category_theory.subobject.well_powered
⟷
Mathlib.CategoryTheory.Subobject.WellPowered
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.Basic
-import Mathbin.CategoryTheory.EssentiallySmall
+import CategoryTheory.Subobject.Basic
+import CategoryTheory.EssentiallySmall
#align_import category_theory.subobject.well_powered from "leanprover-community/mathlib"@"ce38d86c0b2d427ce208c3cee3159cb421d2b3c4"
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.well_powered
-! leanprover-community/mathlib commit ce38d86c0b2d427ce208c3cee3159cb421d2b3c4
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.CategoryTheory.Subobject.Basic
import Mathbin.CategoryTheory.EssentiallySmall
+#align_import category_theory.subobject.well_powered from "leanprover-community/mathlib"@"ce38d86c0b2d427ce208c3cee3159cb421d2b3c4"
+
/-!
# Well-powered categories
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -95,16 +95,20 @@ section Equivalence
variable {D : Type u₂} [Category.{v} D]
+#print CategoryTheory.wellPowered_of_equiv /-
theorem wellPowered_of_equiv (e : C ≌ D) [WellPowered C] : WellPowered D :=
wellPowered_of_essentiallySmall_monoOver fun X =>
(essentiallySmall_congr (MonoOver.congr X e.symm)).2 <| by infer_instance
#align category_theory.well_powered_of_equiv CategoryTheory.wellPowered_of_equiv
+-/
+#print CategoryTheory.wellPowered_congr /-
/-- Being well-powered is preserved by equivalences, as long as the two categories involved have
their morphisms in the same universe. -/
theorem wellPowered_congr (e : C ≌ D) : WellPowered C ↔ WellPowered D :=
⟨fun i => well_powered_of_equiv e, fun i => well_powered_of_equiv e.symm⟩
#align category_theory.well_powered_congr CategoryTheory.wellPowered_congr
+-/
end Equivalence
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -95,23 +95,11 @@ section Equivalence
variable {D : Type u₂} [Category.{v} D]
-/- warning: category_theory.well_powered_of_equiv -> CategoryTheory.wellPowered_of_equiv is a dubious translation:
-lean 3 declaration is
- forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {D : Type.{u3}} [_inst_2 : CategoryTheory.Category.{u1, u3} D], (CategoryTheory.Equivalence.{u1, u1, u2, u3} C _inst_1 D _inst_2) -> (forall [_inst_3 : CategoryTheory.WellPowered.{u1, u2} C _inst_1], CategoryTheory.WellPowered.{u1, u3} D _inst_2)
-but is expected to have type
- forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {D : Type.{u3}} [_inst_2 : CategoryTheory.Category.{u1, u3} D], (CategoryTheory.Equivalence.{u1, u1, u2, u3} C D _inst_1 _inst_2) -> (forall [_inst_3 : CategoryTheory.WellPowered.{u1, u2} C _inst_1], CategoryTheory.WellPowered.{u1, u3} D _inst_2)
-Case conversion may be inaccurate. Consider using '#align category_theory.well_powered_of_equiv CategoryTheory.wellPowered_of_equivₓ'. -/
theorem wellPowered_of_equiv (e : C ≌ D) [WellPowered C] : WellPowered D :=
wellPowered_of_essentiallySmall_monoOver fun X =>
(essentiallySmall_congr (MonoOver.congr X e.symm)).2 <| by infer_instance
#align category_theory.well_powered_of_equiv CategoryTheory.wellPowered_of_equiv
-/- warning: category_theory.well_powered_congr -> CategoryTheory.wellPowered_congr is a dubious translation:
-lean 3 declaration is
- forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {D : Type.{u3}} [_inst_2 : CategoryTheory.Category.{u1, u3} D], (CategoryTheory.Equivalence.{u1, u1, u2, u3} C _inst_1 D _inst_2) -> (Iff (CategoryTheory.WellPowered.{u1, u2} C _inst_1) (CategoryTheory.WellPowered.{u1, u3} D _inst_2))
-but is expected to have type
- forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {D : Type.{u3}} [_inst_2 : CategoryTheory.Category.{u1, u3} D], (CategoryTheory.Equivalence.{u1, u1, u2, u3} C D _inst_1 _inst_2) -> (Iff (CategoryTheory.WellPowered.{u1, u2} C _inst_1) (CategoryTheory.WellPowered.{u1, u3} D _inst_2))
-Case conversion may be inaccurate. Consider using '#align category_theory.well_powered_congr CategoryTheory.wellPowered_congrₓ'. -/
/-- Being well-powered is preserved by equivalences, as long as the two categories involved have
their morphisms in the same universe. -/
theorem wellPowered_congr (e : C ≌ D) : WellPowered C ↔ WellPowered D :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/cd8fafa2fac98e1a67097e8a91ad9901cfde48af
@@ -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.well_powered
-! leanprover-community/mathlib commit 29b834dfbba4ed1b7950628bbf5e69ab98c15b4c
+! leanprover-community/mathlib commit ce38d86c0b2d427ce208c3cee3159cb421d2b3c4
! 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.EssentiallySmall
/-!
# Well-powered categories
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
A category `(C : Type u) [category.{v} C]` is `[well_powered C]` if
for every `X : C`, we have `small.{v} (subobject X)`.
mathlib commit https://github.com/leanprover-community/mathlib/commit/17ad94b4953419f3e3ce3e77da3239c62d1d09f0
@@ -36,6 +36,7 @@ namespace CategoryTheory
variable (C : Type u₁) [Category.{v} C]
+#print CategoryTheory.WellPowered /-
/--
A category (with morphisms in `Type v`) is well-powered if `subobject X` is `v`-small for every `X`.
@@ -45,34 +46,45 @@ that this is the case if and only if `mono_over X` is `v`-essentially small for
class WellPowered : Prop where
subobject_small : ∀ X : C, Small.{v} (Subobject X) := by infer_instance
#align category_theory.well_powered CategoryTheory.WellPowered
+-/
+#print CategoryTheory.small_subobject /-
instance small_subobject [WellPowered C] (X : C) : Small.{v} (Subobject X) :=
WellPowered.subobject_small X
#align category_theory.small_subobject CategoryTheory.small_subobject
+-/
+#print CategoryTheory.wellPowered_of_smallCategory /-
instance (priority := 100) wellPowered_of_smallCategory (C : Type u₁) [SmallCategory C] :
WellPowered C where
#align category_theory.well_powered_of_small_category CategoryTheory.wellPowered_of_smallCategory
+-/
variable {C}
+#print CategoryTheory.essentiallySmall_monoOver_iff_small_subobject /-
theorem essentiallySmall_monoOver_iff_small_subobject (X : C) :
EssentiallySmall.{v} (MonoOver X) ↔ Small.{v} (Subobject X) :=
essentiallySmall_iff_of_thin
#align category_theory.essentially_small_mono_over_iff_small_subobject CategoryTheory.essentiallySmall_monoOver_iff_small_subobject
+-/
+#print CategoryTheory.wellPowered_of_essentiallySmall_monoOver /-
theorem wellPowered_of_essentiallySmall_monoOver (h : ∀ X : C, EssentiallySmall.{v} (MonoOver X)) :
WellPowered C :=
{ subobject_small := fun X => (essentiallySmall_monoOver_iff_small_subobject X).mp (h X) }
#align category_theory.well_powered_of_essentially_small_mono_over CategoryTheory.wellPowered_of_essentiallySmall_monoOver
+-/
section
variable [WellPowered C]
+#print CategoryTheory.essentiallySmall_monoOver /-
instance essentiallySmall_monoOver (X : C) : EssentiallySmall.{v} (MonoOver X) :=
(essentiallySmall_monoOver_iff_small_subobject X).mpr (WellPowered.subobject_small X)
#align category_theory.essentially_small_mono_over CategoryTheory.essentiallySmall_monoOver
+-/
end
@@ -80,11 +92,23 @@ section Equivalence
variable {D : Type u₂} [Category.{v} D]
+/- warning: category_theory.well_powered_of_equiv -> CategoryTheory.wellPowered_of_equiv is a dubious translation:
+lean 3 declaration is
+ forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {D : Type.{u3}} [_inst_2 : CategoryTheory.Category.{u1, u3} D], (CategoryTheory.Equivalence.{u1, u1, u2, u3} C _inst_1 D _inst_2) -> (forall [_inst_3 : CategoryTheory.WellPowered.{u1, u2} C _inst_1], CategoryTheory.WellPowered.{u1, u3} D _inst_2)
+but is expected to have type
+ forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {D : Type.{u3}} [_inst_2 : CategoryTheory.Category.{u1, u3} D], (CategoryTheory.Equivalence.{u1, u1, u2, u3} C D _inst_1 _inst_2) -> (forall [_inst_3 : CategoryTheory.WellPowered.{u1, u2} C _inst_1], CategoryTheory.WellPowered.{u1, u3} D _inst_2)
+Case conversion may be inaccurate. Consider using '#align category_theory.well_powered_of_equiv CategoryTheory.wellPowered_of_equivₓ'. -/
theorem wellPowered_of_equiv (e : C ≌ D) [WellPowered C] : WellPowered D :=
wellPowered_of_essentiallySmall_monoOver fun X =>
(essentiallySmall_congr (MonoOver.congr X e.symm)).2 <| by infer_instance
#align category_theory.well_powered_of_equiv CategoryTheory.wellPowered_of_equiv
+/- warning: category_theory.well_powered_congr -> CategoryTheory.wellPowered_congr is a dubious translation:
+lean 3 declaration is
+ forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {D : Type.{u3}} [_inst_2 : CategoryTheory.Category.{u1, u3} D], (CategoryTheory.Equivalence.{u1, u1, u2, u3} C _inst_1 D _inst_2) -> (Iff (CategoryTheory.WellPowered.{u1, u2} C _inst_1) (CategoryTheory.WellPowered.{u1, u3} D _inst_2))
+but is expected to have type
+ forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {D : Type.{u3}} [_inst_2 : CategoryTheory.Category.{u1, u3} D], (CategoryTheory.Equivalence.{u1, u1, u2, u3} C D _inst_1 _inst_2) -> (Iff (CategoryTheory.WellPowered.{u1, u2} C _inst_1) (CategoryTheory.WellPowered.{u1, u3} D _inst_2))
+Case conversion may be inaccurate. Consider using '#align category_theory.well_powered_congr CategoryTheory.wellPowered_congrₓ'. -/
/-- Being well-powered is preserved by equivalences, as long as the two categories involved have
their morphisms in the same universe. -/
theorem wellPowered_congr (e : C ≌ D) : WellPowered C ↔ WellPowered D :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/3ade05ac9447ae31a22d2ea5423435e054131240
@@ -70,9 +70,9 @@ section
variable [WellPowered C]
-instance essentiallySmallMonoOver (X : C) : EssentiallySmall.{v} (MonoOver X) :=
+instance essentiallySmall_monoOver (X : C) : EssentiallySmall.{v} (MonoOver X) :=
(essentiallySmall_monoOver_iff_small_subobject X).mpr (WellPowered.subobject_small X)
-#align category_theory.essentially_small_mono_over CategoryTheory.essentiallySmallMonoOver
+#align category_theory.essentially_small_mono_over CategoryTheory.essentiallySmall_monoOver
end
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
@@ -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.well_powered
-! leanprover-community/mathlib commit 29b834dfbba4ed1b7950628bbf5e69ab98c15b4c
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.CategoryTheory.Subobject.Basic
import Mathlib.CategoryTheory.EssentiallySmall
+#align_import category_theory.subobject.well_powered from "leanprover-community/mathlib"@"29b834dfbba4ed1b7950628bbf5e69ab98c15b4c"
+
/-!
# Well-powered categories
I ran codespell Mathlib
and got tired halfway through the suggestions.
@@ -17,7 +17,7 @@ import Mathlib.CategoryTheory.EssentiallySmall
A category `(C : Type u) [Category.{v} C]` is `[WellPowered C]` if
for every `X : C`, we have `Small.{v} (Subobject X)`.
-(Note that in this situtation `Subobject X : Type (max u v)`,
+(Note that in this situation `Subobject X : Type (max u v)`,
so this is a nontrivial condition for large categories,
but automatic for small categories.)
All dependencies are ported!