category_theory.subobject.types
⟷
Mathlib.CategoryTheory.Subobject.Types
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 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
-import Mathbin.CategoryTheory.Subobject.WellPowered
-import Mathbin.CategoryTheory.Types
+import CategoryTheory.Subobject.WellPowered
+import CategoryTheory.Types
#align_import category_theory.subobject.types from "leanprover-community/mathlib"@"8eb9c42d4d34c77f6ee84ea766ae4070233a973c"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,15 +2,12 @@
Copyright (c) 2021 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.subobject.types
-! leanprover-community/mathlib commit 8eb9c42d4d34c77f6ee84ea766ae4070233a973c
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.CategoryTheory.Subobject.WellPowered
import Mathbin.CategoryTheory.Types
+#align_import category_theory.subobject.types from "leanprover-community/mathlib"@"8eb9c42d4d34c77f6ee84ea766ae4070233a973c"
+
/-!
# `Type u` is well-powered
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -45,6 +45,7 @@ theorem subtype_val_mono {α : Type u} (s : Set α) : Mono (↾(Subtype.val : s
attribute [local instance] subtype_val_mono
+#print Types.monoOverEquivalenceSet /-
/-- The category of `mono_over α`, for `α : Type u`, is equivalent to the partial order `set α`.
-/
@[simps]
@@ -68,6 +69,7 @@ noncomputable def Types.monoOverEquivalenceSet (α : Type u) : MonoOver α ≌ S
(by tidy)
counitIso := NatIso.ofComponents (fun s => eqToIso Subtype.range_val) (by tidy)
#align types.mono_over_equivalence_set Types.monoOverEquivalenceSet
+-/
instance : WellPowered (Type u) :=
wellPowered_of_essentiallySmall_monoOver fun α =>
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -35,7 +35,7 @@ open CategoryTheory
open CategoryTheory.Subobject
-open CategoryTheory.Type
+open scoped CategoryTheory.Type
#print subtype_val_mono /-
theorem subtype_val_mono {α : Type u} (s : Set α) : Mono (↾(Subtype.val : s → α)) :=
@@ -73,9 +73,11 @@ instance : WellPowered (Type u) :=
wellPowered_of_essentiallySmall_monoOver fun α =>
EssentiallySmall.mk' (Types.monoOverEquivalenceSet α)
+#print Types.subobjectEquivSet /-
/-- For `α : Type u`, `subobject α` is order isomorphic to `set α`.
-/
noncomputable def Types.subobjectEquivSet (α : Type u) : Subobject α ≃o Set α :=
(Types.monoOverEquivalenceSet α).thinSkeletonOrderIso
#align types.subobject_equiv_set Types.subobjectEquivSet
+-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -45,12 +45,6 @@ theorem subtype_val_mono {α : Type u} (s : Set α) : Mono (↾(Subtype.val : s
attribute [local instance] subtype_val_mono
-/- warning: types.mono_over_equivalence_set -> Types.monoOverEquivalenceSet is a dubious translation:
-lean 3 declaration is
- forall (α : Type.{u1}), CategoryTheory.Equivalence.{u1, u1, succ u1, u1} (CategoryTheory.MonoOver.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1} α) (CategoryTheory.MonoOver.category.{succ u1, u1} Type.{u1} CategoryTheory.types.{u1} α) (Set.{u1} α) (Preorder.smallCategory.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.completeBooleanAlgebra.{u1} α))))))))
-but is expected to have type
- forall (α : Type.{u1}), CategoryTheory.Equivalence.{u1, u1, succ u1, u1} (CategoryTheory.MonoOver.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1} α) (Set.{u1} α) (CategoryTheory.instCategoryMonoOver.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1} α) (Preorder.smallCategory.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α)))))))))
-Case conversion may be inaccurate. Consider using '#align types.mono_over_equivalence_set Types.monoOverEquivalenceSetₓ'. -/
/-- The category of `mono_over α`, for `α : Type u`, is equivalent to the partial order `set α`.
-/
@[simps]
@@ -79,12 +73,6 @@ instance : WellPowered (Type u) :=
wellPowered_of_essentiallySmall_monoOver fun α =>
EssentiallySmall.mk' (Types.monoOverEquivalenceSet α)
-/- warning: types.subobject_equiv_set -> Types.subobjectEquivSet is a dubious translation:
-lean 3 declaration is
- forall (α : Type.{u1}), OrderIso.{succ u1, u1} (CategoryTheory.Subobject.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1} α) (Set.{u1} α) (Preorder.toHasLe.{succ u1} (CategoryTheory.ThinSkeleton.{u1, succ u1} (CategoryTheory.MonoOver.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1} α) (CategoryTheory.MonoOver.category.{succ u1, u1} Type.{u1} CategoryTheory.types.{u1} α)) (CategoryTheory.ThinSkeleton.preorder.{u1, succ u1} (CategoryTheory.MonoOver.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1} α) (CategoryTheory.MonoOver.category.{succ u1, u1} Type.{u1} CategoryTheory.types.{u1} α))) (Set.hasLe.{u1} α)
-but is expected to have type
- forall (α : Type.{u1}), OrderIso.{succ u1, u1} (CategoryTheory.Subobject.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1} α) (Set.{u1} α) (Preorder.toLE.{succ u1} (CategoryTheory.Subobject.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1} α) (PartialOrder.toPreorder.{succ u1} (CategoryTheory.Subobject.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1} α) (CategoryTheory.instPartialOrderSubobject.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1} α))) (Set.instLESet.{u1} α)
-Case conversion may be inaccurate. Consider using '#align types.subobject_equiv_set Types.subobjectEquivSetₓ'. -/
/-- For `α : Type u`, `subobject α` is order isomorphic to `set α`.
-/
noncomputable def Types.subobjectEquivSet (α : Type u) : Subobject α ≃o Set α :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -66,10 +66,7 @@ noncomputable def Types.monoOverEquivalenceSet (α : Type u) : MonoOver α ≌ S
inverse :=
{ obj := fun s => MonoOver.mk' (Subtype.val : s → α)
map := fun s t b =>
- MonoOver.homMk (fun w => ⟨w.1, Set.mem_of_mem_of_subset w.2 b.le⟩)
- (by
- ext
- simp) }
+ MonoOver.homMk (fun w => ⟨w.1, Set.mem_of_mem_of_subset w.2 b.le⟩) (by ext; simp) }
unitIso :=
NatIso.ofComponents
(fun f =>
mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8
@@ -82,11 +82,15 @@ instance : WellPowered (Type u) :=
wellPowered_of_essentiallySmall_monoOver fun α =>
EssentiallySmall.mk' (Types.monoOverEquivalenceSet α)
-#print Types.subobjectEquivSet /-
+/- warning: types.subobject_equiv_set -> Types.subobjectEquivSet is a dubious translation:
+lean 3 declaration is
+ forall (α : Type.{u1}), OrderIso.{succ u1, u1} (CategoryTheory.Subobject.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1} α) (Set.{u1} α) (Preorder.toHasLe.{succ u1} (CategoryTheory.ThinSkeleton.{u1, succ u1} (CategoryTheory.MonoOver.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1} α) (CategoryTheory.MonoOver.category.{succ u1, u1} Type.{u1} CategoryTheory.types.{u1} α)) (CategoryTheory.ThinSkeleton.preorder.{u1, succ u1} (CategoryTheory.MonoOver.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1} α) (CategoryTheory.MonoOver.category.{succ u1, u1} Type.{u1} CategoryTheory.types.{u1} α))) (Set.hasLe.{u1} α)
+but is expected to have type
+ forall (α : Type.{u1}), OrderIso.{succ u1, u1} (CategoryTheory.Subobject.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1} α) (Set.{u1} α) (Preorder.toLE.{succ u1} (CategoryTheory.Subobject.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1} α) (PartialOrder.toPreorder.{succ u1} (CategoryTheory.Subobject.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1} α) (CategoryTheory.instPartialOrderSubobject.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1} α))) (Set.instLESet.{u1} α)
+Case conversion may be inaccurate. Consider using '#align types.subobject_equiv_set Types.subobjectEquivSetₓ'. -/
/-- For `α : Type u`, `subobject α` is order isomorphic to `set α`.
-/
noncomputable def Types.subobjectEquivSet (α : Type u) : Subobject α ≃o Set α :=
(Types.monoOverEquivalenceSet α).thinSkeletonOrderIso
#align types.subobject_equiv_set Types.subobjectEquivSet
--/
mathlib commit https://github.com/leanprover-community/mathlib/commit/730c6d4cab72b9d84fcfb9e95e8796e9cd8f40ba
@@ -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.subobject.types
-! leanprover-community/mathlib commit 610955826b3be3caaab5170fef04ecd5458521bf
+! leanprover-community/mathlib commit 8eb9c42d4d34c77f6ee84ea766ae4070233a973c
! 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.Types
/-!
# `Type u` is well-powered
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
By building a categorical equivalence `mono_over α ≌ set α` for any `α : Type u`,
we deduce that `subobject α ≃o set α` and that `Type u` is well-powered.
mathlib commit https://github.com/leanprover-community/mathlib/commit/cd8fafa2fac98e1a67097e8a91ad9901cfde48af
@@ -34,12 +34,20 @@ open CategoryTheory.Subobject
open CategoryTheory.Type
+#print subtype_val_mono /-
theorem subtype_val_mono {α : Type u} (s : Set α) : Mono (↾(Subtype.val : s → α)) :=
(mono_iff_injective _).mpr Subtype.val_injective
#align subtype_val_mono subtype_val_mono
+-/
attribute [local instance] subtype_val_mono
+/- warning: types.mono_over_equivalence_set -> Types.monoOverEquivalenceSet is a dubious translation:
+lean 3 declaration is
+ forall (α : Type.{u1}), CategoryTheory.Equivalence.{u1, u1, succ u1, u1} (CategoryTheory.MonoOver.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1} α) (CategoryTheory.MonoOver.category.{succ u1, u1} Type.{u1} CategoryTheory.types.{u1} α) (Set.{u1} α) (Preorder.smallCategory.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.completeBooleanAlgebra.{u1} α))))))))
+but is expected to have type
+ forall (α : Type.{u1}), CategoryTheory.Equivalence.{u1, u1, succ u1, u1} (CategoryTheory.MonoOver.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1} α) (Set.{u1} α) (CategoryTheory.instCategoryMonoOver.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1} α) (Preorder.smallCategory.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α)))))))))
+Case conversion may be inaccurate. Consider using '#align types.mono_over_equivalence_set Types.monoOverEquivalenceSetₓ'. -/
/-- The category of `mono_over α`, for `α : Type u`, is equivalent to the partial order `set α`.
-/
@[simps]
@@ -71,9 +79,11 @@ instance : WellPowered (Type u) :=
wellPowered_of_essentiallySmall_monoOver fun α =>
EssentiallySmall.mk' (Types.monoOverEquivalenceSet α)
+#print Types.subobjectEquivSet /-
/-- For `α : Type u`, `subobject α` is order isomorphic to `set α`.
-/
noncomputable def Types.subobjectEquivSet (α : Type u) : Subobject α ≃o Set α :=
(Types.monoOverEquivalenceSet α).thinSkeletonOrderIso
#align types.subobject_equiv_set Types.subobjectEquivSet
+-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
Subsingleton,Nontrivial
off of Data.Set.Basic
(#11832)
Moves definition of and lemmas related to Set.Subsingleton
and Set.Nontrivial
to a new file, so that Basic
can be shorter.
@@ -5,7 +5,7 @@ Authors: Scott Morrison
-/
import Mathlib.CategoryTheory.Subobject.WellPowered
import Mathlib.CategoryTheory.Types
-import Mathlib.Data.Set.Basic
+import Mathlib.Data.Set.Subsingleton
#align_import category_theory.subobject.types from "leanprover-community/mathlib"@"610955826b3be3caaab5170fef04ecd5458521bf"
Data.Set.Basic
from scripts/noshake.json
.example
s only,
move these example
s to a new test file.Order.Filter.Basic
dependency on Control.Traversable.Instances
,
as the relevant parts were moved to Order.Filter.ListTraverse
.lake exe shake --fix
.@@ -5,6 +5,7 @@ Authors: Scott Morrison
-/
import Mathlib.CategoryTheory.Subobject.WellPowered
import Mathlib.CategoryTheory.Types
+import Mathlib.Data.Set.Basic
#align_import category_theory.subobject.types from "leanprover-community/mathlib"@"610955826b3be3caaab5170fef04ecd5458521bf"
@@ -2,15 +2,12 @@
Copyright (c) 2021 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.subobject.types
-! leanprover-community/mathlib commit 610955826b3be3caaab5170fef04ecd5458521bf
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.CategoryTheory.Subobject.WellPowered
import Mathlib.CategoryTheory.Types
+#align_import category_theory.subobject.types from "leanprover-community/mathlib"@"610955826b3be3caaab5170fef04ecd5458521bf"
+
/-!
# `Type u` is well-powered
@@ -51,18 +51,11 @@ noncomputable def Types.monoOverEquivalenceSet (α : Type u) : MonoOver α ≌ S
exact ⟨t.1 x, congr_fun t.w x⟩) }
inverse :=
{ obj := fun s => MonoOver.mk' (Subtype.val : s → α)
- map := fun {s t} b =>
- MonoOver.homMk (fun w => ⟨w.1, Set.mem_of_mem_of_subset w.2 b.le⟩)
- (by
- funext
- simp) }
+ map := fun {s t} b => MonoOver.homMk (fun w => ⟨w.1, Set.mem_of_mem_of_subset w.2 b.le⟩) }
unitIso :=
- NatIso.ofComponents
- (fun f =>
- MonoOver.isoMk (Equiv.ofInjective f.1.hom ((mono_iff_injective _).mp f.2)).toIso
- (by aesop_cat))
- (by aesop_cat)
- counitIso := NatIso.ofComponents (fun s => eqToIso Subtype.range_val) (by aesop_cat)
+ NatIso.ofComponents fun f =>
+ MonoOver.isoMk (Equiv.ofInjective f.1.hom ((mono_iff_injective _).mp f.2)).toIso
+ counitIso := NatIso.ofComponents fun s => eqToIso Subtype.range_val
#align types.mono_over_equivalence_set Types.monoOverEquivalenceSet
instance : WellPowered (Type u) :=
All dependencies are ported!