category_theory.conj
⟷
Mathlib.CategoryTheory.Conj
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
@@ -3,7 +3,7 @@ Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
-import Algebra.Hom.Equiv.Units.Basic
+import Algebra.Group.Units.Equiv
import CategoryTheory.Endomorphism
#align_import category_theory.conj from "leanprover-community/mathlib"@"23aa88e32dcc9d2a24cca7bc23268567ed4cd7d6"
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,8 +3,8 @@ Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
-import Mathbin.Algebra.Hom.Equiv.Units.Basic
-import Mathbin.CategoryTheory.Endomorphism
+import Algebra.Hom.Equiv.Units.Basic
+import CategoryTheory.Endomorphism
#align_import category_theory.conj from "leanprover-community/mathlib"@"23aa88e32dcc9d2a24cca7bc23268567ed4cd7d6"
mathlib commit https://github.com/leanprover-community/mathlib/commit/32a7e535287f9c73f2e4d2aef306a39190f0b504
@@ -102,7 +102,7 @@ theorem conj_apply (f : End X) : α.conj f = α.inv ≫ f ≫ α.Hom :=
#print CategoryTheory.Iso.conj_comp /-
@[simp]
theorem conj_comp (f g : End X) : α.conj (f ≫ g) = α.conj f ≫ α.conj g :=
- α.conj.map_mul g f
+ α.conj.map_hMul g f
#align category_theory.iso.conj_comp CategoryTheory.Iso.conj_comp
-/
@@ -179,7 +179,7 @@ theorem trans_conjAut {Z : C} (β : Y ≅ Z) (f : Aut X) :
#print CategoryTheory.Iso.conjAut_mul /-
@[simp]
theorem conjAut_mul (f g : Aut X) : α.conjAut (f * g) = α.conjAut f * α.conjAut g :=
- α.conjAut.map_mul f g
+ α.conjAut.map_hMul f g
#align category_theory.iso.conj_Aut_mul CategoryTheory.Iso.conjAut_mul
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,15 +2,12 @@
Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-
-! This file was ported from Lean 3 source module category_theory.conj
-! leanprover-community/mathlib commit 23aa88e32dcc9d2a24cca7bc23268567ed4cd7d6
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.Algebra.Hom.Equiv.Units.Basic
import Mathbin.CategoryTheory.Endomorphism
+#align_import category_theory.conj from "leanprover-community/mathlib"@"23aa88e32dcc9d2a24cca7bc23268567ed4cd7d6"
+
/-!
# Conjugate morphisms by isomorphisms
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -96,84 +96,116 @@ def conj : End X ≃* End Y :=
#align category_theory.iso.conj CategoryTheory.Iso.conj
-/
+#print CategoryTheory.Iso.conj_apply /-
theorem conj_apply (f : End X) : α.conj f = α.inv ≫ f ≫ α.Hom :=
rfl
#align category_theory.iso.conj_apply CategoryTheory.Iso.conj_apply
+-/
+#print CategoryTheory.Iso.conj_comp /-
@[simp]
theorem conj_comp (f g : End X) : α.conj (f ≫ g) = α.conj f ≫ α.conj g :=
α.conj.map_mul g f
#align category_theory.iso.conj_comp CategoryTheory.Iso.conj_comp
+-/
+#print CategoryTheory.Iso.conj_id /-
@[simp]
theorem conj_id : α.conj (𝟙 X) = 𝟙 Y :=
α.conj.map_one
#align category_theory.iso.conj_id CategoryTheory.Iso.conj_id
+-/
+#print CategoryTheory.Iso.refl_conj /-
@[simp]
theorem refl_conj (f : End X) : (Iso.refl X).conj f = f := by
rw [conj_apply, iso.refl_inv, iso.refl_hom, category.id_comp, category.comp_id]
#align category_theory.iso.refl_conj CategoryTheory.Iso.refl_conj
+-/
+#print CategoryTheory.Iso.trans_conj /-
@[simp]
theorem trans_conj {Z : C} (β : Y ≅ Z) (f : End X) : (α ≪≫ β).conj f = β.conj (α.conj f) :=
homCongr_trans α α β β f
#align category_theory.iso.trans_conj CategoryTheory.Iso.trans_conj
+-/
+#print CategoryTheory.Iso.symm_self_conj /-
@[simp]
theorem symm_self_conj (f : End X) : α.symm.conj (α.conj f) = f := by
rw [← trans_conj, α.self_symm_id, refl_conj]
#align category_theory.iso.symm_self_conj CategoryTheory.Iso.symm_self_conj
+-/
+#print CategoryTheory.Iso.self_symm_conj /-
@[simp]
theorem self_symm_conj (f : End Y) : α.conj (α.symm.conj f) = f :=
α.symm.symm_self_conj f
#align category_theory.iso.self_symm_conj CategoryTheory.Iso.self_symm_conj
+-/
+#print CategoryTheory.Iso.conj_pow /-
@[simp]
theorem conj_pow (f : End X) (n : ℕ) : α.conj (f ^ n) = α.conj f ^ n :=
α.conj.toMonoidHom.map_pow f n
#align category_theory.iso.conj_pow CategoryTheory.Iso.conj_pow
+-/
+#print CategoryTheory.Iso.conjAut /-
/-- `conj` defines a group isomorphisms between groups of automorphisms -/
def conjAut : Aut X ≃* Aut Y :=
(Aut.unitsEndEquivAut X).symm.trans <| (Units.mapEquiv α.conj).trans <| Aut.unitsEndEquivAut Y
#align category_theory.iso.conj_Aut CategoryTheory.Iso.conjAut
+-/
+#print CategoryTheory.Iso.conjAut_apply /-
theorem conjAut_apply (f : Aut X) : α.conjAut f = α.symm ≪≫ f ≪≫ α := by
cases f <;> cases α <;> ext <;> rfl
#align category_theory.iso.conj_Aut_apply CategoryTheory.Iso.conjAut_apply
+-/
+#print CategoryTheory.Iso.conjAut_hom /-
@[simp]
theorem conjAut_hom (f : Aut X) : (α.conjAut f).Hom = α.conj f.Hom :=
rfl
#align category_theory.iso.conj_Aut_hom CategoryTheory.Iso.conjAut_hom
+-/
+#print CategoryTheory.Iso.trans_conjAut /-
@[simp]
theorem trans_conjAut {Z : C} (β : Y ≅ Z) (f : Aut X) :
(α ≪≫ β).conjAut f = β.conjAut (α.conjAut f) := by
simp only [conj_Aut_apply, iso.trans_symm, iso.trans_assoc]
#align category_theory.iso.trans_conj_Aut CategoryTheory.Iso.trans_conjAut
+-/
+#print CategoryTheory.Iso.conjAut_mul /-
@[simp]
theorem conjAut_mul (f g : Aut X) : α.conjAut (f * g) = α.conjAut f * α.conjAut g :=
α.conjAut.map_mul f g
#align category_theory.iso.conj_Aut_mul CategoryTheory.Iso.conjAut_mul
+-/
+#print CategoryTheory.Iso.conjAut_trans /-
@[simp]
theorem conjAut_trans (f g : Aut X) : α.conjAut (f ≪≫ g) = α.conjAut f ≪≫ α.conjAut g :=
conjAut_mul α g f
#align category_theory.iso.conj_Aut_trans CategoryTheory.Iso.conjAut_trans
+-/
+#print CategoryTheory.Iso.conjAut_pow /-
@[simp]
theorem conjAut_pow (f : Aut X) (n : ℕ) : α.conjAut (f ^ n) = α.conjAut f ^ n :=
α.conjAut.toMonoidHom.map_pow f n
#align category_theory.iso.conj_Aut_pow CategoryTheory.Iso.conjAut_pow
+-/
+#print CategoryTheory.Iso.conjAut_zpow /-
@[simp]
theorem conjAut_zpow (f : Aut X) (n : ℤ) : α.conjAut (f ^ n) = α.conjAut f ^ n :=
α.conjAut.toMonoidHom.map_zpow f n
#align category_theory.iso.conj_Aut_zpow CategoryTheory.Iso.conjAut_zpow
+-/
end Iso
@@ -183,19 +215,25 @@ universe v₁ u₁
variable {C : Type u} [Category.{v} C] {D : Type u₁} [Category.{v₁} D] (F : C ⥤ D)
+#print CategoryTheory.Functor.map_homCongr /-
theorem map_homCongr {X Y X₁ Y₁ : C} (α : X ≅ X₁) (β : Y ≅ Y₁) (f : X ⟶ Y) :
F.map (Iso.homCongr α β f) = Iso.homCongr (F.mapIso α) (F.mapIso β) (F.map f) := by simp
#align category_theory.functor.map_hom_congr CategoryTheory.Functor.map_homCongr
+-/
+#print CategoryTheory.Functor.map_conj /-
theorem map_conj {X Y : C} (α : X ≅ Y) (f : End X) :
F.map (α.conj f) = (F.mapIso α).conj (F.map f) :=
map_homCongr F α α f
#align category_theory.functor.map_conj CategoryTheory.Functor.map_conj
+-/
+#print CategoryTheory.Functor.map_conjAut /-
theorem map_conjAut (F : C ⥤ D) {X Y : C} (α : X ≅ Y) (f : Aut X) :
F.mapIso (α.conjAut f) = (F.mapIso α).conjAut (F.mapIso f) := by
ext <;> simp only [map_iso_hom, iso.conj_Aut_hom, F.map_conj]
#align category_theory.functor.map_conj_Aut CategoryTheory.Functor.map_conjAut
+-/
-- alternative proof: by simp only [iso.conj_Aut_apply, F.map_iso_trans, F.map_iso_symm]
end Functor
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -96,143 +96,80 @@ def conj : End X ≃* End Y :=
#align category_theory.iso.conj CategoryTheory.Iso.conj
-/
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theorem conj_apply (f : End X) : α.conj f = α.inv ≫ f ≫ α.Hom :=
rfl
#align category_theory.iso.conj_apply CategoryTheory.Iso.conj_apply
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@[simp]
theorem conj_comp (f g : End X) : α.conj (f ≫ g) = α.conj f ≫ α.conj g :=
α.conj.map_mul g f
#align category_theory.iso.conj_comp CategoryTheory.Iso.conj_comp
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@[simp]
theorem conj_id : α.conj (𝟙 X) = 𝟙 Y :=
α.conj.map_one
#align category_theory.iso.conj_id CategoryTheory.Iso.conj_id
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@[simp]
theorem refl_conj (f : End X) : (Iso.refl X).conj f = f := by
rw [conj_apply, iso.refl_inv, iso.refl_hom, category.id_comp, category.comp_id]
#align category_theory.iso.refl_conj CategoryTheory.Iso.refl_conj
-/- warning: category_theory.iso.trans_conj -> CategoryTheory.Iso.trans_conj is a dubious translation:
-<too large>
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@[simp]
theorem trans_conj {Z : C} (β : Y ≅ Z) (f : End X) : (α ≪≫ β).conj f = β.conj (α.conj f) :=
homCongr_trans α α β β f
#align category_theory.iso.trans_conj CategoryTheory.Iso.trans_conj
-/- warning: category_theory.iso.symm_self_conj -> CategoryTheory.Iso.symm_self_conj is a dubious translation:
-<too large>
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@[simp]
theorem symm_self_conj (f : End X) : α.symm.conj (α.conj f) = f := by
rw [← trans_conj, α.self_symm_id, refl_conj]
#align category_theory.iso.symm_self_conj CategoryTheory.Iso.symm_self_conj
-/- warning: category_theory.iso.self_symm_conj -> CategoryTheory.Iso.self_symm_conj is a dubious translation:
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@[simp]
theorem self_symm_conj (f : End Y) : α.conj (α.symm.conj f) = f :=
α.symm.symm_self_conj f
#align category_theory.iso.self_symm_conj CategoryTheory.Iso.self_symm_conj
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@[simp]
theorem conj_pow (f : End X) (n : ℕ) : α.conj (f ^ n) = α.conj f ^ n :=
α.conj.toMonoidHom.map_pow f n
#align category_theory.iso.conj_pow CategoryTheory.Iso.conj_pow
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/-- `conj` defines a group isomorphisms between groups of automorphisms -/
def conjAut : Aut X ≃* Aut Y :=
(Aut.unitsEndEquivAut X).symm.trans <| (Units.mapEquiv α.conj).trans <| Aut.unitsEndEquivAut Y
#align category_theory.iso.conj_Aut CategoryTheory.Iso.conjAut
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-Case conversion may be inaccurate. Consider using '#align category_theory.iso.conj_Aut_apply CategoryTheory.Iso.conjAut_applyₓ'. -/
theorem conjAut_apply (f : Aut X) : α.conjAut f = α.symm ≪≫ f ≪≫ α := by
cases f <;> cases α <;> ext <;> rfl
#align category_theory.iso.conj_Aut_apply CategoryTheory.Iso.conjAut_apply
-/- warning: category_theory.iso.conj_Aut_hom -> CategoryTheory.Iso.conjAut_hom is a dubious translation:
-<too large>
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@[simp]
theorem conjAut_hom (f : Aut X) : (α.conjAut f).Hom = α.conj f.Hom :=
rfl
#align category_theory.iso.conj_Aut_hom CategoryTheory.Iso.conjAut_hom
-/- warning: category_theory.iso.trans_conj_Aut -> CategoryTheory.Iso.trans_conjAut is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.iso.trans_conj_Aut CategoryTheory.Iso.trans_conjAutₓ'. -/
@[simp]
theorem trans_conjAut {Z : C} (β : Y ≅ Z) (f : Aut X) :
(α ≪≫ β).conjAut f = β.conjAut (α.conjAut f) := by
simp only [conj_Aut_apply, iso.trans_symm, iso.trans_assoc]
#align category_theory.iso.trans_conj_Aut CategoryTheory.Iso.trans_conjAut
-/- warning: category_theory.iso.conj_Aut_mul -> CategoryTheory.Iso.conjAut_mul is a dubious translation:
-<too large>
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@[simp]
theorem conjAut_mul (f g : Aut X) : α.conjAut (f * g) = α.conjAut f * α.conjAut g :=
α.conjAut.map_mul f g
#align category_theory.iso.conj_Aut_mul CategoryTheory.Iso.conjAut_mul
-/- warning: category_theory.iso.conj_Aut_trans -> CategoryTheory.Iso.conjAut_trans is a dubious translation:
-<too large>
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@[simp]
theorem conjAut_trans (f g : Aut X) : α.conjAut (f ≪≫ g) = α.conjAut f ≪≫ α.conjAut g :=
conjAut_mul α g f
#align category_theory.iso.conj_Aut_trans CategoryTheory.Iso.conjAut_trans
-/- warning: category_theory.iso.conj_Aut_pow -> CategoryTheory.Iso.conjAut_pow is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.iso.conj_Aut_pow CategoryTheory.Iso.conjAut_powₓ'. -/
@[simp]
theorem conjAut_pow (f : Aut X) (n : ℕ) : α.conjAut (f ^ n) = α.conjAut f ^ n :=
α.conjAut.toMonoidHom.map_pow f n
#align category_theory.iso.conj_Aut_pow CategoryTheory.Iso.conjAut_pow
-/- warning: category_theory.iso.conj_Aut_zpow -> CategoryTheory.Iso.conjAut_zpow is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.iso.conj_Aut_zpow CategoryTheory.Iso.conjAut_zpowₓ'. -/
@[simp]
theorem conjAut_zpow (f : Aut X) (n : ℤ) : α.conjAut (f ^ n) = α.conjAut f ^ n :=
α.conjAut.toMonoidHom.map_zpow f n
@@ -246,24 +183,15 @@ universe v₁ u₁
variable {C : Type u} [Category.{v} C] {D : Type u₁} [Category.{v₁} D] (F : C ⥤ D)
-/- warning: category_theory.functor.map_hom_congr -> CategoryTheory.Functor.map_homCongr is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.functor.map_hom_congr CategoryTheory.Functor.map_homCongrₓ'. -/
theorem map_homCongr {X Y X₁ Y₁ : C} (α : X ≅ X₁) (β : Y ≅ Y₁) (f : X ⟶ Y) :
F.map (Iso.homCongr α β f) = Iso.homCongr (F.mapIso α) (F.mapIso β) (F.map f) := by simp
#align category_theory.functor.map_hom_congr CategoryTheory.Functor.map_homCongr
-/- warning: category_theory.functor.map_conj -> CategoryTheory.Functor.map_conj is a dubious translation:
-<too large>
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theorem map_conj {X Y : C} (α : X ≅ Y) (f : End X) :
F.map (α.conj f) = (F.mapIso α).conj (F.map f) :=
map_homCongr F α α f
#align category_theory.functor.map_conj CategoryTheory.Functor.map_conj
-/- warning: category_theory.functor.map_conj_Aut -> CategoryTheory.Functor.map_conjAut is a dubious translation:
-<too large>
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theorem map_conjAut (F : C ⥤ D) {X Y : C} (α : X ≅ Y) (f : Aut X) :
F.mapIso (α.conjAut f) = (F.mapIso α).conjAut (F.mapIso f) := by
ext <;> simp only [map_iso_hom, iso.conj_Aut_hom, F.map_conj]
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -107,10 +107,7 @@ theorem conj_apply (f : End X) : α.conj f = α.inv ≫ f ≫ α.Hom :=
#align category_theory.iso.conj_apply CategoryTheory.Iso.conj_apply
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Case conversion may be inaccurate. Consider using '#align category_theory.iso.conj_comp CategoryTheory.Iso.conj_compₓ'. -/
@[simp]
theorem conj_comp (f g : End X) : α.conj (f ≫ g) = α.conj f ≫ α.conj g :=
@@ -140,10 +137,7 @@ theorem refl_conj (f : End X) : (Iso.refl X).conj f = f := by
#align category_theory.iso.refl_conj CategoryTheory.Iso.refl_conj
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Case conversion may be inaccurate. Consider using '#align category_theory.iso.trans_conj CategoryTheory.Iso.trans_conjₓ'. -/
@[simp]
theorem trans_conj {Z : C} (β : Y ≅ Z) (f : End X) : (α ≪≫ β).conj f = β.conj (α.conj f) :=
@@ -151,10 +145,7 @@ theorem trans_conj {Z : C} (β : Y ≅ Z) (f : End X) : (α ≪≫ β).conj f =
#align category_theory.iso.trans_conj CategoryTheory.Iso.trans_conj
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Case conversion may be inaccurate. Consider using '#align category_theory.iso.symm_self_conj CategoryTheory.Iso.symm_self_conjₓ'. -/
@[simp]
theorem symm_self_conj (f : End X) : α.symm.conj (α.conj f) = f := by
@@ -162,10 +153,7 @@ theorem symm_self_conj (f : End X) : α.symm.conj (α.conj f) = f := by
#align category_theory.iso.symm_self_conj CategoryTheory.Iso.symm_self_conj
/- warning: category_theory.iso.self_symm_conj -> CategoryTheory.Iso.self_symm_conj is a dubious translation:
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Case conversion may be inaccurate. Consider using '#align category_theory.iso.self_symm_conj CategoryTheory.Iso.self_symm_conjₓ'. -/
@[simp]
theorem self_symm_conj (f : End Y) : α.conj (α.symm.conj f) = f :=
@@ -173,10 +161,7 @@ theorem self_symm_conj (f : End Y) : α.conj (α.symm.conj f) = f :=
#align category_theory.iso.self_symm_conj CategoryTheory.Iso.self_symm_conj
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Case conversion may be inaccurate. Consider using '#align category_theory.iso.conj_pow CategoryTheory.Iso.conj_powₓ'. -/
@[simp]
theorem conj_pow (f : End X) (n : ℕ) : α.conj (f ^ n) = α.conj f ^ n :=
@@ -205,10 +190,7 @@ theorem conjAut_apply (f : Aut X) : α.conjAut f = α.symm ≪≫ f ≪≫ α :=
#align category_theory.iso.conj_Aut_apply CategoryTheory.Iso.conjAut_apply
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Case conversion may be inaccurate. Consider using '#align category_theory.iso.conj_Aut_hom CategoryTheory.Iso.conjAut_homₓ'. -/
@[simp]
theorem conjAut_hom (f : Aut X) : (α.conjAut f).Hom = α.conj f.Hom :=
@@ -216,10 +198,7 @@ theorem conjAut_hom (f : Aut X) : (α.conjAut f).Hom = α.conj f.Hom :=
#align category_theory.iso.conj_Aut_hom CategoryTheory.Iso.conjAut_hom
/- warning: category_theory.iso.trans_conj_Aut -> CategoryTheory.Iso.trans_conjAut is a dubious translation:
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Z) (Monoid.toMulOneClass.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 Z) (DivInvMonoid.toMonoid.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 Z) (Group.toDivInvMonoid.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 Z) (CategoryTheory.Aut.instGroupAut.{u1, u2} C _inst_1 Z)))))) (CategoryTheory.Aut.{u1, u2} C _inst_1 X) (CategoryTheory.Aut.{u1, u2} C _inst_1 Z) (EquivLike.toEmbeddingLike.{succ u1, succ u1, succ u1} (MulEquiv.{u1, u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 X) (CategoryTheory.Aut.{u1, u2} C _inst_1 Z) (MulOneClass.toMul.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 X) (Monoid.toMulOneClass.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 X) (DivInvMonoid.toMonoid.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 X) (Group.toDivInvMonoid.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 X) (CategoryTheory.Aut.instGroupAut.{u1, u2} C _inst_1 X))))) (MulOneClass.toMul.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 Z) (Monoid.toMulOneClass.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 Z) 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(CategoryTheory.Aut.{u1, u2} C _inst_1 Z) (CategoryTheory.Aut.instGroupAut.{u1, u2} C _inst_1 Z)))))) (CategoryTheory.Aut.{u1, u2} C _inst_1 X) (CategoryTheory.Aut.{u1, u2} C _inst_1 Z) (MulOneClass.toMul.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 X) (Monoid.toMulOneClass.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 X) (DivInvMonoid.toMonoid.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 X) (Group.toDivInvMonoid.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 X) (CategoryTheory.Aut.instGroupAut.{u1, u2} C _inst_1 X))))) (MulOneClass.toMul.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 Z) (Monoid.toMulOneClass.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 Z) (DivInvMonoid.toMonoid.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 Z) (Group.toDivInvMonoid.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 Z) (CategoryTheory.Aut.instGroupAut.{u1, u2} C _inst_1 Z))))) (MulEquiv.instMulEquivClassMulEquiv.{u1, u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 X) (CategoryTheory.Aut.{u1, u2} C _inst_1 Z) (MulOneClass.toMul.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 X) (Monoid.toMulOneClass.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 X) (DivInvMonoid.toMonoid.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 X) (Group.toDivInvMonoid.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 X) (CategoryTheory.Aut.instGroupAut.{u1, u2} C _inst_1 X))))) (MulOneClass.toMul.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 Z) (Monoid.toMulOneClass.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 Z) (DivInvMonoid.toMonoid.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 Z) (Group.toDivInvMonoid.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 Z) (CategoryTheory.Aut.instGroupAut.{u1, u2} C _inst_1 Z))))))))) (CategoryTheory.Iso.conjAut.{u1, u2} C _inst_1 X Z (CategoryTheory.Iso.trans.{u1, u2} C _inst_1 X Y Z α β)) f) (FunLike.coe.{succ u1, succ u1, succ u1} (MulEquiv.{u1, u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 Y) (CategoryTheory.Aut.{u1, u2} C _inst_1 Z) (MulOneClass.toMul.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 Y) (Monoid.toMulOneClass.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 Y) (DivInvMonoid.toMonoid.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 Y) (Group.toDivInvMonoid.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 Y) (CategoryTheory.Aut.instGroupAut.{u1, u2} C _inst_1 Y))))) (MulOneClass.toMul.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 Z) (Monoid.toMulOneClass.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 Z) (DivInvMonoid.toMonoid.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 Z) (Group.toDivInvMonoid.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 Z) (CategoryTheory.Aut.instGroupAut.{u1, u2} C _inst_1 Z)))))) (CategoryTheory.Aut.{u1, u2} C _inst_1 Y) (fun (_x : CategoryTheory.Aut.{u1, u2} C _inst_1 Y) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : CategoryTheory.Aut.{u1, u2} C _inst_1 Y) => CategoryTheory.Aut.{u1, u2} C _inst_1 Z) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (MulEquiv.{u1, u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 Y) (CategoryTheory.Aut.{u1, u2} C _inst_1 Z) 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(Monoid.toMulOneClass.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 Z) (DivInvMonoid.toMonoid.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 Z) (Group.toDivInvMonoid.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 Z) (CategoryTheory.Aut.instGroupAut.{u1, u2} C _inst_1 Z))))) (MulEquiv.instMulEquivClassMulEquiv.{u1, u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 Y) (CategoryTheory.Aut.{u1, u2} C _inst_1 Z) (MulOneClass.toMul.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 Y) (Monoid.toMulOneClass.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 Y) (DivInvMonoid.toMonoid.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 Y) (Group.toDivInvMonoid.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 Y) (CategoryTheory.Aut.instGroupAut.{u1, u2} C _inst_1 Y))))) (MulOneClass.toMul.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 Z) (Monoid.toMulOneClass.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 Z) (DivInvMonoid.toMonoid.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 Z) (Group.toDivInvMonoid.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 Z) (CategoryTheory.Aut.instGroupAut.{u1, u2} C _inst_1 Z))))))))) (CategoryTheory.Iso.conjAut.{u1, u2} C _inst_1 Y Z β) (FunLike.coe.{succ u1, succ u1, succ u1} (MulEquiv.{u1, u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 X) (CategoryTheory.Aut.{u1, u2} C _inst_1 Y) (MulOneClass.toMul.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 X) (Monoid.toMulOneClass.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 X) (DivInvMonoid.toMonoid.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 X) (Group.toDivInvMonoid.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 X) (CategoryTheory.Aut.instGroupAut.{u1, u2} C _inst_1 X))))) (MulOneClass.toMul.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 Y) (Monoid.toMulOneClass.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 Y) (DivInvMonoid.toMonoid.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 Y) (Group.toDivInvMonoid.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 Y) (CategoryTheory.Aut.instGroupAut.{u1, u2} C _inst_1 Y)))))) (CategoryTheory.Aut.{u1, u2} C _inst_1 X) (fun (_x : CategoryTheory.Aut.{u1, u2} C _inst_1 X) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : CategoryTheory.Aut.{u1, u2} C _inst_1 X) => CategoryTheory.Aut.{u1, u2} C _inst_1 Y) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (MulEquiv.{u1, u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 X) (CategoryTheory.Aut.{u1, u2} C _inst_1 Y) (MulOneClass.toMul.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 X) (Monoid.toMulOneClass.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 X) (DivInvMonoid.toMonoid.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 X) (Group.toDivInvMonoid.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 X) (CategoryTheory.Aut.instGroupAut.{u1, u2} C _inst_1 X))))) (MulOneClass.toMul.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 Y) (Monoid.toMulOneClass.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 Y) (DivInvMonoid.toMonoid.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 Y) (Group.toDivInvMonoid.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 Y) (CategoryTheory.Aut.instGroupAut.{u1, u2} C _inst_1 Y)))))) (CategoryTheory.Aut.{u1, u2} C _inst_1 X) (CategoryTheory.Aut.{u1, u2} C _inst_1 Y) (EquivLike.toEmbeddingLike.{succ u1, succ u1, succ u1} (MulEquiv.{u1, u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 X) (CategoryTheory.Aut.{u1, u2} C _inst_1 Y) (MulOneClass.toMul.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 X) (Monoid.toMulOneClass.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 X) (DivInvMonoid.toMonoid.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 X) (Group.toDivInvMonoid.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 X) (CategoryTheory.Aut.instGroupAut.{u1, u2} C _inst_1 X))))) (MulOneClass.toMul.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 Y) (Monoid.toMulOneClass.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 Y) (DivInvMonoid.toMonoid.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 Y) (Group.toDivInvMonoid.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 Y) (CategoryTheory.Aut.instGroupAut.{u1, u2} C _inst_1 Y)))))) (CategoryTheory.Aut.{u1, u2} C _inst_1 X) (CategoryTheory.Aut.{u1, u2} C _inst_1 Y) 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(CategoryTheory.Aut.{u1, u2} C _inst_1 X) (DivInvMonoid.toMonoid.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 X) (Group.toDivInvMonoid.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 X) (CategoryTheory.Aut.instGroupAut.{u1, u2} C _inst_1 X))))) (MulOneClass.toMul.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 Y) (Monoid.toMulOneClass.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 Y) (DivInvMonoid.toMonoid.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 Y) (Group.toDivInvMonoid.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 Y) (CategoryTheory.Aut.instGroupAut.{u1, u2} C _inst_1 Y))))) (MulEquiv.instMulEquivClassMulEquiv.{u1, u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 X) (CategoryTheory.Aut.{u1, u2} C _inst_1 Y) (MulOneClass.toMul.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 X) (Monoid.toMulOneClass.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 X) (DivInvMonoid.toMonoid.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 X) (Group.toDivInvMonoid.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 X) (CategoryTheory.Aut.instGroupAut.{u1, u2} C _inst_1 X))))) (MulOneClass.toMul.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 Y) (Monoid.toMulOneClass.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 Y) (DivInvMonoid.toMonoid.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 Y) (Group.toDivInvMonoid.{u1} (CategoryTheory.Aut.{u1, u2} C _inst_1 Y) (CategoryTheory.Aut.instGroupAut.{u1, u2} C _inst_1 Y))))))))) (CategoryTheory.Iso.conjAut.{u1, u2} C _inst_1 X Y α) f))
+<too large>
Case conversion may be inaccurate. Consider using '#align category_theory.iso.trans_conj_Aut CategoryTheory.Iso.trans_conjAutₓ'. -/
@[simp]
theorem trans_conjAut {Z : C} (β : Y ≅ Z) (f : Aut X) :
@@ -228,10 +207,7 @@ theorem trans_conjAut {Z : C} (β : Y ≅ Z) (f : Aut X) :
#align category_theory.iso.trans_conj_Aut CategoryTheory.Iso.trans_conjAut
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+<too large>
Case conversion may be inaccurate. Consider using '#align category_theory.iso.conj_Aut_mul CategoryTheory.Iso.conjAut_mulₓ'. -/
@[simp]
theorem conjAut_mul (f g : Aut X) : α.conjAut (f * g) = α.conjAut f * α.conjAut g :=
@@ -239,10 +215,7 @@ theorem conjAut_mul (f g : Aut X) : α.conjAut (f * g) = α.conjAut f * α.conjA
#align category_theory.iso.conj_Aut_mul CategoryTheory.Iso.conjAut_mul
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+<too large>
Case conversion may be inaccurate. Consider using '#align category_theory.iso.conj_Aut_trans CategoryTheory.Iso.conjAut_transₓ'. -/
@[simp]
theorem conjAut_trans (f g : Aut X) : α.conjAut (f ≪≫ g) = α.conjAut f ≪≫ α.conjAut g :=
@@ -250,10 +223,7 @@ theorem conjAut_trans (f g : Aut X) : α.conjAut (f ≪≫ g) = α.conjAut f ≪
#align category_theory.iso.conj_Aut_trans CategoryTheory.Iso.conjAut_trans
/- warning: category_theory.iso.conj_Aut_pow -> CategoryTheory.Iso.conjAut_pow is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align category_theory.iso.conj_Aut_pow CategoryTheory.Iso.conjAut_powₓ'. -/
@[simp]
theorem conjAut_pow (f : Aut X) (n : ℕ) : α.conjAut (f ^ n) = α.conjAut f ^ n :=
@@ -261,10 +231,7 @@ theorem conjAut_pow (f : Aut X) (n : ℕ) : α.conjAut (f ^ n) = α.conjAut f ^
#align category_theory.iso.conj_Aut_pow CategoryTheory.Iso.conjAut_pow
/- warning: category_theory.iso.conj_Aut_zpow -> CategoryTheory.Iso.conjAut_zpow is a dubious translation:
-lean 3 declaration is
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+<too large>
Case conversion may be inaccurate. Consider using '#align category_theory.iso.conj_Aut_zpow CategoryTheory.Iso.conjAut_zpowₓ'. -/
@[simp]
theorem conjAut_zpow (f : Aut X) (n : ℤ) : α.conjAut (f ^ n) = α.conjAut f ^ n :=
@@ -280,20 +247,14 @@ universe v₁ u₁
variable {C : Type u} [Category.{v} C] {D : Type u₁} [Category.{v₁} D] (F : C ⥤ D)
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Case conversion may be inaccurate. Consider using '#align category_theory.functor.map_hom_congr CategoryTheory.Functor.map_homCongrₓ'. -/
theorem map_homCongr {X Y X₁ Y₁ : C} (α : X ≅ X₁) (β : Y ≅ Y₁) (f : X ⟶ Y) :
F.map (Iso.homCongr α β f) = Iso.homCongr (F.mapIso α) (F.mapIso β) (F.map f) := by simp
#align category_theory.functor.map_hom_congr CategoryTheory.Functor.map_homCongr
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Case conversion may be inaccurate. Consider using '#align category_theory.functor.map_conj CategoryTheory.Functor.map_conjₓ'. -/
theorem map_conj {X Y : C} (α : X ≅ Y) (f : End X) :
F.map (α.conj f) = (F.mapIso α).conj (F.map f) :=
@@ -301,10 +262,7 @@ theorem map_conj {X Y : C} (α : X ≅ Y) (f : End X) :
#align category_theory.functor.map_conj CategoryTheory.Functor.map_conj
/- warning: category_theory.functor.map_conj_Aut -> CategoryTheory.Functor.map_conjAut is a dubious translation:
-lean 3 declaration is
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+<too large>
Case conversion may be inaccurate. Consider using '#align category_theory.functor.map_conj_Aut CategoryTheory.Functor.map_conjAutₓ'. -/
theorem map_conjAut (F : C ⥤ D) {X Y : C} (α : X ≅ Y) (f : Aut X) :
F.mapIso (α.conjAut f) = (F.mapIso α).conjAut (F.mapIso f) := by
mathlib commit https://github.com/leanprover-community/mathlib/commit/95a87616d63b3cb49d3fe678d416fbe9c4217bf4
@@ -283,7 +283,7 @@ variable {C : Type u} [Category.{v} C] {D : Type u₁} [Category.{v₁} D] (F :
lean 3 declaration is
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but is expected to have type
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Case conversion may be inaccurate. Consider using '#align category_theory.functor.map_hom_congr CategoryTheory.Functor.map_homCongrₓ'. -/
theorem map_homCongr {X Y X₁ Y₁ : C} (α : X ≅ X₁) (β : Y ≅ Y₁) (f : X ⟶ Y) :
F.map (Iso.homCongr α β f) = Iso.homCongr (F.mapIso α) (F.mapIso β) (F.map f) := by simp
mathlib commit https://github.com/leanprover-community/mathlib/commit/3180fab693e2cee3bff62675571264cb8778b212
@@ -283,7 +283,7 @@ variable {C : Type u} [Category.{v} C] {D : Type u₁} [Category.{v₁} D] (F :
lean 3 declaration is
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but is expected to have type
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Case conversion may be inaccurate. Consider using '#align category_theory.functor.map_hom_congr CategoryTheory.Functor.map_homCongrₓ'. -/
theorem map_homCongr {X Y X₁ Y₁ : C} (α : X ≅ X₁) (β : Y ≅ Y₁) (f : X ⟶ Y) :
F.map (Iso.homCongr α β f) = Iso.homCongr (F.mapIso α) (F.mapIso β) (F.map f) := by simp
mathlib commit https://github.com/leanprover-community/mathlib/commit/3ade05ac9447ae31a22d2ea5423435e054131240
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
! This file was ported from Lean 3 source module category_theory.conj
-! leanprover-community/mathlib commit cead93130da7100f8a9fe22ee210f7636a91168f
+! leanprover-community/mathlib commit 23aa88e32dcc9d2a24cca7bc23268567ed4cd7d6
! 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.Endomorphism
/-!
# Conjugate morphisms by isomorphisms
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
An isomorphism `α : X ≅ Y` defines
- a monoid isomorphism `conj : End X ≃* End Y` by `α.conj f = α.inv ≫ f ≫ α.hom`;
- a group isomorphism `conj_Aut : Aut X ≃* Aut Y` by `α.conj_Aut f = α.symm ≪≫ f ≪≫ α`.
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
@@ -118,7 +118,7 @@ theorem conj_pow (f : End X) (n : ℕ) : α.conj (f ^ n) = α.conj f ^ n :=
α.conj.toMonoidHom.map_pow f n
#align category_theory.iso.conj_pow CategoryTheory.Iso.conj_pow
--- Porting note: todo: change definition so that `conjAut_apply` becomes a `rfl`?
+-- Porting note (#11215): TODO: change definition so that `conjAut_apply` becomes a `rfl`?
/-- `conj` defines a group isomorphisms between groups of automorphisms -/
def conjAut : Aut X ≃* Aut Y :=
(Aut.unitsEndEquivAut X).symm.trans <| (Units.mapEquiv α.conj).trans <| Aut.unitsEndEquivAut Y
Homogenises porting notes via capitalisation and addition of whitespace.
It makes the following changes:
@@ -118,7 +118,7 @@ theorem conj_pow (f : End X) (n : ℕ) : α.conj (f ^ n) = α.conj f ^ n :=
α.conj.toMonoidHom.map_pow f n
#align category_theory.iso.conj_pow CategoryTheory.Iso.conj_pow
--- porting note: todo: change definition so that `conjAut_apply` becomes a `rfl`?
+-- Porting note: todo: change definition so that `conjAut_apply` becomes a `rfl`?
/-- `conj` defines a group isomorphisms between groups of automorphisms -/
def conjAut : Aut X ≃* Aut Y :=
(Aut.unitsEndEquivAut X).symm.trans <| (Units.mapEquiv α.conj).trans <| Aut.unitsEndEquivAut Y
@@ -44,7 +44,7 @@ def homCongr {X Y X₁ Y₁ : C} (α : X ≅ X₁) (β : Y ≅ Y₁) : (X ⟶ Y)
rw [Category.assoc, Category.assoc, β.inv_hom_id, α.inv_hom_id_assoc, Category.comp_id]
#align category_theory.iso.hom_congr CategoryTheory.Iso.homCongr
--- @[simp, nolint simpNF] Porting note: dsimp can not prove this
+-- @[simp, nolint simpNF] Porting note (#10675): dsimp can not prove this
@[simp]
theorem homCongr_apply {X Y X₁ Y₁ : C} (α : X ≅ X₁) (β : Y ≅ Y₁) (f : X ⟶ Y) :
α.homCongr β f = α.inv ≫ f ≫ β.hom := by
@@ -55,11 +55,11 @@ theorem homCongr_comp {X Y Z X₁ Y₁ Z₁ : C} (α : X ≅ X₁) (β : Y ≅ Y
(g : Y ⟶ Z) : α.homCongr γ (f ≫ g) = α.homCongr β f ≫ β.homCongr γ g := by simp
#align category_theory.iso.hom_congr_comp CategoryTheory.Iso.homCongr_comp
-/- Porting note: removed `@[simp]`; simp can prove this -/
+/- Porting note (#10618): removed `@[simp]`; simp can prove this -/
theorem homCongr_refl {X Y : C} (f : X ⟶ Y) : (Iso.refl X).homCongr (Iso.refl Y) f = f := by simp
#align category_theory.iso.hom_congr_refl CategoryTheory.Iso.homCongr_refl
-/- Porting note: removed `@[simp]`; simp can prove this -/
+/- Porting note (#10618): removed `@[simp]`; simp can prove this -/
theorem homCongr_trans {X₁ Y₁ X₂ Y₂ X₃ Y₃ : C} (α₁ : X₁ ≅ X₂) (β₁ : Y₁ ≅ Y₂) (α₂ : X₂ ≅ X₃)
(β₂ : Y₂ ≅ Y₃) (f : X₁ ⟶ Y₁) :
(α₁ ≪≫ α₂).homCongr (β₁ ≪≫ β₂) f = (α₁.homCongr β₁).trans (α₂.homCongr β₂) f := by simp
@@ -113,7 +113,7 @@ theorem self_symm_conj (f : End Y) : α.conj (α.symm.conj f) = f :=
α.symm.symm_self_conj f
#align category_theory.iso.self_symm_conj CategoryTheory.Iso.self_symm_conj
-/- Porting note: removed `@[simp]`; simp can prove this -/
+/- Porting note (#10618): removed `@[simp]`; simp can prove this -/
theorem conj_pow (f : End X) (n : ℕ) : α.conj (f ^ n) = α.conj f ^ n :=
α.conj.toMonoidHom.map_pow f n
#align category_theory.iso.conj_pow CategoryTheory.Iso.conj_pow
@@ -142,7 +142,7 @@ theorem trans_conjAut {Z : C} (β : Y ≅ Z) (f : Aut X) :
set_option linter.uppercaseLean3 false in
#align category_theory.iso.trans_conj_Aut CategoryTheory.Iso.trans_conjAut
-/- Porting note: removed `@[simp]`; simp can prove this -/
+/- Porting note (#10618): removed `@[simp]`; simp can prove this -/
theorem conjAut_mul (f g : Aut X) : α.conjAut (f * g) = α.conjAut f * α.conjAut g :=
α.conjAut.map_mul f g
set_option linter.uppercaseLean3 false in
@@ -154,13 +154,13 @@ theorem conjAut_trans (f g : Aut X) : α.conjAut (f ≪≫ g) = α.conjAut f ≪
set_option linter.uppercaseLean3 false in
#align category_theory.iso.conj_Aut_trans CategoryTheory.Iso.conjAut_trans
-/- Porting note: removed `@[simp]`; simp can prove this -/
+/- Porting note (#10618): removed `@[simp]`; simp can prove this -/
theorem conjAut_pow (f : Aut X) (n : ℕ) : α.conjAut (f ^ n) = α.conjAut f ^ n :=
α.conjAut.toMonoidHom.map_pow f n
set_option linter.uppercaseLean3 false in
#align category_theory.iso.conj_Aut_pow CategoryTheory.Iso.conjAut_pow
-/- Porting note: removed `@[simp]`; simp can prove this -/
+/- Porting note (#10618): removed `@[simp]`; simp can prove this -/
theorem conjAut_zpow (f : Aut X) (n : ℤ) : α.conjAut (f ^ n) = α.conjAut f ^ n :=
α.conjAut.toMonoidHom.map_zpow f n
set_option linter.uppercaseLean3 false in
Hom
and file name (#8095)
I believe the file defining a type of morphisms belongs alongside the file defining the structure this morphism works on. So I would like to reorganize the files in the Mathlib.Algebra.Hom
folder so that e.g. Mathlib.Algebra.Hom.Ring
becomes Mathlib.Algebra.Ring.Hom
and Mathlib.Algebra.Hom.NonUnitalAlg
becomes Mathlib.Algebra.Algebra.NonUnitalHom
.
While fixing the imports I went ahead and sorted them for good luck.
The full list of changes is: renamed: Mathlib/Algebra/Hom/NonUnitalAlg.lean -> Mathlib/Algebra/Algebra/NonUnitalHom.lean renamed: Mathlib/Algebra/Hom/Aut.lean -> Mathlib/Algebra/Group/Aut.lean renamed: Mathlib/Algebra/Hom/Commute.lean -> Mathlib/Algebra/Group/Commute/Hom.lean renamed: Mathlib/Algebra/Hom/Embedding.lean -> Mathlib/Algebra/Group/Embedding.lean renamed: Mathlib/Algebra/Hom/Equiv/Basic.lean -> Mathlib/Algebra/Group/Equiv/Basic.lean renamed: Mathlib/Algebra/Hom/Equiv/TypeTags.lean -> Mathlib/Algebra/Group/Equiv/TypeTags.lean renamed: Mathlib/Algebra/Hom/Equiv/Units/Basic.lean -> Mathlib/Algebra/Group/Units/Equiv.lean renamed: Mathlib/Algebra/Hom/Equiv/Units/GroupWithZero.lean -> Mathlib/Algebra/GroupWithZero/Units/Equiv.lean renamed: Mathlib/Algebra/Hom/Freiman.lean -> Mathlib/Algebra/Group/Freiman.lean renamed: Mathlib/Algebra/Hom/Group/Basic.lean -> Mathlib/Algebra/Group/Hom/Basic.lean renamed: Mathlib/Algebra/Hom/Group/Defs.lean -> Mathlib/Algebra/Group/Hom/Defs.lean renamed: Mathlib/Algebra/Hom/GroupAction.lean -> Mathlib/GroupTheory/GroupAction/Hom.lean renamed: Mathlib/Algebra/Hom/GroupInstances.lean -> Mathlib/Algebra/Group/Hom/Instances.lean renamed: Mathlib/Algebra/Hom/Iterate.lean -> Mathlib/Algebra/GroupPower/IterateHom.lean renamed: Mathlib/Algebra/Hom/Centroid.lean -> Mathlib/Algebra/Ring/CentroidHom.lean renamed: Mathlib/Algebra/Hom/Ring/Basic.lean -> Mathlib/Algebra/Ring/Hom/Basic.lean renamed: Mathlib/Algebra/Hom/Ring/Defs.lean -> Mathlib/Algebra/Ring/Hom/Defs.lean renamed: Mathlib/Algebra/Hom/Units.lean -> Mathlib/Algebra/Group/Units/Hom.lean
Zulip thread: https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/Reorganizing.20.60Mathlib.2EAlgebra.2EHom.60
@@ -3,7 +3,7 @@ Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
-import Mathlib.Algebra.Hom.Equiv.Units.Basic
+import Mathlib.Algebra.Group.Units.Equiv
import Mathlib.CategoryTheory.Endomorphism
#align_import category_theory.conj from "leanprover-community/mathlib"@"32253a1a1071173b33dc7d6a218cf722c6feb514"
@@ -2,15 +2,12 @@
Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-
-! This file was ported from Lean 3 source module category_theory.conj
-! leanprover-community/mathlib commit 32253a1a1071173b33dc7d6a218cf722c6feb514
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.Algebra.Hom.Equiv.Units.Basic
import Mathlib.CategoryTheory.Endomorphism
+#align_import category_theory.conj from "leanprover-community/mathlib"@"32253a1a1071173b33dc7d6a218cf722c6feb514"
+
/-!
# Conjugate morphisms by isomorphisms
@@ -128,11 +128,7 @@ def conjAut : Aut X ≃* Aut Y :=
set_option linter.uppercaseLean3 false in
#align category_theory.iso.conj_Aut CategoryTheory.Iso.conjAut
-theorem conjAut_apply (f : Aut X) : α.conjAut f = α.symm ≪≫ f ≪≫ α := by
- aesop_cat_nonterminal
- apply CategoryTheory.Iso.ext
- simp only [conjAut, Aut.unitsEndEquivAut, conj]
- rfl
+theorem conjAut_apply (f : Aut X) : α.conjAut f = α.symm ≪≫ f ≪≫ α := by aesop_cat
set_option linter.uppercaseLean3 false in
#align category_theory.iso.conj_Aut_apply CategoryTheory.Iso.conjAut_apply
This commit makes aesop_cat
and aesop_graph
terminal (i.e. they either solve the goal or fail). This appears to solve issues where non-terminal tactics, when used as auto-params, introduce unknown universe variables. See
Since there are some intended nonterminal uses of aesop_cat
, we introduce aesop_cat_nonterminal
as the nonterminal equivalent of aesop_cat
.
@@ -129,7 +129,7 @@ set_option linter.uppercaseLean3 false in
#align category_theory.iso.conj_Aut CategoryTheory.Iso.conjAut
theorem conjAut_apply (f : Aut X) : α.conjAut f = α.symm ≪≫ f ≪≫ α := by
- aesop_cat
+ aesop_cat_nonterminal
apply CategoryTheory.Iso.ext
simp only [conjAut, Aut.unitsEndEquivAut, conj]
rfl
All dependencies are ported!