category_theory.limits.constructions.filtered
⟷
Mathlib.CategoryTheory.Limits.Constructions.Filtered
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/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -83,7 +83,8 @@ open CoproductsFromFiniteFiltered
#print CategoryTheory.Limits.hasCoproducts_of_finite_and_filtered /-
theorem hasCoproducts_of_finite_and_filtered [HasFiniteCoproducts C]
- [HasFilteredColimitsOfSize.{w, w} C] : HasCoproducts.{w} C := fun α => by classical
+ [HasFilteredColimitsOfSize.{w, w} C] : HasCoproducts.{w} C := fun α => by
+ classical exact ⟨fun F => has_colimit.mk (lift_to_finset_colimit_cocone F)⟩
#align category_theory.limits.has_coproducts_of_finite_and_filtered CategoryTheory.Limits.hasCoproducts_of_finite_and_filtered
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -83,8 +83,7 @@ open CoproductsFromFiniteFiltered
#print CategoryTheory.Limits.hasCoproducts_of_finite_and_filtered /-
theorem hasCoproducts_of_finite_and_filtered [HasFiniteCoproducts C]
- [HasFilteredColimitsOfSize.{w, w} C] : HasCoproducts.{w} C := fun α => by
- classical exact ⟨fun F => has_colimit.mk (lift_to_finset_colimit_cocone F)⟩
+ [HasFilteredColimitsOfSize.{w, w} C] : HasCoproducts.{w} C := fun α => by classical
#align category_theory.limits.has_coproducts_of_finite_and_filtered CategoryTheory.Limits.hasCoproducts_of_finite_and_filtered
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,8 +3,8 @@ Copyright (c) 2022 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
-import Mathbin.CategoryTheory.Limits.Constructions.LimitsOfProductsAndEqualizers
-import Mathbin.CategoryTheory.Limits.Opposites
+import CategoryTheory.Limits.Constructions.LimitsOfProductsAndEqualizers
+import CategoryTheory.Limits.Opposites
#align_import category_theory.limits.constructions.filtered from "leanprover-community/mathlib"@"10bf4f825ad729c5653adc039dafa3622e7f93c9"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,15 +2,12 @@
Copyright (c) 2022 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-
-! This file was ported from Lean 3 source module category_theory.limits.constructions.filtered
-! 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.Constructions.LimitsOfProductsAndEqualizers
import Mathbin.CategoryTheory.Limits.Opposites
+#align_import category_theory.limits.constructions.filtered from "leanprover-community/mathlib"@"10bf4f825ad729c5653adc039dafa3622e7f93c9"
+
/-!
# Constructing colimits from finite colimits and filtered colimits
mathlib commit https://github.com/leanprover-community/mathlib/commit/2a0ce625dbb0ffbc7d1316597de0b25c1ec75303
@@ -73,7 +73,7 @@ def liftToFinsetColimitCocone [HasFiniteCoproducts C] [HasFilteredColimitsOfSize
{ pt := s.pt
ι := { app := fun t => Sigma.desc fun x => s.ι.app x } }
uniq := fun s m h => by
- ext (t⟨⟨j, hj⟩⟩)
+ ext t ⟨⟨j, hj⟩⟩
convert h j using 1
· simp [← colimit.w (lift_to_finset F) ⟨⟨Finset.singleton_subset_iff.2 hj⟩⟩]; rfl
· tidy }
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -75,8 +75,7 @@ def liftToFinsetColimitCocone [HasFiniteCoproducts C] [HasFilteredColimitsOfSize
uniq := fun s m h => by
ext (t⟨⟨j, hj⟩⟩)
convert h j using 1
- · simp [← colimit.w (lift_to_finset F) ⟨⟨Finset.singleton_subset_iff.2 hj⟩⟩]
- rfl
+ · simp [← colimit.w (lift_to_finset F) ⟨⟨Finset.singleton_subset_iff.2 hj⟩⟩]; rfl
· tidy }
#align category_theory.limits.coproducts_from_finite_filtered.lift_to_finset_colimit_cocone CategoryTheory.Limits.CoproductsFromFiniteFiltered.liftToFinsetColimitCocone
-/
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: Markus Himmel
! This file was ported from Lean 3 source module category_theory.limits.constructions.filtered
-! leanprover-community/mathlib commit e4ee4e30418efcb8cf304ba76ad653aeec04ba6e
+! 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.Opposites
/-!
# Constructing colimits from finite colimits and filtered colimits
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
We construct colimits of size `w` from finite colimits and filtered colimits of size `w`. Since
`w`-sized colimits are constructured from coequalizers and `w`-sized coproducts, it suffices to
construct `w`-sized coproducts from finite coproducts and `w`-sized filtered colimits.
mathlib commit https://github.com/leanprover-community/mathlib/commit/2af0836443b4cfb5feda0df0051acdb398304931
@@ -39,6 +39,7 @@ namespace CoproductsFromFiniteFiltered
attribute [local tidy] tactic.case_bash
+#print CategoryTheory.Limits.CoproductsFromFiniteFiltered.liftToFinset /-
/-- If `C` has finite coproducts, a functor `discrete α ⥤ C` lifts to a functor
`finset (discrete α) ⥤ C` by taking coproducts. -/
@[simps]
@@ -47,7 +48,9 @@ def liftToFinset [HasFiniteCoproducts C] (F : Discrete α ⥤ C) : Finset (Discr
obj s := ∐ fun x : s => F.obj x
map s t h := Sigma.desc fun y => Sigma.ι (fun x : t => F.obj x) ⟨y, h.down.down y.2⟩
#align category_theory.limits.coproducts_from_finite_filtered.lift_to_finset CategoryTheory.Limits.CoproductsFromFiniteFiltered.liftToFinset
+-/
+#print CategoryTheory.Limits.CoproductsFromFiniteFiltered.liftToFinsetColimitCocone /-
/-- If `C` has finite coproducts and filtered colimits, we can construct arbitrary coproducts by
taking the colimit of the diagram formed by the coproducts of finite sets over the indexing
type. -/
@@ -73,33 +76,42 @@ def liftToFinsetColimitCocone [HasFiniteCoproducts C] [HasFilteredColimitsOfSize
rfl
· tidy }
#align category_theory.limits.coproducts_from_finite_filtered.lift_to_finset_colimit_cocone CategoryTheory.Limits.CoproductsFromFiniteFiltered.liftToFinsetColimitCocone
+-/
end CoproductsFromFiniteFiltered
open CoproductsFromFiniteFiltered
+#print CategoryTheory.Limits.hasCoproducts_of_finite_and_filtered /-
theorem hasCoproducts_of_finite_and_filtered [HasFiniteCoproducts C]
[HasFilteredColimitsOfSize.{w, w} C] : HasCoproducts.{w} C := fun α => by
classical exact ⟨fun F => has_colimit.mk (lift_to_finset_colimit_cocone F)⟩
#align category_theory.limits.has_coproducts_of_finite_and_filtered CategoryTheory.Limits.hasCoproducts_of_finite_and_filtered
+-/
+#print CategoryTheory.Limits.has_colimits_of_finite_and_filtered /-
theorem has_colimits_of_finite_and_filtered [HasFiniteColimits C]
[HasFilteredColimitsOfSize.{w, w} C] : HasColimitsOfSize.{w, w} C :=
have : HasCoproducts.{w} C := hasCoproducts_of_finite_and_filtered
has_colimits_of_has_coequalizers_and_coproducts
#align category_theory.limits.has_colimits_of_finite_and_filtered CategoryTheory.Limits.has_colimits_of_finite_and_filtered
+-/
+#print CategoryTheory.Limits.hasProducts_of_finite_and_cofiltered /-
theorem hasProducts_of_finite_and_cofiltered [HasFiniteProducts C]
[HasCofilteredLimitsOfSize.{w, w} C] : HasProducts.{w} C :=
have : HasCoproducts.{w} Cᵒᵖ := hasCoproducts_of_finite_and_filtered
has_products_of_opposite
#align category_theory.limits.has_products_of_finite_and_cofiltered CategoryTheory.Limits.hasProducts_of_finite_and_cofiltered
+-/
+#print CategoryTheory.Limits.has_limits_of_finite_and_cofiltered /-
theorem has_limits_of_finite_and_cofiltered [HasFiniteLimits C]
[HasCofilteredLimitsOfSize.{w, w} C] : HasLimitsOfSize.{w, w} C :=
have : HasProducts.{w} C := hasProducts_of_finite_and_cofiltered
has_limits_of_has_equalizers_and_products
#align category_theory.limits.has_limits_of_finite_and_cofiltered CategoryTheory.Limits.has_limits_of_finite_and_cofiltered
+-/
end CategoryTheory.Limits
mathlib commit https://github.com/leanprover-community/mathlib/commit/9da1b3534b65d9661eb8f42443598a92bbb49211
@@ -56,7 +56,7 @@ def liftToFinsetColimitCocone [HasFiniteCoproducts C] [HasFilteredColimitsOfSize
[DecidableEq α] (F : Discrete α ⥤ C) : ColimitCocone F
where
Cocone :=
- { x := colimit (liftToFinset F)
+ { pt := colimit (liftToFinset F)
ι :=
Discrete.natTrans fun j =>
@Sigma.ι _ _ _ (fun x : ({j} : Finset (Discrete α)) => F.obj x) _ ⟨j, by simp⟩ ≫
@@ -64,7 +64,7 @@ def liftToFinsetColimitCocone [HasFiniteCoproducts C] [HasFilteredColimitsOfSize
IsColimit :=
{ desc := fun s =>
colimit.desc (liftToFinset F)
- { x := s.x
+ { pt := s.pt
ι := { app := fun t => Sigma.desc fun x => s.ι.app x } }
uniq := fun s m h => by
ext (t⟨⟨j, hj⟩⟩)
mathlib commit https://github.com/leanprover-community/mathlib/commit/eb0cb4511aaef0da2462207b67358a0e1fe1e2ee
@@ -66,7 +66,7 @@ def liftToFinsetColimitCocone [HasFiniteCoproducts C] [HasFilteredColimitsOfSize
colimit.desc (liftToFinset F)
{ x := s.x
ι := { app := fun t => Sigma.desc fun x => s.ι.app x } }
- uniq' := fun s m h => by
+ uniq := fun s m h => by
ext (t⟨⟨j, hj⟩⟩)
convert h j using 1
· simp [← colimit.w (lift_to_finset F) ⟨⟨Finset.singleton_subset_iff.2 hj⟩⟩]
@@ -83,11 +83,11 @@ theorem hasCoproducts_of_finite_and_filtered [HasFiniteCoproducts C]
classical exact ⟨fun F => has_colimit.mk (lift_to_finset_colimit_cocone F)⟩
#align category_theory.limits.has_coproducts_of_finite_and_filtered CategoryTheory.Limits.hasCoproducts_of_finite_and_filtered
-theorem hasColimitsOfFiniteAndFiltered [HasFiniteColimits C] [HasFilteredColimitsOfSize.{w, w} C] :
- HasColimitsOfSize.{w, w} C :=
+theorem has_colimits_of_finite_and_filtered [HasFiniteColimits C]
+ [HasFilteredColimitsOfSize.{w, w} C] : HasColimitsOfSize.{w, w} C :=
have : HasCoproducts.{w} C := hasCoproducts_of_finite_and_filtered
has_colimits_of_has_coequalizers_and_coproducts
-#align category_theory.limits.has_colimits_of_finite_and_filtered CategoryTheory.Limits.hasColimitsOfFiniteAndFiltered
+#align category_theory.limits.has_colimits_of_finite_and_filtered CategoryTheory.Limits.has_colimits_of_finite_and_filtered
theorem hasProducts_of_finite_and_cofiltered [HasFiniteProducts C]
[HasCofilteredLimitsOfSize.{w, w} C] : HasProducts.{w} C :=
@@ -95,11 +95,11 @@ theorem hasProducts_of_finite_and_cofiltered [HasFiniteProducts C]
has_products_of_opposite
#align category_theory.limits.has_products_of_finite_and_cofiltered CategoryTheory.Limits.hasProducts_of_finite_and_cofiltered
-theorem hasLimitsOfFiniteAndCofiltered [HasFiniteLimits C] [HasCofilteredLimitsOfSize.{w, w} C] :
- HasLimitsOfSize.{w, w} C :=
+theorem has_limits_of_finite_and_cofiltered [HasFiniteLimits C]
+ [HasCofilteredLimitsOfSize.{w, w} C] : HasLimitsOfSize.{w, w} C :=
have : HasProducts.{w} C := hasProducts_of_finite_and_cofiltered
has_limits_of_has_equalizers_and_products
-#align category_theory.limits.has_limits_of_finite_and_cofiltered CategoryTheory.Limits.hasLimitsOfFiniteAndCofiltered
+#align category_theory.limits.has_limits_of_finite_and_cofiltered CategoryTheory.Limits.has_limits_of_finite_and_cofiltered
end CategoryTheory.Limits
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
IsDirected
instances (#6169)
This way IsDirected (Finset α) (· ≤ ·)
doesn't need [DecidableEq α]
.
@@ -48,7 +48,7 @@ def liftToFinset [HasFiniteCoproducts C] (F : Discrete α ⥤ C) : Finset (Discr
type. -/
@[simps!]
def liftToFinsetColimitCocone [HasFiniteCoproducts C] [HasFilteredColimitsOfSize.{w, w} C]
- [DecidableEq α] (F : Discrete α ⥤ C) : ColimitCocone F where
+ (F : Discrete α ⥤ C) : ColimitCocone F where
cocone :=
{ pt := colimit (liftToFinset F)
ι :=
@@ -2,15 +2,12 @@
Copyright (c) 2022 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-
-! This file was ported from Lean 3 source module category_theory.limits.constructions.filtered
-! leanprover-community/mathlib commit e4ee4e30418efcb8cf304ba76ad653aeec04ba6e
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.CategoryTheory.Limits.Constructions.LimitsOfProductsAndEqualizers
import Mathlib.CategoryTheory.Limits.Opposites
+#align_import category_theory.limits.constructions.filtered from "leanprover-community/mathlib"@"e4ee4e30418efcb8cf304ba76ad653aeec04ba6e"
+
/-!
# Constructing colimits from finite colimits and filtered colimits
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.
@@ -70,9 +70,9 @@ def liftToFinsetColimitCocone [HasFiniteCoproducts C] [HasFilteredColimitsOfSize
apply colimit.hom_ext
rintro ⟨⟨j, hj⟩⟩
convert h j using 1
- . simp [← colimit.w (liftToFinset F) ⟨⟨Finset.singleton_subset_iff.2 hj⟩⟩]
+ · simp [← colimit.w (liftToFinset F) ⟨⟨Finset.singleton_subset_iff.2 hj⟩⟩]
rfl
- . aesop_cat }
+ · aesop_cat }
#align category_theory.limits.coproducts_from_finite_filtered.lift_to_finset_colimit_cocone CategoryTheory.Limits.CoproductsFromFiniteFiltered.liftToFinsetColimitCocone
end CoproductsFromFiniteFiltered
@@ -15,7 +15,7 @@ import Mathlib.CategoryTheory.Limits.Opposites
# Constructing colimits from finite colimits and filtered colimits
We construct colimits of size `w` from finite colimits and filtered colimits of size `w`. Since
-`w`-sized colimits are constructured from coequalizers and `w`-sized coproducts, it suffices to
+`w`-sized colimits are constructed from coequalizers and `w`-sized coproducts, it suffices to
construct `w`-sized coproducts from finite coproducts and `w`-sized filtered colimits.
The idea is simple: to construct coproducts of shape `α`, we take the colimit of the filtered
Co-authored-by: Parcly Taxel <reddeloostw@gmail.com> Co-authored-by: Joël Riou <joel.riou@universite-paris-saclay.fr>
The unported dependencies are