topology.category.TopCommRing
⟷
Mathlib.Topology.Category.TopCommRingCat
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
@@ -138,7 +138,7 @@ instance forgetToTopCatTopologicalRing (R : TopCommRingCat) :
/-- The forgetful functors to `Type` do not reflect isomorphisms,
but the forgetful functor from `TopCommRing` to `Top` does.
-/
-instance : ReflectsIsomorphisms (forget₂ TopCommRingCat.{u} TopCat.{u})
+instance : CategoryTheory.Functor.ReflectsIsomorphisms (forget₂ TopCommRingCat.{u} TopCat.{u})
where reflects X Y f _ := by
skip
-- We have an isomorphism in `Top`,
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import Algebra.Category.Ring.Basic
-import Topology.Category.Top.Basic
+import Topology.Category.TopCat.Basic
import Topology.Algebra.Ring.Basic
#align_import topology.category.TopCommRing from "leanprover-community/mathlib"@"33c67ae661dd8988516ff7f247b0be3018cdd952"
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,9 +3,9 @@ Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
-import Mathbin.Algebra.Category.Ring.Basic
-import Mathbin.Topology.Category.Top.Basic
-import Mathbin.Topology.Algebra.Ring.Basic
+import Algebra.Category.Ring.Basic
+import Topology.Category.Top.Basic
+import Topology.Algebra.Ring.Basic
#align_import topology.category.TopCommRing from "leanprover-community/mathlib"@"33c67ae661dd8988516ff7f247b0be3018cdd952"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,16 +2,13 @@
Copyright (c) 2019 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 topology.category.TopCommRing
-! leanprover-community/mathlib commit 33c67ae661dd8988516ff7f247b0be3018cdd952
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.Algebra.Category.Ring.Basic
import Mathbin.Topology.Category.Top.Basic
import Mathbin.Topology.Algebra.Ring.Basic
+#align_import topology.category.TopCommRing from "leanprover-community/mathlib"@"33c67ae661dd8988516ff7f247b0be3018cdd952"
+
/-!
# Category of topological commutative rings
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -82,45 +82,61 @@ theorem coe_of (X : Type u) [CommRing X] [TopologicalSpace X] [TopologicalRing X
#align TopCommRing.coe_of TopCommRingCat.coe_of
-/
+#print TopCommRingCat.forgetTopologicalSpace /-
instance forgetTopologicalSpace (R : TopCommRingCat) :
TopologicalSpace ((forget TopCommRingCat).obj R) :=
R.isTopologicalSpace
#align TopCommRing.forget_topological_space TopCommRingCat.forgetTopologicalSpace
+-/
+#print TopCommRingCat.forgetCommRing /-
instance forgetCommRing (R : TopCommRingCat) : CommRing ((forget TopCommRingCat).obj R) :=
R.isCommRing
#align TopCommRing.forget_comm_ring TopCommRingCat.forgetCommRing
+-/
+#print TopCommRingCat.forgetTopologicalRing /-
instance forgetTopologicalRing (R : TopCommRingCat) :
TopologicalRing ((forget TopCommRingCat).obj R) :=
R.is_topologicalRing
#align TopCommRing.forget_topological_ring TopCommRingCat.forgetTopologicalRing
+-/
+#print TopCommRingCat.hasForgetToCommRingCat /-
instance hasForgetToCommRingCat : HasForget₂ TopCommRingCat CommRingCat :=
HasForget₂.mk' (fun R => CommRingCat.of R) (fun x => rfl) (fun R S f => f.val) fun R S f =>
HEq.rfl
#align TopCommRing.has_forget_to_CommRing TopCommRingCat.hasForgetToCommRingCat
+-/
+#print TopCommRingCat.forgetToCommRingCatTopologicalSpace /-
instance forgetToCommRingCatTopologicalSpace (R : TopCommRingCat) :
TopologicalSpace ((forget₂ TopCommRingCat CommRingCat).obj R) :=
R.isTopologicalSpace
#align TopCommRing.forget_to_CommRing_topological_space TopCommRingCat.forgetToCommRingCatTopologicalSpace
+-/
+#print TopCommRingCat.hasForgetToTopCat /-
/-- The forgetful functor to Top. -/
instance hasForgetToTopCat : HasForget₂ TopCommRingCat TopCat :=
HasForget₂.mk' (fun R => TopCat.of R) (fun x => rfl) (fun R S f => ⟨⇑f.1, f.2⟩) fun R S f =>
HEq.rfl
#align TopCommRing.has_forget_to_Top TopCommRingCat.hasForgetToTopCat
+-/
+#print TopCommRingCat.forgetToTopCatCommRing /-
instance forgetToTopCatCommRing (R : TopCommRingCat) :
CommRing ((forget₂ TopCommRingCat TopCat).obj R) :=
R.isCommRing
#align TopCommRing.forget_to_Top_comm_ring TopCommRingCat.forgetToTopCatCommRing
+-/
+#print TopCommRingCat.forgetToTopCatTopologicalRing /-
instance forgetToTopCatTopologicalRing (R : TopCommRingCat) :
TopologicalRing ((forget₂ TopCommRingCat TopCat).obj R) :=
R.is_topologicalRing
#align TopCommRing.forget_to_Top_topological_ring TopCommRingCat.forgetToTopCatTopologicalRing
+-/
/-- The forgetful functors to `Type` do not reflect isomorphisms,
but the forgetful functor from `TopCommRing` to `Top` does.
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -82,89 +82,41 @@ theorem coe_of (X : Type u) [CommRing X] [TopologicalSpace X] [TopologicalRing X
#align TopCommRing.coe_of TopCommRingCat.coe_of
-/
-/- warning: TopCommRing.forget_topological_space -> TopCommRingCat.forgetTopologicalSpace is a dubious translation:
-lean 3 declaration is
- forall (R : TopCommRingCat.{u1}), TopologicalSpace.{u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCommRingCat.{u1} TopCommRingCat.CategoryTheory.category.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCommRingCat.{u1} TopCommRingCat.CategoryTheory.category.{u1} TopCommRingCat.CategoryTheory.concreteCategory.{u1}) R)
-but is expected to have type
- forall (R : TopCommRingCat.{u1}), TopologicalSpace.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCommRingCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCommRingCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCommRingCat.{u1} TopCommRingCat.instCategoryTopCommRingCat.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCommRingCat.{u1} TopCommRingCat.instCategoryTopCommRingCat.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCommRingCat.{u1} TopCommRingCat.instCategoryTopCommRingCat.{u1} TopCommRingCat.instConcreteCategoryTopCommRingCatInstCategoryTopCommRingCat.{u1})) R)
-Case conversion may be inaccurate. Consider using '#align TopCommRing.forget_topological_space TopCommRingCat.forgetTopologicalSpaceₓ'. -/
instance forgetTopologicalSpace (R : TopCommRingCat) :
TopologicalSpace ((forget TopCommRingCat).obj R) :=
R.isTopologicalSpace
#align TopCommRing.forget_topological_space TopCommRingCat.forgetTopologicalSpace
-/- warning: TopCommRing.forget_comm_ring -> TopCommRingCat.forgetCommRing is a dubious translation:
-lean 3 declaration is
- forall (R : TopCommRingCat.{u1}), CommRing.{u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCommRingCat.{u1} TopCommRingCat.CategoryTheory.category.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCommRingCat.{u1} TopCommRingCat.CategoryTheory.category.{u1} TopCommRingCat.CategoryTheory.concreteCategory.{u1}) R)
-but is expected to have type
- forall (R : TopCommRingCat.{u1}), CommRing.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCommRingCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCommRingCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCommRingCat.{u1} TopCommRingCat.instCategoryTopCommRingCat.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCommRingCat.{u1} TopCommRingCat.instCategoryTopCommRingCat.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCommRingCat.{u1} TopCommRingCat.instCategoryTopCommRingCat.{u1} TopCommRingCat.instConcreteCategoryTopCommRingCatInstCategoryTopCommRingCat.{u1})) R)
-Case conversion may be inaccurate. Consider using '#align TopCommRing.forget_comm_ring TopCommRingCat.forgetCommRingₓ'. -/
instance forgetCommRing (R : TopCommRingCat) : CommRing ((forget TopCommRingCat).obj R) :=
R.isCommRing
#align TopCommRing.forget_comm_ring TopCommRingCat.forgetCommRing
-/- warning: TopCommRing.forget_topological_ring -> TopCommRingCat.forgetTopologicalRing is a dubious translation:
-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 TopCommRing.forget_topological_ring TopCommRingCat.forgetTopologicalRingₓ'. -/
instance forgetTopologicalRing (R : TopCommRingCat) :
TopologicalRing ((forget TopCommRingCat).obj R) :=
R.is_topologicalRing
#align TopCommRing.forget_topological_ring TopCommRingCat.forgetTopologicalRing
-/- warning: TopCommRing.has_forget_to_CommRing -> TopCommRingCat.hasForgetToCommRingCat is a dubious translation:
-lean 3 declaration is
- CategoryTheory.HasForget₂.{succ u1, succ u1, u1, u1, u1} TopCommRingCat.{u1} CommRingCat.{u1} TopCommRingCat.CategoryTheory.category.{u1} TopCommRingCat.CategoryTheory.concreteCategory.{u1} CommRingCat.largeCategory.{u1} CommRingCat.concreteCategory.{u1}
-but is expected to have type
- CategoryTheory.HasForget₂.{succ u1, succ u1, u1, u1, u1} TopCommRingCat.{u1} CommRingCat.{u1} TopCommRingCat.instCategoryTopCommRingCat.{u1} TopCommRingCat.instConcreteCategoryTopCommRingCatInstCategoryTopCommRingCat.{u1} instCommRingCatLargeCategory.{u1} CommRingCat.instConcreteCategoryCommRingCatInstCommRingCatLargeCategory.{u1}
-Case conversion may be inaccurate. Consider using '#align TopCommRing.has_forget_to_CommRing TopCommRingCat.hasForgetToCommRingCatₓ'. -/
instance hasForgetToCommRingCat : HasForget₂ TopCommRingCat CommRingCat :=
HasForget₂.mk' (fun R => CommRingCat.of R) (fun x => rfl) (fun R S f => f.val) fun R S f =>
HEq.rfl
#align TopCommRing.has_forget_to_CommRing TopCommRingCat.hasForgetToCommRingCat
-/- warning: TopCommRing.forget_to_CommRing_topological_space -> TopCommRingCat.forgetToCommRingCatTopologicalSpace is a dubious translation:
-lean 3 declaration is
- forall (R : TopCommRingCat.{u1}), TopologicalSpace.{u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCommRingCat.{u1} TopCommRingCat.CategoryTheory.category.{u1} CommRingCat.{u1} CommRingCat.largeCategory.{u1} (CategoryTheory.forget₂.{succ u1, succ u1, u1, u1, u1} TopCommRingCat.{u1} CommRingCat.{u1} TopCommRingCat.CategoryTheory.category.{u1} TopCommRingCat.CategoryTheory.concreteCategory.{u1} CommRingCat.largeCategory.{u1} CommRingCat.concreteCategory.{u1} TopCommRingCat.hasForgetToCommRingCat.{u1}) R))
-but is expected to have type
- forall (R : TopCommRingCat.{u1}), TopologicalSpace.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCommRingCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCommRingCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCommRingCat.{u1} TopCommRingCat.instCategoryTopCommRingCat.{u1})) CommRingCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CommRingCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CommRingCat.{u1} instCommRingCatLargeCategory.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCommRingCat.{u1} TopCommRingCat.instCategoryTopCommRingCat.{u1} CommRingCat.{u1} instCommRingCatLargeCategory.{u1} (CategoryTheory.forget₂.{succ u1, succ u1, u1, u1, u1} TopCommRingCat.{u1} CommRingCat.{u1} TopCommRingCat.instCategoryTopCommRingCat.{u1} TopCommRingCat.instConcreteCategoryTopCommRingCatInstCategoryTopCommRingCat.{u1} instCommRingCatLargeCategory.{u1} CommRingCat.instConcreteCategoryCommRingCatInstCommRingCatLargeCategory.{u1} TopCommRingCat.hasForgetToCommRingCat.{u1})) R))
-Case conversion may be inaccurate. Consider using '#align TopCommRing.forget_to_CommRing_topological_space TopCommRingCat.forgetToCommRingCatTopologicalSpaceₓ'. -/
instance forgetToCommRingCatTopologicalSpace (R : TopCommRingCat) :
TopologicalSpace ((forget₂ TopCommRingCat CommRingCat).obj R) :=
R.isTopologicalSpace
#align TopCommRing.forget_to_CommRing_topological_space TopCommRingCat.forgetToCommRingCatTopologicalSpace
-/- warning: TopCommRing.has_forget_to_Top -> TopCommRingCat.hasForgetToTopCat is a dubious translation:
-lean 3 declaration is
- CategoryTheory.HasForget₂.{succ u1, succ u1, u1, u1, u1} TopCommRingCat.{u1} TopCat.{u1} TopCommRingCat.CategoryTheory.category.{u1} TopCommRingCat.CategoryTheory.concreteCategory.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}
-but is expected to have type
- CategoryTheory.HasForget₂.{succ u1, succ u1, u1, u1, u1} TopCommRingCat.{u1} TopCat.{u1} TopCommRingCat.instCategoryTopCommRingCat.{u1} TopCommRingCat.instConcreteCategoryTopCommRingCatInstCategoryTopCommRingCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1}
-Case conversion may be inaccurate. Consider using '#align TopCommRing.has_forget_to_Top TopCommRingCat.hasForgetToTopCatₓ'. -/
/-- The forgetful functor to Top. -/
instance hasForgetToTopCat : HasForget₂ TopCommRingCat TopCat :=
HasForget₂.mk' (fun R => TopCat.of R) (fun x => rfl) (fun R S f => ⟨⇑f.1, f.2⟩) fun R S f =>
HEq.rfl
#align TopCommRing.has_forget_to_Top TopCommRingCat.hasForgetToTopCat
-/- warning: TopCommRing.forget_to_Top_comm_ring -> TopCommRingCat.forgetToTopCatCommRing is a dubious translation:
-lean 3 declaration is
- forall (R : TopCommRingCat.{u1}), CommRing.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCommRingCat.{u1} TopCommRingCat.CategoryTheory.category.{u1} TopCat.{u1} TopCat.largeCategory.{u1} (CategoryTheory.forget₂.{succ u1, succ u1, u1, u1, u1} TopCommRingCat.{u1} TopCat.{u1} TopCommRingCat.CategoryTheory.category.{u1} TopCommRingCat.CategoryTheory.concreteCategory.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1} TopCommRingCat.hasForgetToTopCat.{u1}) R))
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- forall (R : TopCommRingCat.{u1}), CommRing.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCommRingCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCommRingCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCommRingCat.{u1} TopCommRingCat.instCategoryTopCommRingCat.{u1})) TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCommRingCat.{u1} TopCommRingCat.instCategoryTopCommRingCat.{u1} TopCat.{u1} instTopCatLargeCategory.{u1} (CategoryTheory.forget₂.{succ u1, succ u1, u1, u1, u1} TopCommRingCat.{u1} TopCat.{u1} TopCommRingCat.instCategoryTopCommRingCat.{u1} TopCommRingCat.instConcreteCategoryTopCommRingCatInstCategoryTopCommRingCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1} TopCommRingCat.hasForgetToTopCat.{u1})) R))
-Case conversion may be inaccurate. Consider using '#align TopCommRing.forget_to_Top_comm_ring TopCommRingCat.forgetToTopCatCommRingₓ'. -/
instance forgetToTopCatCommRing (R : TopCommRingCat) :
CommRing ((forget₂ TopCommRingCat TopCat).obj R) :=
R.isCommRing
#align TopCommRing.forget_to_Top_comm_ring TopCommRingCat.forgetToTopCatCommRing
-/- warning: TopCommRing.forget_to_Top_topological_ring -> TopCommRingCat.forgetToTopCatTopologicalRing is a dubious translation:
-lean 3 declaration is
- forall (R : TopCommRingCat.{u1}), TopologicalRing.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCommRingCat.{u1} TopCommRingCat.CategoryTheory.category.{u1} TopCat.{u1} TopCat.largeCategory.{u1} (CategoryTheory.forget₂.{succ u1, succ u1, u1, u1, u1} TopCommRingCat.{u1} TopCat.{u1} TopCommRingCat.CategoryTheory.category.{u1} TopCommRingCat.CategoryTheory.concreteCategory.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1} TopCommRingCat.hasForgetToTopCat.{u1}) R)) (TopCat.topologicalSpace.{u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCommRingCat.{u1} TopCommRingCat.CategoryTheory.category.{u1} TopCat.{u1} TopCat.largeCategory.{u1} (CategoryTheory.forget₂.{succ u1, succ u1, u1, u1, u1} TopCommRingCat.{u1} TopCat.{u1} TopCommRingCat.CategoryTheory.category.{u1} TopCommRingCat.CategoryTheory.concreteCategory.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1} TopCommRingCat.hasForgetToTopCat.{u1}) R)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCommRingCat.{u1} TopCommRingCat.CategoryTheory.category.{u1} TopCat.{u1} TopCat.largeCategory.{u1} (CategoryTheory.forget₂.{succ u1, succ u1, u1, u1, u1} TopCommRingCat.{u1} TopCat.{u1} TopCommRingCat.CategoryTheory.category.{u1} TopCommRingCat.CategoryTheory.concreteCategory.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1} TopCommRingCat.hasForgetToTopCat.{u1}) R)) (Ring.toNonAssocRing.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCommRingCat.{u1} TopCommRingCat.CategoryTheory.category.{u1} TopCat.{u1} TopCat.largeCategory.{u1} (CategoryTheory.forget₂.{succ u1, succ u1, u1, u1, u1} TopCommRingCat.{u1} TopCat.{u1} TopCommRingCat.CategoryTheory.category.{u1} TopCommRingCat.CategoryTheory.concreteCategory.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1} TopCommRingCat.hasForgetToTopCat.{u1}) R)) (CommRing.toRing.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCommRingCat.{u1} TopCommRingCat.CategoryTheory.category.{u1} TopCat.{u1} TopCat.largeCategory.{u1} (CategoryTheory.forget₂.{succ u1, succ u1, u1, u1, u1} TopCommRingCat.{u1} TopCat.{u1} TopCommRingCat.CategoryTheory.category.{u1} TopCommRingCat.CategoryTheory.concreteCategory.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1} TopCommRingCat.hasForgetToTopCat.{u1}) R)) (TopCommRingCat.forgetToTopCatCommRing.{u1} R))))
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TopCat.concreteCategory.{u1} TopCommRingCat.hasForgetToTopCat.{u1})) R)) (TopCat.topologicalSpace_coe.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCommRingCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCommRingCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCommRingCat.{u1} TopCommRingCat.instCategoryTopCommRingCat.{u1})) TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCommRingCat.{u1} TopCommRingCat.instCategoryTopCommRingCat.{u1} TopCat.{u1} instTopCatLargeCategory.{u1} (CategoryTheory.forget₂.{succ u1, succ u1, u1, u1, u1} TopCommRingCat.{u1} TopCat.{u1} TopCommRingCat.instCategoryTopCommRingCat.{u1} TopCommRingCat.instConcreteCategoryTopCommRingCatInstCategoryTopCommRingCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1} 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TopCommRingCat.instConcreteCategoryTopCommRingCatInstCategoryTopCommRingCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1} TopCommRingCat.hasForgetToTopCat.{u1})) R)) (CommRing.toRing.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCommRingCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCommRingCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCommRingCat.{u1} TopCommRingCat.instCategoryTopCommRingCat.{u1})) TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCommRingCat.{u1} TopCommRingCat.instCategoryTopCommRingCat.{u1} TopCat.{u1} instTopCatLargeCategory.{u1} (CategoryTheory.forget₂.{succ u1, succ u1, u1, u1, u1} TopCommRingCat.{u1} TopCat.{u1} TopCommRingCat.instCategoryTopCommRingCat.{u1} TopCommRingCat.instConcreteCategoryTopCommRingCatInstCategoryTopCommRingCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1} TopCommRingCat.hasForgetToTopCat.{u1})) R)) (TopCommRingCat.forgetToTopCatCommRing.{u1} R))))
-Case conversion may be inaccurate. Consider using '#align TopCommRing.forget_to_Top_topological_ring TopCommRingCat.forgetToTopCatTopologicalRingₓ'. -/
instance forgetToTopCatTopologicalRing (R : TopCommRingCat) :
TopologicalRing ((forget₂ TopCommRingCat TopCat).obj R) :=
R.is_topologicalRing
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -183,11 +183,7 @@ instance : ReflectsIsomorphisms (forget₂ TopCommRingCat.{u} TopCat.{u})
-- Putting these together we obtain the isomorphism we're after:
exact
⟨⟨⟨e_Ring.symm, i_Top.inv.2⟩,
- ⟨by
- ext x
- exact e_Ring.left_inv x, by
- ext x
- exact e_Ring.right_inv x⟩⟩⟩
+ ⟨by ext x; exact e_Ring.left_inv x, by ext x; exact e_Ring.right_inv x⟩⟩⟩
end TopCommRingCat
mathlib commit https://github.com/leanprover-community/mathlib/commit/33c67ae661dd8988516ff7f247b0be3018cdd952
@@ -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 topology.category.TopCommRing
-! leanprover-community/mathlib commit 9a59dcb7a2d06bf55da57b9030169219980660cd
+! leanprover-community/mathlib commit 33c67ae661dd8988516ff7f247b0be3018cdd952
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -15,6 +15,9 @@ import Mathbin.Topology.Algebra.Ring.Basic
/-!
# Category of topological commutative rings
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
We introduce the category `TopCommRing` of topological commutative rings together with the relevant
forgetful functors to topological spaces and commutative rings.
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/c89fe2d59ae06402c3f55f978016d1ada444f57e
@@ -24,25 +24,27 @@ universe u
open CategoryTheory
+#print TopCommRingCat /-
/-- A bundled topological commutative ring. -/
-structure TopCommRing where
+structure TopCommRingCat where
α : Type u
[isCommRing : CommRing α]
[isTopologicalSpace : TopologicalSpace α]
[is_topologicalRing : TopologicalRing α]
-#align TopCommRing TopCommRing
+#align TopCommRing TopCommRingCat
+-/
-namespace TopCommRing
+namespace TopCommRingCat
-instance : Inhabited TopCommRing :=
+instance : Inhabited TopCommRingCat :=
⟨⟨PUnit⟩⟩
-instance : CoeSort TopCommRing (Type u) :=
- ⟨TopCommRing.α⟩
+instance : CoeSort TopCommRingCat (Type u) :=
+ ⟨TopCommRingCat.α⟩
attribute [instance] is_comm_ring is_topological_space is_topological_ring
-instance : Category TopCommRing.{u}
+instance : Category TopCommRingCat.{u}
where
Hom R S := { f : R →+* S // Continuous f }
id R := ⟨RingHom.id R, by obviously⟩
@@ -55,69 +57,124 @@ instance : Category TopCommRing.{u}
cases g
dsimp; apply Continuous.comp <;> assumption⟩
-instance : ConcreteCategory TopCommRing.{u}
+instance : ConcreteCategory TopCommRingCat.{u}
where
forget :=
{ obj := fun R => R
map := fun R S f => f.val }
forget_faithful := { }
+#print TopCommRingCat.of /-
/-- Construct a bundled `TopCommRing` from the underlying type and the appropriate typeclasses. -/
-def of (X : Type u) [CommRing X] [TopologicalSpace X] [TopologicalRing X] : TopCommRing :=
+def of (X : Type u) [CommRing X] [TopologicalSpace X] [TopologicalRing X] : TopCommRingCat :=
⟨X⟩
-#align TopCommRing.of TopCommRing.of
+#align TopCommRing.of TopCommRingCat.of
+-/
+#print TopCommRingCat.coe_of /-
@[simp]
theorem coe_of (X : Type u) [CommRing X] [TopologicalSpace X] [TopologicalRing X] :
(of X : Type u) = X :=
rfl
-#align TopCommRing.coe_of TopCommRing.coe_of
+#align TopCommRing.coe_of TopCommRingCat.coe_of
+-/
-instance forgetTopologicalSpace (R : TopCommRing) : TopologicalSpace ((forget TopCommRing).obj R) :=
+/- warning: TopCommRing.forget_topological_space -> TopCommRingCat.forgetTopologicalSpace is a dubious translation:
+lean 3 declaration is
+ forall (R : TopCommRingCat.{u1}), TopologicalSpace.{u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCommRingCat.{u1} TopCommRingCat.CategoryTheory.category.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCommRingCat.{u1} TopCommRingCat.CategoryTheory.category.{u1} TopCommRingCat.CategoryTheory.concreteCategory.{u1}) R)
+but is expected to have type
+ forall (R : TopCommRingCat.{u1}), TopologicalSpace.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCommRingCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCommRingCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCommRingCat.{u1} TopCommRingCat.instCategoryTopCommRingCat.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCommRingCat.{u1} TopCommRingCat.instCategoryTopCommRingCat.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCommRingCat.{u1} TopCommRingCat.instCategoryTopCommRingCat.{u1} TopCommRingCat.instConcreteCategoryTopCommRingCatInstCategoryTopCommRingCat.{u1})) R)
+Case conversion may be inaccurate. Consider using '#align TopCommRing.forget_topological_space TopCommRingCat.forgetTopologicalSpaceₓ'. -/
+instance forgetTopologicalSpace (R : TopCommRingCat) :
+ TopologicalSpace ((forget TopCommRingCat).obj R) :=
R.isTopologicalSpace
-#align TopCommRing.forget_topological_space TopCommRing.forgetTopologicalSpace
-
-instance forgetCommRing (R : TopCommRing) : CommRing ((forget TopCommRing).obj R) :=
+#align TopCommRing.forget_topological_space TopCommRingCat.forgetTopologicalSpace
+
+/- warning: TopCommRing.forget_comm_ring -> TopCommRingCat.forgetCommRing is a dubious translation:
+lean 3 declaration is
+ forall (R : TopCommRingCat.{u1}), CommRing.{u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCommRingCat.{u1} TopCommRingCat.CategoryTheory.category.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCommRingCat.{u1} TopCommRingCat.CategoryTheory.category.{u1} TopCommRingCat.CategoryTheory.concreteCategory.{u1}) R)
+but is expected to have type
+ forall (R : TopCommRingCat.{u1}), CommRing.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCommRingCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCommRingCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCommRingCat.{u1} TopCommRingCat.instCategoryTopCommRingCat.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCommRingCat.{u1} TopCommRingCat.instCategoryTopCommRingCat.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCommRingCat.{u1} TopCommRingCat.instCategoryTopCommRingCat.{u1} TopCommRingCat.instConcreteCategoryTopCommRingCatInstCategoryTopCommRingCat.{u1})) R)
+Case conversion may be inaccurate. Consider using '#align TopCommRing.forget_comm_ring TopCommRingCat.forgetCommRingₓ'. -/
+instance forgetCommRing (R : TopCommRingCat) : CommRing ((forget TopCommRingCat).obj R) :=
R.isCommRing
-#align TopCommRing.forget_comm_ring TopCommRing.forgetCommRing
-
-instance forget_topologicalRing (R : TopCommRing) : TopologicalRing ((forget TopCommRing).obj R) :=
+#align TopCommRing.forget_comm_ring TopCommRingCat.forgetCommRing
+
+/- warning: TopCommRing.forget_topological_ring -> TopCommRingCat.forgetTopologicalRing is a dubious translation:
+lean 3 declaration is
+ forall (R : TopCommRingCat.{u1}), TopologicalRing.{u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCommRingCat.{u1} TopCommRingCat.CategoryTheory.category.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCommRingCat.{u1} TopCommRingCat.CategoryTheory.category.{u1} TopCommRingCat.CategoryTheory.concreteCategory.{u1}) R) (TopCommRingCat.forgetTopologicalSpace.{u1} R) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCommRingCat.{u1} TopCommRingCat.CategoryTheory.category.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCommRingCat.{u1} TopCommRingCat.CategoryTheory.category.{u1} TopCommRingCat.CategoryTheory.concreteCategory.{u1}) R) (Ring.toNonAssocRing.{u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCommRingCat.{u1} TopCommRingCat.CategoryTheory.category.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCommRingCat.{u1} TopCommRingCat.CategoryTheory.category.{u1} TopCommRingCat.CategoryTheory.concreteCategory.{u1}) R) (CommRing.toRing.{u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCommRingCat.{u1} TopCommRingCat.CategoryTheory.category.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCommRingCat.{u1} TopCommRingCat.CategoryTheory.category.{u1} TopCommRingCat.CategoryTheory.concreteCategory.{u1}) R) (TopCommRingCat.forgetCommRing.{u1} R))))
+but is expected to have type
+ forall (R : TopCommRingCat.{u1}), TopologicalRing.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCommRingCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCommRingCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCommRingCat.{u1} TopCommRingCat.instCategoryTopCommRingCat.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCommRingCat.{u1} TopCommRingCat.instCategoryTopCommRingCat.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCommRingCat.{u1} TopCommRingCat.instCategoryTopCommRingCat.{u1} TopCommRingCat.instConcreteCategoryTopCommRingCatInstCategoryTopCommRingCat.{u1})) R) (TopCommRingCat.forgetTopologicalSpace.{u1} R) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCommRingCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCommRingCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCommRingCat.{u1} TopCommRingCat.instCategoryTopCommRingCat.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCommRingCat.{u1} TopCommRingCat.instCategoryTopCommRingCat.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCommRingCat.{u1} TopCommRingCat.instCategoryTopCommRingCat.{u1} TopCommRingCat.instConcreteCategoryTopCommRingCatInstCategoryTopCommRingCat.{u1})) R) (Ring.toNonAssocRing.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCommRingCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCommRingCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCommRingCat.{u1} TopCommRingCat.instCategoryTopCommRingCat.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCommRingCat.{u1} TopCommRingCat.instCategoryTopCommRingCat.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCommRingCat.{u1} TopCommRingCat.instCategoryTopCommRingCat.{u1} TopCommRingCat.instConcreteCategoryTopCommRingCatInstCategoryTopCommRingCat.{u1})) R) (CommRing.toRing.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCommRingCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCommRingCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCommRingCat.{u1} TopCommRingCat.instCategoryTopCommRingCat.{u1})) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCommRingCat.{u1} TopCommRingCat.instCategoryTopCommRingCat.{u1} Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{succ u1, u1, u1} TopCommRingCat.{u1} TopCommRingCat.instCategoryTopCommRingCat.{u1} TopCommRingCat.instConcreteCategoryTopCommRingCatInstCategoryTopCommRingCat.{u1})) R) (TopCommRingCat.forgetCommRing.{u1} R))))
+Case conversion may be inaccurate. Consider using '#align TopCommRing.forget_topological_ring TopCommRingCat.forgetTopologicalRingₓ'. -/
+instance forgetTopologicalRing (R : TopCommRingCat) :
+ TopologicalRing ((forget TopCommRingCat).obj R) :=
R.is_topologicalRing
-#align TopCommRing.forget_topological_ring TopCommRing.forget_topologicalRing
-
-instance hasForgetToCommRing : HasForget₂ TopCommRing CommRingCat :=
+#align TopCommRing.forget_topological_ring TopCommRingCat.forgetTopologicalRing
+
+/- warning: TopCommRing.has_forget_to_CommRing -> TopCommRingCat.hasForgetToCommRingCat is a dubious translation:
+lean 3 declaration is
+ CategoryTheory.HasForget₂.{succ u1, succ u1, u1, u1, u1} TopCommRingCat.{u1} CommRingCat.{u1} TopCommRingCat.CategoryTheory.category.{u1} TopCommRingCat.CategoryTheory.concreteCategory.{u1} CommRingCat.largeCategory.{u1} CommRingCat.concreteCategory.{u1}
+but is expected to have type
+ CategoryTheory.HasForget₂.{succ u1, succ u1, u1, u1, u1} TopCommRingCat.{u1} CommRingCat.{u1} TopCommRingCat.instCategoryTopCommRingCat.{u1} TopCommRingCat.instConcreteCategoryTopCommRingCatInstCategoryTopCommRingCat.{u1} instCommRingCatLargeCategory.{u1} CommRingCat.instConcreteCategoryCommRingCatInstCommRingCatLargeCategory.{u1}
+Case conversion may be inaccurate. Consider using '#align TopCommRing.has_forget_to_CommRing TopCommRingCat.hasForgetToCommRingCatₓ'. -/
+instance hasForgetToCommRingCat : HasForget₂ TopCommRingCat CommRingCat :=
HasForget₂.mk' (fun R => CommRingCat.of R) (fun x => rfl) (fun R S f => f.val) fun R S f =>
HEq.rfl
-#align TopCommRing.has_forget_to_CommRing TopCommRing.hasForgetToCommRing
-
-instance forgetToCommRingTopologicalSpace (R : TopCommRing) :
- TopologicalSpace ((forget₂ TopCommRing CommRingCat).obj R) :=
+#align TopCommRing.has_forget_to_CommRing TopCommRingCat.hasForgetToCommRingCat
+
+/- warning: TopCommRing.forget_to_CommRing_topological_space -> TopCommRingCat.forgetToCommRingCatTopologicalSpace is a dubious translation:
+lean 3 declaration is
+ forall (R : TopCommRingCat.{u1}), TopologicalSpace.{u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCommRingCat.{u1} TopCommRingCat.CategoryTheory.category.{u1} CommRingCat.{u1} CommRingCat.largeCategory.{u1} (CategoryTheory.forget₂.{succ u1, succ u1, u1, u1, u1} TopCommRingCat.{u1} CommRingCat.{u1} TopCommRingCat.CategoryTheory.category.{u1} TopCommRingCat.CategoryTheory.concreteCategory.{u1} CommRingCat.largeCategory.{u1} CommRingCat.concreteCategory.{u1} TopCommRingCat.hasForgetToCommRingCat.{u1}) R))
+but is expected to have type
+ forall (R : TopCommRingCat.{u1}), TopologicalSpace.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCommRingCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCommRingCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCommRingCat.{u1} TopCommRingCat.instCategoryTopCommRingCat.{u1})) CommRingCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} CommRingCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} CommRingCat.{u1} instCommRingCatLargeCategory.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCommRingCat.{u1} TopCommRingCat.instCategoryTopCommRingCat.{u1} CommRingCat.{u1} instCommRingCatLargeCategory.{u1} (CategoryTheory.forget₂.{succ u1, succ u1, u1, u1, u1} TopCommRingCat.{u1} CommRingCat.{u1} TopCommRingCat.instCategoryTopCommRingCat.{u1} TopCommRingCat.instConcreteCategoryTopCommRingCatInstCategoryTopCommRingCat.{u1} instCommRingCatLargeCategory.{u1} CommRingCat.instConcreteCategoryCommRingCatInstCommRingCatLargeCategory.{u1} TopCommRingCat.hasForgetToCommRingCat.{u1})) R))
+Case conversion may be inaccurate. Consider using '#align TopCommRing.forget_to_CommRing_topological_space TopCommRingCat.forgetToCommRingCatTopologicalSpaceₓ'. -/
+instance forgetToCommRingCatTopologicalSpace (R : TopCommRingCat) :
+ TopologicalSpace ((forget₂ TopCommRingCat CommRingCat).obj R) :=
R.isTopologicalSpace
-#align TopCommRing.forget_to_CommRing_topological_space TopCommRing.forgetToCommRingTopologicalSpace
-
+#align TopCommRing.forget_to_CommRing_topological_space TopCommRingCat.forgetToCommRingCatTopologicalSpace
+
+/- warning: TopCommRing.has_forget_to_Top -> TopCommRingCat.hasForgetToTopCat is a dubious translation:
+lean 3 declaration is
+ CategoryTheory.HasForget₂.{succ u1, succ u1, u1, u1, u1} TopCommRingCat.{u1} TopCat.{u1} TopCommRingCat.CategoryTheory.category.{u1} TopCommRingCat.CategoryTheory.concreteCategory.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1}
+but is expected to have type
+ CategoryTheory.HasForget₂.{succ u1, succ u1, u1, u1, u1} TopCommRingCat.{u1} TopCat.{u1} TopCommRingCat.instCategoryTopCommRingCat.{u1} TopCommRingCat.instConcreteCategoryTopCommRingCatInstCategoryTopCommRingCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1}
+Case conversion may be inaccurate. Consider using '#align TopCommRing.has_forget_to_Top TopCommRingCat.hasForgetToTopCatₓ'. -/
/-- The forgetful functor to Top. -/
-instance hasForgetToTop : HasForget₂ TopCommRing TopCat :=
+instance hasForgetToTopCat : HasForget₂ TopCommRingCat TopCat :=
HasForget₂.mk' (fun R => TopCat.of R) (fun x => rfl) (fun R S f => ⟨⇑f.1, f.2⟩) fun R S f =>
HEq.rfl
-#align TopCommRing.has_forget_to_Top TopCommRing.hasForgetToTop
-
-instance forgetToTopCommRing (R : TopCommRing) : CommRing ((forget₂ TopCommRing TopCat).obj R) :=
+#align TopCommRing.has_forget_to_Top TopCommRingCat.hasForgetToTopCat
+
+/- warning: TopCommRing.forget_to_Top_comm_ring -> TopCommRingCat.forgetToTopCatCommRing is a dubious translation:
+lean 3 declaration is
+ forall (R : TopCommRingCat.{u1}), CommRing.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCommRingCat.{u1} TopCommRingCat.CategoryTheory.category.{u1} TopCat.{u1} TopCat.largeCategory.{u1} (CategoryTheory.forget₂.{succ u1, succ u1, u1, u1, u1} TopCommRingCat.{u1} TopCat.{u1} TopCommRingCat.CategoryTheory.category.{u1} TopCommRingCat.CategoryTheory.concreteCategory.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1} TopCommRingCat.hasForgetToTopCat.{u1}) R))
+but is expected to have type
+ forall (R : TopCommRingCat.{u1}), CommRing.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCommRingCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCommRingCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCommRingCat.{u1} TopCommRingCat.instCategoryTopCommRingCat.{u1})) TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCommRingCat.{u1} TopCommRingCat.instCategoryTopCommRingCat.{u1} TopCat.{u1} instTopCatLargeCategory.{u1} (CategoryTheory.forget₂.{succ u1, succ u1, u1, u1, u1} TopCommRingCat.{u1} TopCat.{u1} TopCommRingCat.instCategoryTopCommRingCat.{u1} TopCommRingCat.instConcreteCategoryTopCommRingCatInstCategoryTopCommRingCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1} TopCommRingCat.hasForgetToTopCat.{u1})) R))
+Case conversion may be inaccurate. Consider using '#align TopCommRing.forget_to_Top_comm_ring TopCommRingCat.forgetToTopCatCommRingₓ'. -/
+instance forgetToTopCatCommRing (R : TopCommRingCat) :
+ CommRing ((forget₂ TopCommRingCat TopCat).obj R) :=
R.isCommRing
-#align TopCommRing.forget_to_Top_comm_ring TopCommRing.forgetToTopCommRing
-
-instance forget_to_topCat_topologicalRing (R : TopCommRing) :
- TopologicalRing ((forget₂ TopCommRing TopCat).obj R) :=
+#align TopCommRing.forget_to_Top_comm_ring TopCommRingCat.forgetToTopCatCommRing
+
+/- warning: TopCommRing.forget_to_Top_topological_ring -> TopCommRingCat.forgetToTopCatTopologicalRing is a dubious translation:
+lean 3 declaration is
+ forall (R : TopCommRingCat.{u1}), TopologicalRing.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCommRingCat.{u1} TopCommRingCat.CategoryTheory.category.{u1} TopCat.{u1} TopCat.largeCategory.{u1} (CategoryTheory.forget₂.{succ u1, succ u1, u1, u1, u1} TopCommRingCat.{u1} TopCat.{u1} TopCommRingCat.CategoryTheory.category.{u1} TopCommRingCat.CategoryTheory.concreteCategory.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1} TopCommRingCat.hasForgetToTopCat.{u1}) R)) (TopCat.topologicalSpace.{u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCommRingCat.{u1} TopCommRingCat.CategoryTheory.category.{u1} TopCat.{u1} TopCat.largeCategory.{u1} (CategoryTheory.forget₂.{succ u1, succ u1, u1, u1, u1} TopCommRingCat.{u1} TopCat.{u1} TopCommRingCat.CategoryTheory.category.{u1} TopCommRingCat.CategoryTheory.concreteCategory.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1} TopCommRingCat.hasForgetToTopCat.{u1}) R)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCommRingCat.{u1} TopCommRingCat.CategoryTheory.category.{u1} TopCat.{u1} TopCat.largeCategory.{u1} (CategoryTheory.forget₂.{succ u1, succ u1, u1, u1, u1} TopCommRingCat.{u1} TopCat.{u1} TopCommRingCat.CategoryTheory.category.{u1} TopCommRingCat.CategoryTheory.concreteCategory.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1} TopCommRingCat.hasForgetToTopCat.{u1}) R)) (Ring.toNonAssocRing.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCommRingCat.{u1} TopCommRingCat.CategoryTheory.category.{u1} TopCat.{u1} TopCat.largeCategory.{u1} (CategoryTheory.forget₂.{succ u1, succ u1, u1, u1, u1} TopCommRingCat.{u1} TopCat.{u1} TopCommRingCat.CategoryTheory.category.{u1} TopCommRingCat.CategoryTheory.concreteCategory.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1} TopCommRingCat.hasForgetToTopCat.{u1}) R)) (CommRing.toRing.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} (CategoryTheory.Functor.obj.{u1, u1, succ u1, succ u1} TopCommRingCat.{u1} TopCommRingCat.CategoryTheory.category.{u1} TopCat.{u1} TopCat.largeCategory.{u1} (CategoryTheory.forget₂.{succ u1, succ u1, u1, u1, u1} TopCommRingCat.{u1} TopCat.{u1} TopCommRingCat.CategoryTheory.category.{u1} TopCommRingCat.CategoryTheory.concreteCategory.{u1} TopCat.largeCategory.{u1} TopCat.concreteCategory.{u1} TopCommRingCat.hasForgetToTopCat.{u1}) R)) (TopCommRingCat.forgetToTopCatCommRing.{u1} R))))
+but is expected to have type
+ forall (R : TopCommRingCat.{u1}), TopologicalRing.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCommRingCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCommRingCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCommRingCat.{u1} TopCommRingCat.instCategoryTopCommRingCat.{u1})) TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCommRingCat.{u1} TopCommRingCat.instCategoryTopCommRingCat.{u1} TopCat.{u1} instTopCatLargeCategory.{u1} (CategoryTheory.forget₂.{succ u1, succ u1, u1, u1, u1} TopCommRingCat.{u1} TopCat.{u1} TopCommRingCat.instCategoryTopCommRingCat.{u1} TopCommRingCat.instConcreteCategoryTopCommRingCatInstCategoryTopCommRingCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1} TopCommRingCat.hasForgetToTopCat.{u1})) R)) (TopCat.topologicalSpace_coe.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCommRingCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCommRingCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCommRingCat.{u1} TopCommRingCat.instCategoryTopCommRingCat.{u1})) TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCommRingCat.{u1} TopCommRingCat.instCategoryTopCommRingCat.{u1} TopCat.{u1} instTopCatLargeCategory.{u1} (CategoryTheory.forget₂.{succ u1, succ u1, u1, u1, u1} TopCommRingCat.{u1} TopCat.{u1} TopCommRingCat.instCategoryTopCommRingCat.{u1} TopCommRingCat.instConcreteCategoryTopCommRingCatInstCategoryTopCommRingCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1} TopCommRingCat.hasForgetToTopCat.{u1})) R)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCommRingCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCommRingCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCommRingCat.{u1} TopCommRingCat.instCategoryTopCommRingCat.{u1})) TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCommRingCat.{u1} TopCommRingCat.instCategoryTopCommRingCat.{u1} TopCat.{u1} instTopCatLargeCategory.{u1} (CategoryTheory.forget₂.{succ u1, succ u1, u1, u1, u1} TopCommRingCat.{u1} TopCat.{u1} TopCommRingCat.instCategoryTopCommRingCat.{u1} TopCommRingCat.instConcreteCategoryTopCommRingCatInstCategoryTopCommRingCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1} TopCommRingCat.hasForgetToTopCat.{u1})) R)) (Ring.toNonAssocRing.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCommRingCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCommRingCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCommRingCat.{u1} TopCommRingCat.instCategoryTopCommRingCat.{u1})) TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCommRingCat.{u1} TopCommRingCat.instCategoryTopCommRingCat.{u1} TopCat.{u1} instTopCatLargeCategory.{u1} (CategoryTheory.forget₂.{succ u1, succ u1, u1, u1, u1} TopCommRingCat.{u1} TopCat.{u1} TopCommRingCat.instCategoryTopCommRingCat.{u1} TopCommRingCat.instConcreteCategoryTopCommRingCatInstCategoryTopCommRingCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1} TopCommRingCat.hasForgetToTopCat.{u1})) R)) (CommRing.toRing.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (Prefunctor.obj.{succ u1, succ u1, succ u1, succ u1} TopCommRingCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCommRingCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCommRingCat.{u1} TopCommRingCat.instCategoryTopCommRingCat.{u1})) TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, succ u1, succ u1} TopCommRingCat.{u1} TopCommRingCat.instCategoryTopCommRingCat.{u1} TopCat.{u1} instTopCatLargeCategory.{u1} (CategoryTheory.forget₂.{succ u1, succ u1, u1, u1, u1} TopCommRingCat.{u1} TopCat.{u1} TopCommRingCat.instCategoryTopCommRingCat.{u1} TopCommRingCat.instConcreteCategoryTopCommRingCatInstCategoryTopCommRingCat.{u1} instTopCatLargeCategory.{u1} TopCat.concreteCategory.{u1} TopCommRingCat.hasForgetToTopCat.{u1})) R)) (TopCommRingCat.forgetToTopCatCommRing.{u1} R))))
+Case conversion may be inaccurate. Consider using '#align TopCommRing.forget_to_Top_topological_ring TopCommRingCat.forgetToTopCatTopologicalRingₓ'. -/
+instance forgetToTopCatTopologicalRing (R : TopCommRingCat) :
+ TopologicalRing ((forget₂ TopCommRingCat TopCat).obj R) :=
R.is_topologicalRing
-#align TopCommRing.forget_to_Top_topological_ring TopCommRing.forget_to_topCat_topologicalRing
+#align TopCommRing.forget_to_Top_topological_ring TopCommRingCat.forgetToTopCatTopologicalRing
/-- The forgetful functors to `Type` do not reflect isomorphisms,
but the forgetful functor from `TopCommRing` to `Top` does.
-/
-instance : ReflectsIsomorphisms (forget₂ TopCommRing.{u} TopCat.{u})
+instance : ReflectsIsomorphisms (forget₂ TopCommRingCat.{u} TopCat.{u})
where reflects X Y f _ := by
skip
-- We have an isomorphism in `Top`,
- let i_Top := as_iso ((forget₂ TopCommRing TopCat).map f)
+ let i_Top := as_iso ((forget₂ TopCommRingCat TopCat).map f)
-- and a `ring_equiv`.
let e_Ring : X ≃+* Y := { f.1, ((forget TopCat).mapIso i_Top).toEquiv with }
-- Putting these together we obtain the isomorphism we're after:
@@ -129,5 +186,5 @@ instance : ReflectsIsomorphisms (forget₂ TopCommRing.{u} TopCat.{u})
ext x
exact e_Ring.right_inv x⟩⟩⟩
-end TopCommRing
+end TopCommRingCat
mathlib commit https://github.com/leanprover-community/mathlib/commit/62e8311c791f02c47451bf14aa2501048e7c2f33
@@ -4,13 +4,13 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
! This file was ported from Lean 3 source module topology.category.TopCommRing
-! leanprover-community/mathlib commit 79ffb5563b56fefdea3d60b5736dad168a9494ab
+! leanprover-community/mathlib commit 9a59dcb7a2d06bf55da57b9030169219980660cd
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
import Mathbin.Algebra.Category.Ring.Basic
import Mathbin.Topology.Category.Top.Basic
-import Mathbin.Topology.Algebra.Ring
+import Mathbin.Topology.Algebra.Ring.Basic
/-!
# Category of topological commutative rings
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
These notions on functors are now Functor.Full
, Functor.Faithful
, Functor.EssSurj
, Functor.IsEquivalence
, Functor.ReflectsIsomorphisms
. Deprecated aliases are introduced for the previous names.
@@ -112,7 +112,7 @@ instance forgetToTopCatTopologicalRing (R : TopCommRingCat) :
/-- The forgetful functors to `Type` do not reflect isomorphisms,
but the forgetful functor from `TopCommRingCat` to `TopCat` does.
-/
-instance : ReflectsIsomorphisms (forget₂ TopCommRingCat.{u} TopCat.{u}) where
+instance : (forget₂ TopCommRingCat.{u} TopCat.{u}).ReflectsIsomorphisms where
reflects {X Y} f _ := by
-- We have an isomorphism in `TopCat`,
let i_Top := asIso ((forget₂ TopCommRingCat TopCat).map f)
@@ -21,7 +21,7 @@ universe u
open CategoryTheory
-set_option linter.uppercaseLean3 false -- `TopCommRing`
+set_option linter.uppercaseLean3 false -- `TopCommRingCat`
/-- A bundled topological commutative ring. -/
structure TopCommRingCat where
In this pull request, I have systematically eliminated the leading whitespace preceding the colon (:
) within all unlabelled or unclassified porting notes. This adjustment facilitates a more efficient review process for the remaining notes by ensuring no entries are overlooked due to formatting inconsistencies.
@@ -56,7 +56,7 @@ instance : ConcreteCategory TopCommRingCat.{u} where
forget :=
{ obj := fun R => R
map := fun f => f.val }
- -- Porting note : Old proof was `forget_faithful := { }`
+ -- Porting note: Old proof was `forget_faithful := { }`
forget_faithful :=
{ map_injective := fun {_ _ a b} h => Subtype.ext <| RingHom.coe_inj h }
@@ -2,16 +2,13 @@
Copyright (c) 2019 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 topology.category.TopCommRing
-! leanprover-community/mathlib commit 9a59dcb7a2d06bf55da57b9030169219980660cd
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.Algebra.Category.Ring.Basic
import Mathlib.Topology.Category.TopCat.Basic
import Mathlib.Topology.Algebra.Ring.Basic
+#align_import topology.category.TopCommRing from "leanprover-community/mathlib"@"9a59dcb7a2d06bf55da57b9030169219980660cd"
+
/-!
# Category of topological commutative rings
@@ -51,7 +51,7 @@ instance : Category TopCommRingCat.{u} where
comp f g :=
⟨g.val.comp f.val, by
-- TODO automate
- cases f;
+ cases f
cases g
dsimp; apply Continuous.comp <;> assumption⟩
@@ -9,7 +9,7 @@ Authors: Scott Morrison
! if you have ported upstream changes.
-/
import Mathlib.Algebra.Category.Ring.Basic
-import Mathlib.Topology.Category.Top.Basic
+import Mathlib.Topology.Category.TopCat.Basic
import Mathlib.Topology.Algebra.Ring.Basic
/-!
The unported dependencies are