryTheory.pi.hasLimit_of_hasLimit_comp_eval
+-/
end
@@ -133,6 +147,7 @@ section
variable [∀ i, HasColimit (F ⋙ Pi.eval C i)]
+#print CategoryTheory.pi.hasColimit_of_hasColimit_comp_eval /-
/-- If we have a functor `F : J ⥤ Π i, C i` into a category of indexed families,
and colimits exist for each of the `F ⋙ pi.eval C i`,
there is a colimit for `F`.
@@ -142,6 +157,7 @@ theorem hasColimit_of_hasColimit_comp_eval : HasColimit F :=
{ Cocone := coconeOfCoconeCompEval fun i => colimit.cocone _
IsColimit := coconeOfCoconeEvalIsColimit fun i => colimit.isColimit _ }
#align category_theory.pi.has_colimit_of_has_colimit_comp_eval CategoryTheory.pi.hasColimit_of_hasColimit_comp_eval
+-/
end
mathlib commit https://github.com/leanprover-community/mathlib/commit/9da1b3534b65d9661eb8f42443598a92bbb49211
@@ -40,7 +40,7 @@ variable {F : J ⥤ ∀ i, C i}
-/
def coneCompEval (c : Cone F) (i : I) : Cone (F ⋙ Pi.eval C i)
where
- x := c.x i
+ pt := c.pt i
π :=
{ app := fun j => c.π.app j i
naturality' := fun j j' f => congr_fun (c.π.naturality f) i }
@@ -51,7 +51,7 @@ A cocone over `F : J ⥤ Π i, C i` has as its components cocones over each of t
-/
def coconeCompEval (c : Cocone F) (i : I) : Cocone (F ⋙ Pi.eval C i)
where
- x := c.x i
+ pt := c.pt i
ι :=
{ app := fun j => c.ι.app j i
naturality' := fun j j' f => congr_fun (c.ι.naturality f) i }
@@ -62,7 +62,7 @@ Given a family of cones over the `F ⋙ pi.eval C i`, we can assemble these toge
-/
def coneOfConeCompEval (c : ∀ i, Cone (F ⋙ Pi.eval C i)) : Cone F
where
- x i := (c i).x
+ pt i := (c i).pt
π :=
{ app := fun j i => (c i).π.app j
naturality' := fun j j' f => by
@@ -75,7 +75,7 @@ we can assemble these together as a `cocone F`.
-/
def coconeOfCoconeCompEval (c : ∀ i, Cocone (F ⋙ Pi.eval C i)) : Cocone F
where
- x i := (c i).x
+ pt i := (c i).pt
ι :=
{ app := fun j i => (c i).ι.app j
naturality' := fun j j' f => by
@@ -123,7 +123,7 @@ then `F` has a limit.
-/
theorem hasLimit_of_hasLimit_comp_eval : HasLimit F :=
HasLimit.mk
- { Cone := coneOfConeCompEval fun i => Limit.cone _
+ { Cone := coneOfConeCompEval fun i => limit.cone _
IsLimit := coneOfConeEvalIsLimit fun i => limit.isLimit _ }
#align category_theory.pi.has_limit_of_has_limit_comp_eval CategoryTheory.pi.hasLimit_of_hasLimit_comp_eval
@@ -139,7 +139,7 @@ there is a colimit for `F`.
-/
theorem hasColimit_of_hasColimit_comp_eval : HasColimit F :=
HasColimit.mk
- { Cocone := coconeOfCoconeCompEval fun i => Colimit.cocone _
+ { Cocone := coconeOfCoconeCompEval fun i => colimit.cocone _
IsColimit := coconeOfCoconeEvalIsColimit fun i => colimit.isColimit _ }
#align category_theory.pi.has_colimit_of_has_colimit_comp_eval CategoryTheory.pi.hasColimit_of_hasColimit_comp_eval
mathlib commit https://github.com/leanprover-community/mathlib/commit/eb0cb4511aaef0da2462207b67358a0e1fe1e2ee
@@ -90,10 +90,10 @@ def coneOfConeEvalIsLimit {c : ∀ i, Cone (F ⋙ Pi.eval C i)} (P : ∀ i, IsLi
IsLimit (coneOfConeCompEval c)
where
lift s i := (P i).lift (coneCompEval s i)
- fac' s j := by
+ fac s j := by
ext i
exact (P i).fac (cone_comp_eval s i) j
- uniq' s m w := by
+ uniq s m w := by
ext i
exact (P i).uniq (cone_comp_eval s i) (m i) fun j => congr_fun (w j) i
#align category_theory.pi.cone_of_cone_eval_is_limit CategoryTheory.pi.coneOfConeEvalIsLimit
@@ -105,10 +105,10 @@ def coconeOfCoconeEvalIsColimit {c : ∀ i, Cocone (F ⋙ Pi.eval C i)} (P : ∀
IsColimit (coconeOfCoconeCompEval c)
where
desc s i := (P i).desc (coconeCompEval s i)
- fac' s j := by
+ fac s j := by
ext i
exact (P i).fac (cocone_comp_eval s i) j
- uniq' s m w := by
+ uniq s m w := by
ext i
exact (P i).uniq (cocone_comp_eval s i) (m i) fun j => congr_fun (w j) i
#align category_theory.pi.cocone_of_cocone_eval_is_colimit CategoryTheory.pi.coconeOfCoconeEvalIsColimit
@@ -121,11 +121,11 @@ variable [∀ i, HasLimit (F ⋙ Pi.eval C i)]
and we have limits for each of the `F ⋙ pi.eval C i`,
then `F` has a limit.
-/
-theorem hasLimitOfHasLimitCompEval : HasLimit F :=
+theorem hasLimit_of_hasLimit_comp_eval : HasLimit F :=
HasLimit.mk
{ Cone := coneOfConeCompEval fun i => Limit.cone _
IsLimit := coneOfConeEvalIsLimit fun i => limit.isLimit _ }
-#align category_theory.pi.has_limit_of_has_limit_comp_eval CategoryTheory.pi.hasLimitOfHasLimitCompEval
+#align category_theory.pi.has_limit_of_has_limit_comp_eval CategoryTheory.pi.hasLimit_of_hasLimit_comp_eval
end
@@ -137,11 +137,11 @@ variable [∀ i, HasColimit (F ⋙ Pi.eval C i)]
and colimits exist for each of the `F ⋙ pi.eval C i`,
there is a colimit for `F`.
-/
-theorem hasColimitOfHasColimitCompEval : HasColimit F :=
+theorem hasColimit_of_hasColimit_comp_eval : HasColimit F :=
HasColimit.mk
{ Cocone := coconeOfCoconeCompEval fun i => Colimit.cocone _
IsColimit := coconeOfCoconeEvalIsColimit fun i => colimit.isColimit _ }
-#align category_theory.pi.has_colimit_of_has_colimit_comp_eval CategoryTheory.pi.hasColimitOfHasColimitCompEval
+#align category_theory.pi.has_colimit_of_has_colimit_comp_eval CategoryTheory.pi.hasColimit_of_hasColimit_comp_eval
end
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
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)
@@ -28,9 +28,7 @@ namespace CategoryTheory.pi
universe v₁ v₂ u₁ u₂
variable {I : Type v₁} {C : I → Type u₁} [∀ i, Category.{v₁} (C i)]
-
variable {J : Type v₁} [SmallCategory J]
-
variable {F : J ⥤ ∀ i, C i}
/-- A cone over `F : J ⥤ Π i, C i` has as its components cones over each of the `F ⋙ Pi.eval C i`.
@@ -144,7 +144,7 @@ With the addition of
`import CategoryTheory.Limits.Shapes.Types`
we can use:
```
-local attribute [instance] hasLimit_of_hasLimit_comp_eval
+attribute [local instance] hasLimit_of_hasLimit_comp_eval
example : hasBinaryProducts (I → Type v₁) := ⟨by infer_instance⟩
```
-/
@@ -2,15 +2,12 @@
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-
-! This file was ported from Lean 3 source module category_theory.limits.pi
-! leanprover-community/mathlib commit 744d59af0b28d0c42f631038627df9b85ae1d1ce
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.CategoryTheory.Pi.Basic
import Mathlib.CategoryTheory.Limits.HasLimits
+#align_import category_theory.limits.pi from "leanprover-community/mathlib"@"744d59af0b28d0c42f631038627df9b85ae1d1ce"
+
/-!
# Limits in the category of indexed families of objects.
@@ -148,7 +148,7 @@ With the addition of
we can use:
```
local attribute [instance] hasLimit_of_hasLimit_comp_eval
-example : hasBinaryProducts (I → Type v₁) := ⟨by apply_instance⟩
+example : hasBinaryProducts (I → Type v₁) := ⟨by infer_instance⟩
```
-/
All dependencies are ported!