algebra.category.Group.Z_Module_equivalence
⟷
Mathlib.Algebra.Category.GroupCat.ZModuleEquivalence
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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(last sync)
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -28,9 +28,9 @@ universe u
namespace ModuleCat
-#print ModuleCat.forget₂AddCommGroupFull /-
+#print ModuleCat.forget₂_addCommGroup_full /-
/-- The forgetful functor from `ℤ` modules to `AddCommGroup` is full. -/
-instance forget₂AddCommGroupFull :
+instance forget₂_addCommGroup_full :
CategoryTheory.Functor.Full (forget₂ (ModuleCat ℤ) AddCommGroupCat.{u})
where preimage A B
f :=-- `add_monoid_hom.to_int_linear_map` doesn't work here because `A` and `B` are not definitionally
@@ -39,7 +39,7 @@ instance forget₂AddCommGroupFull :
map_add' := AddMonoidHom.map_add f
map_smul' := fun n x => by
rw [int_smul_eq_zsmul, int_smul_eq_zsmul, map_zsmul, RingHom.id_apply] }
-#align Module.forget₂_AddCommGroup_full ModuleCat.forget₂AddCommGroupFull
+#align Module.forget₂_AddCommGroup_full ModuleCat.forget₂_addCommGroup_full
-/
#print ModuleCat.forget₂_addCommGroupCat_essSurj /-
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -30,7 +30,8 @@ namespace ModuleCat
#print ModuleCat.forget₂AddCommGroupFull /-
/-- The forgetful functor from `ℤ` modules to `AddCommGroup` is full. -/
-instance forget₂AddCommGroupFull : Full (forget₂ (ModuleCat ℤ) AddCommGroupCat.{u})
+instance forget₂AddCommGroupFull :
+ CategoryTheory.Functor.Full (forget₂ (ModuleCat ℤ) AddCommGroupCat.{u})
where preimage A B
f :=-- `add_monoid_hom.to_int_linear_map` doesn't work here because `A` and `B` are not definitionally
-- equal to the canonical `add_comm_group.int_module` module instances it expects.
@@ -43,7 +44,8 @@ instance forget₂AddCommGroupFull : Full (forget₂ (ModuleCat ℤ) AddCommGrou
#print ModuleCat.forget₂_addCommGroupCat_essSurj /-
/-- The forgetful functor from `ℤ` modules to `AddCommGroup` is essentially surjective. -/
-instance forget₂_addCommGroupCat_essSurj : EssSurj (forget₂ (ModuleCat ℤ) AddCommGroupCat.{u})
+instance forget₂_addCommGroupCat_essSurj :
+ CategoryTheory.Functor.EssSurj (forget₂ (ModuleCat ℤ) AddCommGroupCat.{u})
where mem_essImage A :=
⟨ModuleCat.of ℤ A,
⟨{ Hom := 𝟙 A
@@ -53,8 +55,9 @@ instance forget₂_addCommGroupCat_essSurj : EssSurj (forget₂ (ModuleCat ℤ)
#print ModuleCat.forget₂AddCommGroupIsEquivalence /-
noncomputable instance forget₂AddCommGroupIsEquivalence :
- IsEquivalence (forget₂ (ModuleCat ℤ) AddCommGroupCat.{u}) :=
- Equivalence.ofFullyFaithfullyEssSurj (forget₂ (ModuleCat ℤ) AddCommGroupCat)
+ CategoryTheory.Functor.IsEquivalence (forget₂ (ModuleCat ℤ) AddCommGroupCat.{u}) :=
+ CategoryTheory.Functor.IsEquivalence.ofFullyFaithfullyEssSurj
+ (forget₂ (ModuleCat ℤ) AddCommGroupCat)
#align Module.forget₂_AddCommGroup_is_equivalence ModuleCat.forget₂AddCommGroupIsEquivalence
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -3,7 +3,7 @@ Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
-import Algebra.Category.Module.Basic
+import Algebra.Category.ModuleCat.Basic
#align_import algebra.category.Group.Z_Module_equivalence from "leanprover-community/mathlib"@"ef55335933293309ff8c0b1d20ffffeecbe5c39f"
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,7 +3,7 @@ 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.Algebra.Category.Module.Basic
+import Algebra.Category.Module.Basic
#align_import algebra.category.Group.Z_Module_equivalence from "leanprover-community/mathlib"@"ef55335933293309ff8c0b1d20ffffeecbe5c39f"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,14 +2,11 @@
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 algebra.category.Group.Z_Module_equivalence
-! leanprover-community/mathlib commit ef55335933293309ff8c0b1d20ffffeecbe5c39f
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.Algebra.Category.Module.Basic
+#align_import algebra.category.Group.Z_Module_equivalence from "leanprover-community/mathlib"@"ef55335933293309ff8c0b1d20ffffeecbe5c39f"
+
/-!
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corresponding PR to mathlib4.
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -31,6 +31,7 @@ universe u
namespace ModuleCat
+#print ModuleCat.forget₂AddCommGroupFull /-
/-- The forgetful functor from `ℤ` modules to `AddCommGroup` is full. -/
instance forget₂AddCommGroupFull : Full (forget₂ (ModuleCat ℤ) AddCommGroupCat.{u})
where preimage A B
@@ -41,7 +42,9 @@ instance forget₂AddCommGroupFull : Full (forget₂ (ModuleCat ℤ) AddCommGrou
map_smul' := fun n x => by
rw [int_smul_eq_zsmul, int_smul_eq_zsmul, map_zsmul, RingHom.id_apply] }
#align Module.forget₂_AddCommGroup_full ModuleCat.forget₂AddCommGroupFull
+-/
+#print ModuleCat.forget₂_addCommGroupCat_essSurj /-
/-- The forgetful functor from `ℤ` modules to `AddCommGroup` is essentially surjective. -/
instance forget₂_addCommGroupCat_essSurj : EssSurj (forget₂ (ModuleCat ℤ) AddCommGroupCat.{u})
where mem_essImage A :=
@@ -49,11 +52,14 @@ instance forget₂_addCommGroupCat_essSurj : EssSurj (forget₂ (ModuleCat ℤ)
⟨{ Hom := 𝟙 A
inv := 𝟙 A }⟩⟩
#align Module.forget₂_AddCommGroup_ess_surj ModuleCat.forget₂_addCommGroupCat_essSurj
+-/
+#print ModuleCat.forget₂AddCommGroupIsEquivalence /-
noncomputable instance forget₂AddCommGroupIsEquivalence :
IsEquivalence (forget₂ (ModuleCat ℤ) AddCommGroupCat.{u}) :=
Equivalence.ofFullyFaithfullyEssSurj (forget₂ (ModuleCat ℤ) AddCommGroupCat)
#align Module.forget₂_AddCommGroup_is_equivalence ModuleCat.forget₂AddCommGroupIsEquivalence
+-/
end ModuleCat
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -31,12 +31,6 @@ universe u
namespace ModuleCat
-/- warning: Module.forget₂_AddCommGroup_full -> ModuleCat.forget₂AddCommGroupFull is a dubious translation:
-lean 3 declaration is
- CategoryTheory.Full.{u1, u1, succ u1, succ u1} (ModuleCat.{u1, 0} Int Int.ring) (ModuleCat.moduleCategory.{u1, 0} Int Int.ring) AddCommGroupCat.{u1} AddCommGroupCat.largeCategory.{u1} (CategoryTheory.forget₂.{succ u1, succ u1, u1, u1, u1} (ModuleCat.{u1, 0} Int Int.ring) AddCommGroupCat.{u1} (ModuleCat.moduleCategory.{u1, 0} Int Int.ring) (ModuleCat.moduleConcreteCategory.{u1, 0} Int Int.ring) AddCommGroupCat.largeCategory.{u1} AddCommGroupCat.concreteCategory.{u1} (ModuleCat.hasForgetToAddCommGroup.{0, u1} Int Int.ring))
-but is expected to have type
- CategoryTheory.Full.{u1, u1, succ u1, succ u1} (ModuleCat.{u1, 0} Int Int.instRingInt) (ModuleCat.moduleCategory.{u1, 0} Int Int.instRingInt) AddCommGroupCat.{u1} instAddCommGroupCatLargeCategory.{u1} (CategoryTheory.forget₂.{succ u1, succ u1, u1, u1, u1} (ModuleCat.{u1, 0} Int Int.instRingInt) AddCommGroupCat.{u1} (ModuleCat.moduleCategory.{u1, 0} Int Int.instRingInt) (ModuleCat.moduleConcreteCategory.{u1, 0} Int Int.instRingInt) instAddCommGroupCatLargeCategory.{u1} AddCommGroupCat.concreteCategory.{u1} (ModuleCat.hasForgetToAddCommGroup.{0, u1} Int Int.instRingInt))
-Case conversion may be inaccurate. Consider using '#align Module.forget₂_AddCommGroup_full ModuleCat.forget₂AddCommGroupFullₓ'. -/
/-- The forgetful functor from `ℤ` modules to `AddCommGroup` is full. -/
instance forget₂AddCommGroupFull : Full (forget₂ (ModuleCat ℤ) AddCommGroupCat.{u})
where preimage A B
@@ -48,12 +42,6 @@ instance forget₂AddCommGroupFull : Full (forget₂ (ModuleCat ℤ) AddCommGrou
rw [int_smul_eq_zsmul, int_smul_eq_zsmul, map_zsmul, RingHom.id_apply] }
#align Module.forget₂_AddCommGroup_full ModuleCat.forget₂AddCommGroupFull
-/- warning: Module.forget₂_AddCommGroup_ess_surj -> ModuleCat.forget₂_addCommGroupCat_essSurj is a dubious translation:
-lean 3 declaration is
- CategoryTheory.EssSurj.{u1, u1, succ u1, succ u1} (ModuleCat.{u1, 0} Int Int.ring) AddCommGroupCat.{u1} (ModuleCat.moduleCategory.{u1, 0} Int Int.ring) AddCommGroupCat.largeCategory.{u1} (CategoryTheory.forget₂.{succ u1, succ u1, u1, u1, u1} (ModuleCat.{u1, 0} Int Int.ring) AddCommGroupCat.{u1} (ModuleCat.moduleCategory.{u1, 0} Int Int.ring) (ModuleCat.moduleConcreteCategory.{u1, 0} Int Int.ring) AddCommGroupCat.largeCategory.{u1} AddCommGroupCat.concreteCategory.{u1} (ModuleCat.hasForgetToAddCommGroup.{0, u1} Int Int.ring))
-but is expected to have type
- CategoryTheory.EssSurj.{u1, u1, succ u1, succ u1} (ModuleCat.{u1, 0} Int Int.instRingInt) AddCommGroupCat.{u1} (ModuleCat.moduleCategory.{u1, 0} Int Int.instRingInt) instAddCommGroupCatLargeCategory.{u1} (CategoryTheory.forget₂.{succ u1, succ u1, u1, u1, u1} (ModuleCat.{u1, 0} Int Int.instRingInt) AddCommGroupCat.{u1} (ModuleCat.moduleCategory.{u1, 0} Int Int.instRingInt) (ModuleCat.moduleConcreteCategory.{u1, 0} Int Int.instRingInt) instAddCommGroupCatLargeCategory.{u1} AddCommGroupCat.concreteCategory.{u1} (ModuleCat.hasForgetToAddCommGroup.{0, u1} Int Int.instRingInt))
-Case conversion may be inaccurate. Consider using '#align Module.forget₂_AddCommGroup_ess_surj ModuleCat.forget₂_addCommGroupCat_essSurjₓ'. -/
/-- The forgetful functor from `ℤ` modules to `AddCommGroup` is essentially surjective. -/
instance forget₂_addCommGroupCat_essSurj : EssSurj (forget₂ (ModuleCat ℤ) AddCommGroupCat.{u})
where mem_essImage A :=
@@ -62,12 +50,6 @@ instance forget₂_addCommGroupCat_essSurj : EssSurj (forget₂ (ModuleCat ℤ)
inv := 𝟙 A }⟩⟩
#align Module.forget₂_AddCommGroup_ess_surj ModuleCat.forget₂_addCommGroupCat_essSurj
-/- warning: Module.forget₂_AddCommGroup_is_equivalence -> ModuleCat.forget₂AddCommGroupIsEquivalence is a dubious translation:
-lean 3 declaration is
- CategoryTheory.IsEquivalence.{u1, u1, succ u1, succ u1} (ModuleCat.{u1, 0} Int Int.ring) (ModuleCat.moduleCategory.{u1, 0} Int Int.ring) AddCommGroupCat.{u1} AddCommGroupCat.largeCategory.{u1} (CategoryTheory.forget₂.{succ u1, succ u1, u1, u1, u1} (ModuleCat.{u1, 0} Int Int.ring) AddCommGroupCat.{u1} (ModuleCat.moduleCategory.{u1, 0} Int Int.ring) (ModuleCat.moduleConcreteCategory.{u1, 0} Int Int.ring) AddCommGroupCat.largeCategory.{u1} AddCommGroupCat.concreteCategory.{u1} (ModuleCat.hasForgetToAddCommGroup.{0, u1} Int Int.ring))
-but is expected to have type
- CategoryTheory.IsEquivalence.{u1, u1, succ u1, succ u1} (ModuleCat.{u1, 0} Int Int.instRingInt) (ModuleCat.moduleCategory.{u1, 0} Int Int.instRingInt) AddCommGroupCat.{u1} instAddCommGroupCatLargeCategory.{u1} (CategoryTheory.forget₂.{succ u1, succ u1, u1, u1, u1} (ModuleCat.{u1, 0} Int Int.instRingInt) AddCommGroupCat.{u1} (ModuleCat.moduleCategory.{u1, 0} Int Int.instRingInt) (ModuleCat.moduleConcreteCategory.{u1, 0} Int Int.instRingInt) instAddCommGroupCatLargeCategory.{u1} AddCommGroupCat.concreteCategory.{u1} (ModuleCat.hasForgetToAddCommGroup.{0, u1} Int Int.instRingInt))
-Case conversion may be inaccurate. Consider using '#align Module.forget₂_AddCommGroup_is_equivalence ModuleCat.forget₂AddCommGroupIsEquivalenceₓ'. -/
noncomputable instance forget₂AddCommGroupIsEquivalence :
IsEquivalence (forget₂ (ModuleCat ℤ) AddCommGroupCat.{u}) :=
Equivalence.ofFullyFaithfullyEssSurj (forget₂ (ModuleCat ℤ) AddCommGroupCat)
mathlib commit https://github.com/leanprover-community/mathlib/commit/2f8347015b12b0864dfaf366ec4909eb70c78740
@@ -35,7 +35,7 @@ namespace ModuleCat
lean 3 declaration is
CategoryTheory.Full.{u1, u1, succ u1, succ u1} (ModuleCat.{u1, 0} Int Int.ring) (ModuleCat.moduleCategory.{u1, 0} Int Int.ring) AddCommGroupCat.{u1} AddCommGroupCat.largeCategory.{u1} (CategoryTheory.forget₂.{succ u1, succ u1, u1, u1, u1} (ModuleCat.{u1, 0} Int Int.ring) AddCommGroupCat.{u1} (ModuleCat.moduleCategory.{u1, 0} Int Int.ring) (ModuleCat.moduleConcreteCategory.{u1, 0} Int Int.ring) AddCommGroupCat.largeCategory.{u1} AddCommGroupCat.concreteCategory.{u1} (ModuleCat.hasForgetToAddCommGroup.{0, u1} Int Int.ring))
but is expected to have type
- CategoryTheory.Full.{u1, u1, succ u1, succ u1} (ModuleCat.{u1, 0} Int Int.instRingInt) (ModuleCat.moduleCategory.{u1, 0} Int Int.instRingInt) AddCommGroupCat.{u1} AddCommGroupCat.largeCategory.{u1} (CategoryTheory.forget₂.{succ u1, succ u1, u1, u1, u1} (ModuleCat.{u1, 0} Int Int.instRingInt) AddCommGroupCat.{u1} (ModuleCat.moduleCategory.{u1, 0} Int Int.instRingInt) (ModuleCat.moduleConcreteCategory.{u1, 0} Int Int.instRingInt) AddCommGroupCat.largeCategory.{u1} AddCommGroupCat.concreteCategory.{u1} (ModuleCat.hasForgetToAddCommGroup.{0, u1} Int Int.instRingInt))
+ CategoryTheory.Full.{u1, u1, succ u1, succ u1} (ModuleCat.{u1, 0} Int Int.instRingInt) (ModuleCat.moduleCategory.{u1, 0} Int Int.instRingInt) AddCommGroupCat.{u1} instAddCommGroupCatLargeCategory.{u1} (CategoryTheory.forget₂.{succ u1, succ u1, u1, u1, u1} (ModuleCat.{u1, 0} Int Int.instRingInt) AddCommGroupCat.{u1} (ModuleCat.moduleCategory.{u1, 0} Int Int.instRingInt) (ModuleCat.moduleConcreteCategory.{u1, 0} Int Int.instRingInt) instAddCommGroupCatLargeCategory.{u1} AddCommGroupCat.concreteCategory.{u1} (ModuleCat.hasForgetToAddCommGroup.{0, u1} Int Int.instRingInt))
Case conversion may be inaccurate. Consider using '#align Module.forget₂_AddCommGroup_full ModuleCat.forget₂AddCommGroupFullₓ'. -/
/-- The forgetful functor from `ℤ` modules to `AddCommGroup` is full. -/
instance forget₂AddCommGroupFull : Full (forget₂ (ModuleCat ℤ) AddCommGroupCat.{u})
@@ -52,7 +52,7 @@ instance forget₂AddCommGroupFull : Full (forget₂ (ModuleCat ℤ) AddCommGrou
lean 3 declaration is
CategoryTheory.EssSurj.{u1, u1, succ u1, succ u1} (ModuleCat.{u1, 0} Int Int.ring) AddCommGroupCat.{u1} (ModuleCat.moduleCategory.{u1, 0} Int Int.ring) AddCommGroupCat.largeCategory.{u1} (CategoryTheory.forget₂.{succ u1, succ u1, u1, u1, u1} (ModuleCat.{u1, 0} Int Int.ring) AddCommGroupCat.{u1} (ModuleCat.moduleCategory.{u1, 0} Int Int.ring) (ModuleCat.moduleConcreteCategory.{u1, 0} Int Int.ring) AddCommGroupCat.largeCategory.{u1} AddCommGroupCat.concreteCategory.{u1} (ModuleCat.hasForgetToAddCommGroup.{0, u1} Int Int.ring))
but is expected to have type
- CategoryTheory.EssSurj.{u1, u1, succ u1, succ u1} (ModuleCat.{u1, 0} Int Int.instRingInt) AddCommGroupCat.{u1} (ModuleCat.moduleCategory.{u1, 0} Int Int.instRingInt) AddCommGroupCat.largeCategory.{u1} (CategoryTheory.forget₂.{succ u1, succ u1, u1, u1, u1} (ModuleCat.{u1, 0} Int Int.instRingInt) AddCommGroupCat.{u1} (ModuleCat.moduleCategory.{u1, 0} Int Int.instRingInt) (ModuleCat.moduleConcreteCategory.{u1, 0} Int Int.instRingInt) AddCommGroupCat.largeCategory.{u1} AddCommGroupCat.concreteCategory.{u1} (ModuleCat.hasForgetToAddCommGroup.{0, u1} Int Int.instRingInt))
+ CategoryTheory.EssSurj.{u1, u1, succ u1, succ u1} (ModuleCat.{u1, 0} Int Int.instRingInt) AddCommGroupCat.{u1} (ModuleCat.moduleCategory.{u1, 0} Int Int.instRingInt) instAddCommGroupCatLargeCategory.{u1} (CategoryTheory.forget₂.{succ u1, succ u1, u1, u1, u1} (ModuleCat.{u1, 0} Int Int.instRingInt) AddCommGroupCat.{u1} (ModuleCat.moduleCategory.{u1, 0} Int Int.instRingInt) (ModuleCat.moduleConcreteCategory.{u1, 0} Int Int.instRingInt) instAddCommGroupCatLargeCategory.{u1} AddCommGroupCat.concreteCategory.{u1} (ModuleCat.hasForgetToAddCommGroup.{0, u1} Int Int.instRingInt))
Case conversion may be inaccurate. Consider using '#align Module.forget₂_AddCommGroup_ess_surj ModuleCat.forget₂_addCommGroupCat_essSurjₓ'. -/
/-- The forgetful functor from `ℤ` modules to `AddCommGroup` is essentially surjective. -/
instance forget₂_addCommGroupCat_essSurj : EssSurj (forget₂ (ModuleCat ℤ) AddCommGroupCat.{u})
@@ -66,7 +66,7 @@ instance forget₂_addCommGroupCat_essSurj : EssSurj (forget₂ (ModuleCat ℤ)
lean 3 declaration is
CategoryTheory.IsEquivalence.{u1, u1, succ u1, succ u1} (ModuleCat.{u1, 0} Int Int.ring) (ModuleCat.moduleCategory.{u1, 0} Int Int.ring) AddCommGroupCat.{u1} AddCommGroupCat.largeCategory.{u1} (CategoryTheory.forget₂.{succ u1, succ u1, u1, u1, u1} (ModuleCat.{u1, 0} Int Int.ring) AddCommGroupCat.{u1} (ModuleCat.moduleCategory.{u1, 0} Int Int.ring) (ModuleCat.moduleConcreteCategory.{u1, 0} Int Int.ring) AddCommGroupCat.largeCategory.{u1} AddCommGroupCat.concreteCategory.{u1} (ModuleCat.hasForgetToAddCommGroup.{0, u1} Int Int.ring))
but is expected to have type
- CategoryTheory.IsEquivalence.{u1, u1, succ u1, succ u1} (ModuleCat.{u1, 0} Int Int.instRingInt) (ModuleCat.moduleCategory.{u1, 0} Int Int.instRingInt) AddCommGroupCat.{u1} AddCommGroupCat.largeCategory.{u1} (CategoryTheory.forget₂.{succ u1, succ u1, u1, u1, u1} (ModuleCat.{u1, 0} Int Int.instRingInt) AddCommGroupCat.{u1} (ModuleCat.moduleCategory.{u1, 0} Int Int.instRingInt) (ModuleCat.moduleConcreteCategory.{u1, 0} Int Int.instRingInt) AddCommGroupCat.largeCategory.{u1} AddCommGroupCat.concreteCategory.{u1} (ModuleCat.hasForgetToAddCommGroup.{0, u1} Int Int.instRingInt))
+ CategoryTheory.IsEquivalence.{u1, u1, succ u1, succ u1} (ModuleCat.{u1, 0} Int Int.instRingInt) (ModuleCat.moduleCategory.{u1, 0} Int Int.instRingInt) AddCommGroupCat.{u1} instAddCommGroupCatLargeCategory.{u1} (CategoryTheory.forget₂.{succ u1, succ u1, u1, u1, u1} (ModuleCat.{u1, 0} Int Int.instRingInt) AddCommGroupCat.{u1} (ModuleCat.moduleCategory.{u1, 0} Int Int.instRingInt) (ModuleCat.moduleConcreteCategory.{u1, 0} Int Int.instRingInt) instAddCommGroupCatLargeCategory.{u1} AddCommGroupCat.concreteCategory.{u1} (ModuleCat.hasForgetToAddCommGroup.{0, u1} Int Int.instRingInt))
Case conversion may be inaccurate. Consider using '#align Module.forget₂_AddCommGroup_is_equivalence ModuleCat.forget₂AddCommGroupIsEquivalenceₓ'. -/
noncomputable instance forget₂AddCommGroupIsEquivalence :
IsEquivalence (forget₂ (ModuleCat ℤ) AddCommGroupCat.{u}) :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/36b8aa61ea7c05727161f96a0532897bd72aedab
@@ -4,13 +4,16 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
! This file was ported from Lean 3 source module algebra.category.Group.Z_Module_equivalence
-! leanprover-community/mathlib commit bf1b813e20e108e8868341ca94bb3404a2506ae5
+! leanprover-community/mathlib commit ef55335933293309ff8c0b1d20ffffeecbe5c39f
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
import Mathbin.Algebra.Category.Module.Basic
/-!
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
The forgetful functor from ℤ-modules to additive commutative groups is
an equivalence of categories.
mathlib commit https://github.com/leanprover-community/mathlib/commit/a4f99eae998680d3a2c240da4a2b16354c85ee49
@@ -28,6 +28,12 @@ universe u
namespace ModuleCat
+/- warning: Module.forget₂_AddCommGroup_full -> ModuleCat.forget₂AddCommGroupFull is a dubious translation:
+lean 3 declaration is
+ CategoryTheory.Full.{u1, u1, succ u1, succ u1} (ModuleCat.{u1, 0} Int Int.ring) (ModuleCat.moduleCategory.{u1, 0} Int Int.ring) AddCommGroupCat.{u1} AddCommGroupCat.largeCategory.{u1} (CategoryTheory.forget₂.{succ u1, succ u1, u1, u1, u1} (ModuleCat.{u1, 0} Int Int.ring) AddCommGroupCat.{u1} (ModuleCat.moduleCategory.{u1, 0} Int Int.ring) (ModuleCat.moduleConcreteCategory.{u1, 0} Int Int.ring) AddCommGroupCat.largeCategory.{u1} AddCommGroupCat.concreteCategory.{u1} (ModuleCat.hasForgetToAddCommGroup.{0, u1} Int Int.ring))
+but is expected to have type
+ CategoryTheory.Full.{u1, u1, succ u1, succ u1} (ModuleCat.{u1, 0} Int Int.instRingInt) (ModuleCat.moduleCategory.{u1, 0} Int Int.instRingInt) AddCommGroupCat.{u1} AddCommGroupCat.largeCategory.{u1} (CategoryTheory.forget₂.{succ u1, succ u1, u1, u1, u1} (ModuleCat.{u1, 0} Int Int.instRingInt) AddCommGroupCat.{u1} (ModuleCat.moduleCategory.{u1, 0} Int Int.instRingInt) (ModuleCat.moduleConcreteCategory.{u1, 0} Int Int.instRingInt) AddCommGroupCat.largeCategory.{u1} AddCommGroupCat.concreteCategory.{u1} (ModuleCat.hasForgetToAddCommGroup.{0, u1} Int Int.instRingInt))
+Case conversion may be inaccurate. Consider using '#align Module.forget₂_AddCommGroup_full ModuleCat.forget₂AddCommGroupFullₓ'. -/
/-- The forgetful functor from `ℤ` modules to `AddCommGroup` is full. -/
instance forget₂AddCommGroupFull : Full (forget₂ (ModuleCat ℤ) AddCommGroupCat.{u})
where preimage A B
@@ -39,6 +45,12 @@ instance forget₂AddCommGroupFull : Full (forget₂ (ModuleCat ℤ) AddCommGrou
rw [int_smul_eq_zsmul, int_smul_eq_zsmul, map_zsmul, RingHom.id_apply] }
#align Module.forget₂_AddCommGroup_full ModuleCat.forget₂AddCommGroupFull
+/- warning: Module.forget₂_AddCommGroup_ess_surj -> ModuleCat.forget₂_addCommGroupCat_essSurj is a dubious translation:
+lean 3 declaration is
+ CategoryTheory.EssSurj.{u1, u1, succ u1, succ u1} (ModuleCat.{u1, 0} Int Int.ring) AddCommGroupCat.{u1} (ModuleCat.moduleCategory.{u1, 0} Int Int.ring) AddCommGroupCat.largeCategory.{u1} (CategoryTheory.forget₂.{succ u1, succ u1, u1, u1, u1} (ModuleCat.{u1, 0} Int Int.ring) AddCommGroupCat.{u1} (ModuleCat.moduleCategory.{u1, 0} Int Int.ring) (ModuleCat.moduleConcreteCategory.{u1, 0} Int Int.ring) AddCommGroupCat.largeCategory.{u1} AddCommGroupCat.concreteCategory.{u1} (ModuleCat.hasForgetToAddCommGroup.{0, u1} Int Int.ring))
+but is expected to have type
+ CategoryTheory.EssSurj.{u1, u1, succ u1, succ u1} (ModuleCat.{u1, 0} Int Int.instRingInt) AddCommGroupCat.{u1} (ModuleCat.moduleCategory.{u1, 0} Int Int.instRingInt) AddCommGroupCat.largeCategory.{u1} (CategoryTheory.forget₂.{succ u1, succ u1, u1, u1, u1} (ModuleCat.{u1, 0} Int Int.instRingInt) AddCommGroupCat.{u1} (ModuleCat.moduleCategory.{u1, 0} Int Int.instRingInt) (ModuleCat.moduleConcreteCategory.{u1, 0} Int Int.instRingInt) AddCommGroupCat.largeCategory.{u1} AddCommGroupCat.concreteCategory.{u1} (ModuleCat.hasForgetToAddCommGroup.{0, u1} Int Int.instRingInt))
+Case conversion may be inaccurate. Consider using '#align Module.forget₂_AddCommGroup_ess_surj ModuleCat.forget₂_addCommGroupCat_essSurjₓ'. -/
/-- The forgetful functor from `ℤ` modules to `AddCommGroup` is essentially surjective. -/
instance forget₂_addCommGroupCat_essSurj : EssSurj (forget₂ (ModuleCat ℤ) AddCommGroupCat.{u})
where mem_essImage A :=
@@ -47,6 +59,12 @@ instance forget₂_addCommGroupCat_essSurj : EssSurj (forget₂ (ModuleCat ℤ)
inv := 𝟙 A }⟩⟩
#align Module.forget₂_AddCommGroup_ess_surj ModuleCat.forget₂_addCommGroupCat_essSurj
+/- warning: Module.forget₂_AddCommGroup_is_equivalence -> ModuleCat.forget₂AddCommGroupIsEquivalence is a dubious translation:
+lean 3 declaration is
+ CategoryTheory.IsEquivalence.{u1, u1, succ u1, succ u1} (ModuleCat.{u1, 0} Int Int.ring) (ModuleCat.moduleCategory.{u1, 0} Int Int.ring) AddCommGroupCat.{u1} AddCommGroupCat.largeCategory.{u1} (CategoryTheory.forget₂.{succ u1, succ u1, u1, u1, u1} (ModuleCat.{u1, 0} Int Int.ring) AddCommGroupCat.{u1} (ModuleCat.moduleCategory.{u1, 0} Int Int.ring) (ModuleCat.moduleConcreteCategory.{u1, 0} Int Int.ring) AddCommGroupCat.largeCategory.{u1} AddCommGroupCat.concreteCategory.{u1} (ModuleCat.hasForgetToAddCommGroup.{0, u1} Int Int.ring))
+but is expected to have type
+ CategoryTheory.IsEquivalence.{u1, u1, succ u1, succ u1} (ModuleCat.{u1, 0} Int Int.instRingInt) (ModuleCat.moduleCategory.{u1, 0} Int Int.instRingInt) AddCommGroupCat.{u1} AddCommGroupCat.largeCategory.{u1} (CategoryTheory.forget₂.{succ u1, succ u1, u1, u1, u1} (ModuleCat.{u1, 0} Int Int.instRingInt) AddCommGroupCat.{u1} (ModuleCat.moduleCategory.{u1, 0} Int Int.instRingInt) (ModuleCat.moduleConcreteCategory.{u1, 0} Int Int.instRingInt) AddCommGroupCat.largeCategory.{u1} AddCommGroupCat.concreteCategory.{u1} (ModuleCat.hasForgetToAddCommGroup.{0, u1} Int Int.instRingInt))
+Case conversion may be inaccurate. Consider using '#align Module.forget₂_AddCommGroup_is_equivalence ModuleCat.forget₂AddCommGroupIsEquivalenceₓ'. -/
noncomputable instance forget₂AddCommGroupIsEquivalence :
IsEquivalence (forget₂ (ModuleCat ℤ) AddCommGroupCat.{u}) :=
Equivalence.ofFullyFaithfullyEssSurj (forget₂ (ModuleCat ℤ) AddCommGroupCat)
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
Functor.Full
a Prop (#12449)
Before this PR, Functor.Full
contained the data of the preimage of maps by a full functor F
. This PR makes Functor.Full
a proposition. This is to prevent any diamond to appear.
The lemma Functor.image_preimage
is also renamed Functor.map_preimage
.
Co-authored-by: Joël Riou <37772949+joelriou@users.noreply.github.com>
@@ -26,19 +26,19 @@ universe u
namespace ModuleCat
/-- The forgetful functor from `ℤ` modules to `AddCommGroup` is full. -/
-instance forget₂AddCommGroupFull : (forget₂ (ModuleCat ℤ) AddCommGroupCat.{u}).Full where
- preimage {A B}
+instance forget₂_addCommGroup_full : (forget₂ (ModuleCat ℤ) AddCommGroupCat.{u}).Full where
+ map_surjective {A B}
-- `AddMonoidHom.toIntLinearMap` doesn't work here because `A` and `B` are not
-- definitionally equal to the canonical `AddCommGroup.intModule` module
-- instances it expects.
- f := @LinearMap.mk _ _ _ _ _ _ _ _ _ A.isModule B.isModule
+ f := ⟨@LinearMap.mk _ _ _ _ _ _ _ _ _ A.isModule B.isModule
{ toFun := f,
map_add' := AddMonoidHom.map_add (show A.carrier →+ B.carrier from f) }
(fun n x => by
convert AddMonoidHom.map_zsmul (show A.carrier →+ B.carrier from f) x n <;>
- ext <;> apply int_smul_eq_zsmul)
+ ext <;> apply int_smul_eq_zsmul), rfl⟩
set_option linter.uppercaseLean3 false in
-#align Module.forget₂_AddCommGroup_full ModuleCat.forget₂AddCommGroupFull
+#align Module.forget₂_AddCommGroup_full ModuleCat.forget₂_addCommGroup_full
/-- The forgetful functor from `ℤ` modules to `AddCommGroup` is essentially surjective. -/
instance forget₂_addCommGroupCat_essSurj : (forget₂ (ModuleCat ℤ) AddCommGroupCat.{u}).EssSurj where
These notions on functors are now Functor.Full
, Functor.Faithful
, Functor.EssSurj
, Functor.IsEquivalence
, Functor.ReflectsIsomorphisms
. Deprecated aliases are introduced for the previous names.
@@ -26,7 +26,7 @@ universe u
namespace ModuleCat
/-- The forgetful functor from `ℤ` modules to `AddCommGroup` is full. -/
-instance forget₂AddCommGroupFull : Full (forget₂ (ModuleCat ℤ) AddCommGroupCat.{u}) where
+instance forget₂AddCommGroupFull : (forget₂ (ModuleCat ℤ) AddCommGroupCat.{u}).Full where
preimage {A B}
-- `AddMonoidHom.toIntLinearMap` doesn't work here because `A` and `B` are not
-- definitionally equal to the canonical `AddCommGroup.intModule` module
@@ -41,7 +41,7 @@ set_option linter.uppercaseLean3 false in
#align Module.forget₂_AddCommGroup_full ModuleCat.forget₂AddCommGroupFull
/-- The forgetful functor from `ℤ` modules to `AddCommGroup` is essentially surjective. -/
-instance forget₂_addCommGroupCat_essSurj : EssSurj (forget₂ (ModuleCat ℤ) AddCommGroupCat.{u}) where
+instance forget₂_addCommGroupCat_essSurj : (forget₂ (ModuleCat ℤ) AddCommGroupCat.{u}).EssSurj where
mem_essImage A :=
⟨ModuleCat.of ℤ A,
⟨{ hom := 𝟙 A
@@ -50,8 +50,8 @@ set_option linter.uppercaseLean3 false in
#align Module.forget₂_AddCommGroup_ess_surj ModuleCat.forget₂_addCommGroupCat_essSurj
noncomputable instance forget₂AddCommGroupIsEquivalence :
- IsEquivalence (forget₂ (ModuleCat ℤ) AddCommGroupCat.{u}) :=
- Equivalence.ofFullyFaithfullyEssSurj (forget₂ (ModuleCat ℤ) AddCommGroupCat)
+ (forget₂ (ModuleCat ℤ) AddCommGroupCat.{u}).IsEquivalence :=
+ Functor.IsEquivalence.ofFullyFaithfullyEssSurj (forget₂ (ModuleCat ℤ) AddCommGroupCat)
set_option linter.uppercaseLean3 false in
#align Module.forget₂_AddCommGroup_is_equivalence ModuleCat.forget₂AddCommGroupIsEquivalence
@@ -41,8 +41,8 @@ set_option linter.uppercaseLean3 false in
#align Module.forget₂_AddCommGroup_full ModuleCat.forget₂AddCommGroupFull
/-- The forgetful functor from `ℤ` modules to `AddCommGroup` is essentially surjective. -/
-instance forget₂_addCommGroupCat_essSurj : EssSurj (forget₂ (ModuleCat ℤ) AddCommGroupCat.{u})
- where mem_essImage A :=
+instance forget₂_addCommGroupCat_essSurj : EssSurj (forget₂ (ModuleCat ℤ) AddCommGroupCat.{u}) where
+ mem_essImage A :=
⟨ModuleCat.of ℤ A,
⟨{ hom := 𝟙 A
inv := 𝟙 A }⟩⟩
@@ -2,14 +2,11 @@
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 algebra.category.Group.Z_Module_equivalence
-! leanprover-community/mathlib commit bf1b813e20e108e8868341ca94bb3404a2506ae5
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.Algebra.Category.ModuleCat.Basic
+#align_import algebra.category.Group.Z_Module_equivalence from "leanprover-community/mathlib"@"bf1b813e20e108e8868341ca94bb3404a2506ae5"
+
/-!
The forgetful functor from ℤ-modules to additive commutative groups is
an equivalence of categories.
The unported dependencies are