algebra.category.Module.simple
⟷
Mathlib.Algebra.Category.ModuleCat.Simple
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
@@ -4,8 +4,8 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Pierre-Alexandre Bazin, Scott Morrison
-/
import CategoryTheory.Simple
-import Algebra.Category.Module.Subobject
-import Algebra.Category.Module.Algebra
+import Algebra.Category.ModuleCat.Subobject
+import Algebra.Category.ModuleCat.Algebra
import RingTheory.SimpleModule
import LinearAlgebra.FiniteDimensional
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,11 +3,11 @@ Copyright (c) 2022 Pierre-Alexandre Bazin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Pierre-Alexandre Bazin, Scott Morrison
-/
-import Mathbin.CategoryTheory.Simple
-import Mathbin.Algebra.Category.Module.Subobject
-import Mathbin.Algebra.Category.Module.Algebra
-import Mathbin.RingTheory.SimpleModule
-import Mathbin.LinearAlgebra.FiniteDimensional
+import CategoryTheory.Simple
+import Algebra.Category.Module.Subobject
+import Algebra.Category.Module.Algebra
+import RingTheory.SimpleModule
+import LinearAlgebra.FiniteDimensional
#align_import algebra.category.Module.simple from "leanprover-community/mathlib"@"44e2ae8cffc713925494e4975ee31ec1d06929b3"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,11 +2,6 @@
Copyright (c) 2022 Pierre-Alexandre Bazin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Pierre-Alexandre Bazin, Scott Morrison
-
-! This file was ported from Lean 3 source module algebra.category.Module.simple
-! leanprover-community/mathlib commit 44e2ae8cffc713925494e4975ee31ec1d06929b3
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.CategoryTheory.Simple
import Mathbin.Algebra.Category.Module.Subobject
@@ -14,6 +9,8 @@ import Mathbin.Algebra.Category.Module.Algebra
import Mathbin.RingTheory.SimpleModule
import Mathbin.LinearAlgebra.FiniteDimensional
+#align_import algebra.category.Module.simple from "leanprover-community/mathlib"@"44e2ae8cffc713925494e4975ee31ec1d06929b3"
+
/-!
# Simple objects in the category of `R`-modules
mathlib commit https://github.com/leanprover-community/mathlib/commit/2a0ce625dbb0ffbc7d1316597de0b25c1ec75303
@@ -34,10 +34,10 @@ theorem simple_iff_isSimpleModule : Simple (of R M) ↔ IsSimpleModule R M :=
#align simple_iff_is_simple_module simple_iff_isSimpleModule
-/
-#print simple_iff_is_simple_module' /-
-theorem simple_iff_is_simple_module' (M : ModuleCat R) : Simple M ↔ IsSimpleModule R M :=
+#print simple_iff_isSimpleModule' /-
+theorem simple_iff_isSimpleModule' (M : ModuleCat R) : Simple M ↔ IsSimpleModule R M :=
(Simple.iff_of_iso (ofSelfIso M).symm).trans simple_iff_isSimpleModule
-#align simple_iff_is_simple_module' simple_iff_is_simple_module'
+#align simple_iff_is_simple_module' simple_iff_isSimpleModule'
-/
#print simple_of_isSimpleModule /-
@@ -62,7 +62,7 @@ attribute [local instance] module_of_algebra_Module is_scalar_tower_of_algebra_M
/-- Any `k`-algebra module which is 1-dimensional over `k` is simple. -/
theorem simple_of_finrank_eq_one {k : Type _} [Field k] [Algebra k R] {V : ModuleCat R}
(h : finrank k V = 1) : Simple V :=
- (simple_iff_is_simple_module' V).mpr (is_simple_module_of_finrank_eq_one h)
+ (simple_iff_isSimpleModule' V).mpr (is_simple_module_of_finrank_eq_one h)
#align simple_of_finrank_eq_one simple_of_finrank_eq_one
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/8efcf8022aac8e01df8d302dcebdbc25d6a886c8
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Pierre-Alexandre Bazin, Scott Morrison
! This file was ported from Lean 3 source module algebra.category.Module.simple
-! leanprover-community/mathlib commit 4ed0bcaef698011b0692b93a042a2282f490f6b6
+! leanprover-community/mathlib commit 44e2ae8cffc713925494e4975ee31ec1d06929b3
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -17,6 +17,9 @@ import Mathbin.LinearAlgebra.FiniteDimensional
/-!
# Simple objects in the category of `R`-modules
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
We prove simple modules are exactly simple objects in the category of `R`-modules.
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -25,31 +25,41 @@ variable {R M : Type _} [Ring R] [AddCommGroup M] [Module R M]
open CategoryTheory ModuleCat
+#print simple_iff_isSimpleModule /-
theorem simple_iff_isSimpleModule : Simple (of R M) ↔ IsSimpleModule R M :=
(simple_iff_subobject_isSimpleOrder _).trans (subobjectModule (of R M)).isSimpleOrder_iff
#align simple_iff_is_simple_module simple_iff_isSimpleModule
+-/
+#print simple_iff_is_simple_module' /-
theorem simple_iff_is_simple_module' (M : ModuleCat R) : Simple M ↔ IsSimpleModule R M :=
(Simple.iff_of_iso (ofSelfIso M).symm).trans simple_iff_isSimpleModule
#align simple_iff_is_simple_module' simple_iff_is_simple_module'
+-/
+#print simple_of_isSimpleModule /-
/-- A simple module is a simple object in the category of modules. -/
instance simple_of_isSimpleModule [IsSimpleModule R M] : Simple (of R M) :=
simple_iff_isSimpleModule.mpr ‹_›
#align simple_of_is_simple_module simple_of_isSimpleModule
+-/
+#print isSimpleModule_of_simple /-
/-- A simple object in the category of modules is a simple module. -/
instance isSimpleModule_of_simple (M : ModuleCat R) [Simple M] : IsSimpleModule R M :=
simple_iff_isSimpleModule.mp (Simple.of_iso (ofSelfIso M))
#align is_simple_module_of_simple isSimpleModule_of_simple
+-/
open FiniteDimensional
attribute [local instance] module_of_algebra_Module is_scalar_tower_of_algebra_Module
+#print simple_of_finrank_eq_one /-
/-- Any `k`-algebra module which is 1-dimensional over `k` is simple. -/
theorem simple_of_finrank_eq_one {k : Type _} [Field k] [Algebra k R] {V : ModuleCat R}
(h : finrank k V = 1) : Simple V :=
(simple_iff_is_simple_module' V).mpr (is_simple_module_of_finrank_eq_one h)
#align simple_of_finrank_eq_one simple_of_finrank_eq_one
+-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -18,7 +18,7 @@ We prove simple modules are exactly simple objects in the category of `R`-module
-/
-variable {R M : Type _} [Ring R] [AddCommGroup M] [Module R M]
+variable {R M : Type*} [Ring R] [AddCommGroup M] [Module R M]
open CategoryTheory ModuleCat
@@ -45,7 +45,7 @@ open FiniteDimensional
attribute [local instance] moduleOfAlgebraModule isScalarTower_of_algebra_moduleCat
/-- Any `k`-algebra module which is 1-dimensional over `k` is simple. -/
-theorem simple_of_finrank_eq_one {k : Type _} [Field k] [Algebra k R] {V : ModuleCat R}
+theorem simple_of_finrank_eq_one {k : Type*} [Field k] [Algebra k R] {V : ModuleCat R}
(h : finrank k V = 1) : Simple V :=
(simple_iff_isSimpleModule' V).mpr (is_simple_module_of_finrank_eq_one h)
#align simple_of_finrank_eq_one simple_of_finrank_eq_one
@@ -2,11 +2,6 @@
Copyright (c) 2022 Pierre-Alexandre Bazin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Pierre-Alexandre Bazin, Scott Morrison
-
-! This file was ported from Lean 3 source module algebra.category.Module.simple
-! leanprover-community/mathlib commit 4ed0bcaef698011b0692b93a042a2282f490f6b6
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.CategoryTheory.Simple
import Mathlib.Algebra.Category.ModuleCat.Subobject
@@ -14,6 +9,8 @@ import Mathlib.Algebra.Category.ModuleCat.Algebra
import Mathlib.RingTheory.SimpleModule
import Mathlib.LinearAlgebra.FiniteDimensional
+#align_import algebra.category.Module.simple from "leanprover-community/mathlib"@"4ed0bcaef698011b0692b93a042a2282f490f6b6"
+
/-!
# Simple objects in the category of `R`-modules
@@ -29,9 +29,9 @@ theorem simple_iff_isSimpleModule : Simple (of R M) ↔ IsSimpleModule R M :=
(simple_iff_subobject_isSimpleOrder _).trans (subobjectModule (of R M)).isSimpleOrder_iff
#align simple_iff_is_simple_module simple_iff_isSimpleModule
-theorem simple_iff_is_simple_module' (M : ModuleCat R) : Simple M ↔ IsSimpleModule R M :=
+theorem simple_iff_isSimpleModule' (M : ModuleCat R) : Simple M ↔ IsSimpleModule R M :=
(Simple.iff_of_iso (ofSelfIso M).symm).trans simple_iff_isSimpleModule
-#align simple_iff_is_simple_module' simple_iff_is_simple_module'
+#align simple_iff_is_simple_module' simple_iff_isSimpleModule'
/-- A simple module is a simple object in the category of modules. -/
instance simple_of_isSimpleModule [IsSimpleModule R M] : Simple (of R M) :=
@@ -50,5 +50,5 @@ attribute [local instance] moduleOfAlgebraModule isScalarTower_of_algebra_module
/-- Any `k`-algebra module which is 1-dimensional over `k` is simple. -/
theorem simple_of_finrank_eq_one {k : Type _} [Field k] [Algebra k R] {V : ModuleCat R}
(h : finrank k V = 1) : Simple V :=
- (simple_iff_is_simple_module' V).mpr (is_simple_module_of_finrank_eq_one h)
+ (simple_iff_isSimpleModule' V).mpr (is_simple_module_of_finrank_eq_one h)
#align simple_of_finrank_eq_one simple_of_finrank_eq_one
The unported dependencies are