order.category.omega_complete_partial_order
⟷
Mathlib.Order.Category.OmegaCompletePartialOrder
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 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
-import Mathbin.Order.OmegaCompletePartialOrder
-import Mathbin.CategoryTheory.Limits.Shapes.Products
-import Mathbin.CategoryTheory.Limits.Shapes.Equalizers
-import Mathbin.CategoryTheory.Limits.Constructions.LimitsOfProductsAndEqualizers
-import Mathbin.CategoryTheory.ConcreteCategory.BundledHom
+import Order.OmegaCompletePartialOrder
+import CategoryTheory.Limits.Shapes.Products
+import CategoryTheory.Limits.Shapes.Equalizers
+import CategoryTheory.Limits.Constructions.LimitsOfProductsAndEqualizers
+import CategoryTheory.ConcreteCategory.BundledHom
#align_import order.category.omega_complete_partial_order from "leanprover-community/mathlib"@"d0b1936853671209a866fa35b9e54949c81116e2"
mathlib commit https://github.com/leanprover-community/mathlib/commit/63721b2c3eba6c325ecf8ae8cca27155a4f6306f
@@ -85,7 +85,7 @@ namespace HasProducts
#print ωCPO.HasProducts.product /-
/-- The pi-type gives a cone for a product. -/
def product {J : Type v} (f : J → ωCPO.{v}) : Fan f :=
- Fan.mk (of (∀ j, f j)) fun j => ContinuousHom.ofMono (Pi.evalOrderHom j) fun c => rfl
+ Fan.mk (of (∀ j, f j)) fun j => ContinuousHom.mk (Pi.evalOrderHom j) fun c => rfl
#align ωCPO.has_products.product ωCPO.HasProducts.product
-/
@@ -129,7 +129,7 @@ namespace HasEqualizers
/-- The equalizer inclusion function as a `continuous_hom`. -/
def equalizerι {α β : Type _} [OmegaCompletePartialOrder α] [OmegaCompletePartialOrder β]
(f g : α →𝒄 β) : { a : α // f a = g a } →𝒄 α :=
- ContinuousHom.ofMono (OrderHom.Subtype.val _) fun c => rfl
+ ContinuousHom.mk (OrderHom.Subtype.val _) fun c => rfl
#align ωCPO.has_equalizers.equalizer_ι ωCPO.HasEqualizers.equalizerι
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,11 +2,6 @@
Copyright (c) 2020 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-
-! This file was ported from Lean 3 source module order.category.omega_complete_partial_order
-! leanprover-community/mathlib commit d0b1936853671209a866fa35b9e54949c81116e2
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.Order.OmegaCompletePartialOrder
import Mathbin.CategoryTheory.Limits.Shapes.Products
@@ -14,6 +9,8 @@ import Mathbin.CategoryTheory.Limits.Shapes.Equalizers
import Mathbin.CategoryTheory.Limits.Constructions.LimitsOfProductsAndEqualizers
import Mathbin.CategoryTheory.ConcreteCategory.BundledHom
+#align_import order.category.omega_complete_partial_order from "leanprover-community/mathlib"@"d0b1936853671209a866fa35b9e54949c81116e2"
+
/-!
# Category of types with a omega complete partial order
mathlib commit https://github.com/leanprover-community/mathlib/commit/728ef9dbb281241906f25cbeb30f90d83e0bb451
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
! This file was ported from Lean 3 source module order.category.omega_complete_partial_order
-! leanprover-community/mathlib commit 70fd9563a21e7b963887c9360bd29b2393e6225a
+! leanprover-community/mathlib commit d0b1936853671209a866fa35b9e54949c81116e2
! 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.ConcreteCategory.BundledHom
/-!
# Category of types with a omega complete partial order
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
In this file, we bundle the class `omega_complete_partial_order` into a
concrete category and prove that continuous functions also form
a `omega_complete_partial_order`.
mathlib commit https://github.com/leanprover-community/mathlib/commit/8b981918a93bc45a8600de608cde7944a80d92b9
@@ -33,10 +33,12 @@ open CategoryTheory
universe u v
+#print ωCPO /-
/-- The category of types with a omega complete partial order. -/
def ωCPO : Type (u + 1) :=
Bundled OmegaCompletePartialOrder
#align ωCPO ωCPO
+-/
namespace ωCPO
@@ -54,15 +56,19 @@ deriving instance LargeCategory, ConcreteCategory for ωCPO
instance : CoeSort ωCPO (Type _) :=
Bundled.hasCoeToSort
+#print ωCPO.of /-
/-- Construct a bundled ωCPO from the underlying type and typeclass. -/
def of (α : Type _) [OmegaCompletePartialOrder α] : ωCPO :=
Bundled.of α
#align ωCPO.of ωCPO.of
+-/
+#print ωCPO.coe_of /-
@[simp]
theorem coe_of (α : Type _) [OmegaCompletePartialOrder α] : ↥(of α) = α :=
rfl
#align ωCPO.coe_of ωCPO.coe_of
+-/
instance : Inhabited ωCPO :=
⟨of PUnit⟩
@@ -76,11 +82,14 @@ open CategoryTheory.Limits
namespace HasProducts
+#print ωCPO.HasProducts.product /-
/-- The pi-type gives a cone for a product. -/
def product {J : Type v} (f : J → ωCPO.{v}) : Fan f :=
Fan.mk (of (∀ j, f j)) fun j => ContinuousHom.ofMono (Pi.evalOrderHom j) fun c => rfl
#align ωCPO.has_products.product ωCPO.HasProducts.product
+-/
+#print ωCPO.HasProducts.isProduct /-
/-- The pi-type is a limit cone for the product. -/
def isProduct (J : Type v) (f : J → ωCPO) : IsLimit (product f)
where
@@ -94,12 +103,14 @@ def isProduct (J : Type v) (f : J → ωCPO) : IsLimit (product f)
rfl
fac s j := by cases j; tidy
#align ωCPO.has_products.is_product ωCPO.HasProducts.isProduct
+-/
instance (J : Type v) (f : J → ωCPO.{v}) : HasProduct f :=
HasLimit.mk ⟨_, isProduct _ f⟩
end HasProducts
+#print ωCPO.omegaCompletePartialOrderEqualizer /-
instance omegaCompletePartialOrderEqualizer {α β : Type _} [OmegaCompletePartialOrder α]
[OmegaCompletePartialOrder β] (f g : α →𝒄 β) :
OmegaCompletePartialOrder { a : α // f a = g a } :=
@@ -110,21 +121,27 @@ instance omegaCompletePartialOrderEqualizer {α β : Type _} [OmegaCompleteParti
ext
apply hc _ ⟨_, rfl⟩
#align ωCPO.omega_complete_partial_order_equalizer ωCPO.omegaCompletePartialOrderEqualizer
+-/
namespace HasEqualizers
+#print ωCPO.HasEqualizers.equalizerι /-
/-- The equalizer inclusion function as a `continuous_hom`. -/
def equalizerι {α β : Type _} [OmegaCompletePartialOrder α] [OmegaCompletePartialOrder β]
(f g : α →𝒄 β) : { a : α // f a = g a } →𝒄 α :=
ContinuousHom.ofMono (OrderHom.Subtype.val _) fun c => rfl
#align ωCPO.has_equalizers.equalizer_ι ωCPO.HasEqualizers.equalizerι
+-/
+#print ωCPO.HasEqualizers.equalizer /-
/-- A construction of the equalizer fork. -/
def equalizer {X Y : ωCPO.{v}} (f g : X ⟶ Y) : Fork f g :=
@Fork.ofι _ _ _ _ _ _ (ωCPO.of { a // f a = g a }) (equalizerι f g)
(ContinuousHom.ext _ _ fun x => x.2)
#align ωCPO.has_equalizers.equalizer ωCPO.HasEqualizers.equalizer
+-/
+#print ωCPO.HasEqualizers.isEqualizer /-
/-- The equalizer fork is a limit. -/
def isEqualizer {X Y : ωCPO.{v}} (f g : X ⟶ Y) : IsLimit (equalizer f g) :=
Fork.IsLimit.mk' _ fun s =>
@@ -135,6 +152,7 @@ def isEqualizer {X Y : ωCPO.{v}} (f g : X ⟶ Y) : IsLimit (equalizer f g) :=
ext
apply continuous_hom.congr_fun hm⟩
#align ωCPO.has_equalizers.is_equalizer ωCPO.HasEqualizers.isEqualizer
+-/
end HasEqualizers
mathlib commit https://github.com/leanprover-community/mathlib/commit/2a0ce625dbb0ffbc7d1316597de0b25c1ec75303
@@ -88,7 +88,7 @@ def isProduct (J : Type v) (f : J → ωCPO) : IsLimit (product f)
⟨⟨fun t j => s.π.app ⟨j⟩ t, fun x y h j => (s.π.app ⟨j⟩).Monotone h⟩, fun x =>
funext fun j => (s.π.app ⟨j⟩).Continuous x⟩
uniq s m w := by
- ext (t j)
+ ext t j
change m t j = s.π.app ⟨j⟩ t
rw [← w ⟨j⟩]
rfl
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -92,9 +92,7 @@ def isProduct (J : Type v) (f : J → ωCPO) : IsLimit (product f)
change m t j = s.π.app ⟨j⟩ t
rw [← w ⟨j⟩]
rfl
- fac s j := by
- cases j
- tidy
+ fac s j := by cases j; tidy
#align ωCPO.has_products.is_product ωCPO.HasProducts.isProduct
instance (J : Type v) (f : J → ωCPO.{v}) : HasProduct f :=
@@ -132,11 +130,9 @@ def isEqualizer {X Y : ωCPO.{v}} (f g : X ⟶ Y) : IsLimit (equalizer f g) :=
Fork.IsLimit.mk' _ fun s =>
⟨{ toFun := fun x => ⟨s.ι x, by apply continuous_hom.congr_fun s.condition⟩
monotone' := fun x y h => s.ι.Monotone h
- cont := fun x => Subtype.ext (s.ι.Continuous x) },
+ cont := fun x => Subtype.ext (s.ι.Continuous x) }, by ext; rfl, fun m hm =>
by
ext
- rfl, fun m hm => by
- ext
apply continuous_hom.congr_fun hm⟩
#align ωCPO.has_equalizers.is_equalizer ωCPO.HasEqualizers.isEqualizer
mathlib commit https://github.com/leanprover-community/mathlib/commit/9da1b3534b65d9661eb8f42443598a92bbb49211
@@ -143,7 +143,7 @@ def isEqualizer {X Y : ωCPO.{v}} (f g : X ⟶ Y) : IsLimit (equalizer f g) :=
end HasEqualizers
instance : HasProducts.{v} ωCPO.{v} := fun J =>
- { HasLimit := fun F => hasLimit_of_iso Discrete.natIsoFunctor.symm }
+ { HasLimit := fun F => hasLimitOfIso Discrete.natIsoFunctor.symm }
instance {X Y : ωCPO.{v}} (f g : X ⟶ Y) : HasLimit (parallelPair f g) :=
HasLimit.mk ⟨_, HasEqualizers.isEqualizer f g⟩
mathlib commit https://github.com/leanprover-community/mathlib/commit/eb0cb4511aaef0da2462207b67358a0e1fe1e2ee
@@ -87,12 +87,12 @@ def isProduct (J : Type v) (f : J → ωCPO) : IsLimit (product f)
lift s :=
⟨⟨fun t j => s.π.app ⟨j⟩ t, fun x y h j => (s.π.app ⟨j⟩).Monotone h⟩, fun x =>
funext fun j => (s.π.app ⟨j⟩).Continuous x⟩
- uniq' s m w := by
+ uniq s m w := by
ext (t j)
change m t j = s.π.app ⟨j⟩ t
rw [← w ⟨j⟩]
rfl
- fac' s j := by
+ fac s j := by
cases j
tidy
#align ωCPO.has_products.is_product ωCPO.HasProducts.isProduct
@@ -143,7 +143,7 @@ def isEqualizer {X Y : ωCPO.{v}} (f g : X ⟶ Y) : IsLimit (equalizer f g) :=
end HasEqualizers
instance : HasProducts.{v} ωCPO.{v} := fun J =>
- { HasLimit := fun F => hasLimitOfIso Discrete.natIsoFunctor.symm }
+ { HasLimit := fun F => hasLimit_of_iso Discrete.natIsoFunctor.symm }
instance {X Y : ωCPO.{v}} (f g : X ⟶ Y) : HasLimit (parallelPair f g) :=
HasLimit.mk ⟨_, HasEqualizers.isEqualizer f g⟩
@@ -152,7 +152,7 @@ instance : HasEqualizers ωCPO.{v} :=
hasEqualizers_of_hasLimit_parallelPair _
instance : HasLimits ωCPO.{v} :=
- hasLimitsOfHasEqualizersAndProducts
+ has_limits_of_hasEqualizers_and_products
end
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -51,16 +51,16 @@ instance : BundledHom @ContinuousHom where
deriving instance LargeCategory for ωCPO
instance : ConcreteCategory ωCPO := by unfold ωCPO; infer_instance
-instance : CoeSort ωCPO (Type _) :=
+instance : CoeSort ωCPO (Type*) :=
Bundled.coeSort
/-- Construct a bundled ωCPO from the underlying type and typeclass. -/
-def of (α : Type _) [OmegaCompletePartialOrder α] : ωCPO :=
+def of (α : Type*) [OmegaCompletePartialOrder α] : ωCPO :=
Bundled.of α
#align ωCPO.of ωCPO.of
@[simp]
-theorem coe_of (α : Type _) [OmegaCompletePartialOrder α] : ↥(of α) = α :=
+theorem coe_of (α : Type*) [OmegaCompletePartialOrder α] : ↥(of α) = α :=
rfl
#align ωCPO.coe_of ωCPO.coe_of
@@ -100,7 +100,7 @@ instance (J : Type v) (f : J → ωCPO.{v}) : HasProduct f :=
end HasProducts
-instance omegaCompletePartialOrderEqualizer {α β : Type _} [OmegaCompletePartialOrder α]
+instance omegaCompletePartialOrderEqualizer {α β : Type*} [OmegaCompletePartialOrder α]
[OmegaCompletePartialOrder β] (f g : α →𝒄 β) :
OmegaCompletePartialOrder { a : α // f a = g a } :=
OmegaCompletePartialOrder.subtype _ fun c hc => by
@@ -113,7 +113,7 @@ instance omegaCompletePartialOrderEqualizer {α β : Type _} [OmegaCompleteParti
namespace HasEqualizers
/-- The equalizer inclusion function as a `ContinuousHom`. -/
-def equalizerι {α β : Type _} [OmegaCompletePartialOrder α] [OmegaCompletePartialOrder β]
+def equalizerι {α β : Type*} [OmegaCompletePartialOrder α] [OmegaCompletePartialOrder β]
(f g : α →𝒄 β) : { a : α // f a = g a } →𝒄 α :=
.mk (OrderHom.Subtype.val _) fun _ => rfl
#align ωCPO.has_equalizers.equalizer_ι ωCPO.HasEqualizers.equalizerι
FunLike
for OrderHom
(#5805)
Co-authored-by: Jujian Zhang <jujian.zhang1998@outlook.com> Co-authored-by: Oliver Nash <github@olivernash.org>
@@ -78,7 +78,7 @@ namespace HasProducts
/-- The pi-type gives a cone for a product. -/
def product {J : Type v} (f : J → ωCPO.{v}) : Fan f :=
- Fan.mk (of (∀ j, f j)) fun j => ContinuousHom.ofMono (Pi.evalOrderHom j) fun _ => rfl
+ Fan.mk (of (∀ j, f j)) fun j => .mk (Pi.evalOrderHom j) fun _ => rfl
#align ωCPO.has_products.product ωCPO.HasProducts.product
/-- The pi-type is a limit cone for the product. -/
@@ -115,7 +115,7 @@ namespace HasEqualizers
/-- The equalizer inclusion function as a `ContinuousHom`. -/
def equalizerι {α β : Type _} [OmegaCompletePartialOrder α] [OmegaCompletePartialOrder β]
(f g : α →𝒄 β) : { a : α // f a = g a } →𝒄 α :=
- ContinuousHom.ofMono (OrderHom.Subtype.val _) fun _ => rfl
+ .mk (OrderHom.Subtype.val _) fun _ => rfl
#align ωCPO.has_equalizers.equalizer_ι ωCPO.HasEqualizers.equalizerι
/-- A construction of the equalizer fork. -/
@@ -2,11 +2,6 @@
Copyright (c) 2020 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-
-! This file was ported from Lean 3 source module order.category.omega_complete_partial_order
-! 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.Order.OmegaCompletePartialOrder
import Mathlib.CategoryTheory.Limits.Shapes.Products
@@ -14,6 +9,8 @@ import Mathlib.CategoryTheory.Limits.Shapes.Equalizers
import Mathlib.CategoryTheory.Limits.Constructions.LimitsOfProductsAndEqualizers
import Mathlib.CategoryTheory.ConcreteCategory.BundledHom
+#align_import order.category.omega_complete_partial_order from "leanprover-community/mathlib"@"70fd9563a21e7b963887c9360bd29b2393e6225a"
+
/-!
# Category of types with an omega complete partial order
@@ -15,11 +15,11 @@ import Mathlib.CategoryTheory.Limits.Constructions.LimitsOfProductsAndEqualizers
import Mathlib.CategoryTheory.ConcreteCategory.BundledHom
/-!
-# Category of types with a omega complete partial order
+# Category of types with an omega complete partial order
In this file, we bundle the class `OmegaCompletePartialOrder` into a
concrete category and prove that continuous functions also form
-a `OmegaCompletePartialOrder`.
+an `OmegaCompletePartialOrder`.
## Main definitions
@@ -35,7 +35,7 @@ universe u v
set_option linter.uppercaseLean3 false -- `ωCPO`
-/-- The category of types with a omega complete partial order. -/
+/-- The category of types with an omega complete partial order. -/
def ωCPO : Type (u + 1) :=
Bundled OmegaCompletePartialOrder
#align ωCPO ωCPO
The unported dependencies are