algebra.category.Ring.instancesMathlib.Algebra.Category.Ring.Instances

This file has been ported!

Changes since the initial port

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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Changes in mathlib3port

mathlib3
mathlib3port
Diff
@@ -3,9 +3,9 @@ Copyright (c) 2021 Andrew Yang. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Andrew Yang
 -/
-import Mathbin.Algebra.Category.Ring.Basic
-import Mathbin.RingTheory.Localization.Away.Basic
-import Mathbin.RingTheory.Ideal.LocalRing
+import Algebra.Category.Ring.Basic
+import RingTheory.Localization.Away.Basic
+import RingTheory.Ideal.LocalRing
 
 #align_import algebra.category.Ring.instances from "leanprover-community/mathlib"@"38df578a6450a8c5142b3727e3ae894c2300cae0"
 
Diff
@@ -2,16 +2,13 @@
 Copyright (c) 2021 Andrew Yang. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Andrew Yang
-
-! This file was ported from Lean 3 source module algebra.category.Ring.instances
-! leanprover-community/mathlib commit 38df578a6450a8c5142b3727e3ae894c2300cae0
-! 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.RingTheory.Localization.Away.Basic
 import Mathbin.RingTheory.Ideal.LocalRing
 
+#align_import algebra.category.Ring.instances from "leanprover-community/mathlib"@"38df578a6450a8c5142b3727e3ae894c2300cae0"
+
 /-!
 # Ring-theoretic results in terms of categorical languages
 
Diff
@@ -22,15 +22,19 @@ import Mathbin.RingTheory.Ideal.LocalRing
 
 open CategoryTheory
 
+#print localization_unit_isIso /-
 instance localization_unit_isIso (R : CommRingCat) :
     IsIso (CommRingCat.ofHom <| algebraMap R (Localization.Away (1 : R))) :=
   IsIso.of_iso (IsLocalization.atOne R (Localization.Away (1 : R))).toRingEquiv.toCommRingCatIso
 #align localization_unit_is_iso localization_unit_isIso
+-/
 
+#print localization_unit_isIso' /-
 instance localization_unit_isIso' (R : CommRingCat) :
     @IsIso CommRingCat _ R _ (CommRingCat.ofHom <| algebraMap R (Localization.Away (1 : R))) := by
   cases R; exact localization_unit_isIso _
 #align localization_unit_is_iso' localization_unit_isIso'
+-/
 
 #print IsLocalization.epi /-
 theorem IsLocalization.epi {R : Type _} [CommRing R] (M : Submonoid R) (S : Type _) [CommRing S]
@@ -39,15 +43,19 @@ theorem IsLocalization.epi {R : Type _} [CommRing R] (M : Submonoid R) (S : Type
 #align is_localization.epi IsLocalization.epi
 -/
 
+#print Localization.epi /-
 instance Localization.epi {R : Type _} [CommRing R] (M : Submonoid R) :
     Epi (CommRingCat.ofHom <| algebraMap R <| Localization M) :=
   IsLocalization.epi M _
 #align localization.epi Localization.epi
+-/
 
+#print Localization.epi' /-
 instance Localization.epi' {R : CommRingCat} (M : Submonoid R) :
     @Epi CommRingCat _ R _ (CommRingCat.ofHom <| algebraMap R <| Localization M : _) := by cases R;
   exact IsLocalization.epi M _
 #align localization.epi' Localization.epi'
+-/
 
 #print CommRingCat.isLocalRingHom_comp /-
 instance CommRingCat.isLocalRingHom_comp {R S T : CommRingCat} (f : R ⟶ S) (g : S ⟶ T)
Diff
@@ -22,17 +22,11 @@ import Mathbin.RingTheory.Ideal.LocalRing
 
 open CategoryTheory
 
-/- warning: localization_unit_is_iso -> localization_unit_isIso is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align localization_unit_is_iso localization_unit_isIsoₓ'. -/
 instance localization_unit_isIso (R : CommRingCat) :
     IsIso (CommRingCat.ofHom <| algebraMap R (Localization.Away (1 : R))) :=
   IsIso.of_iso (IsLocalization.atOne R (Localization.Away (1 : R))).toRingEquiv.toCommRingCatIso
 #align localization_unit_is_iso localization_unit_isIso
 
-/- warning: localization_unit_is_iso' -> localization_unit_isIso' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align localization_unit_is_iso' localization_unit_isIso'ₓ'. -/
 instance localization_unit_isIso' (R : CommRingCat) :
     @IsIso CommRingCat _ R _ (CommRingCat.ofHom <| algebraMap R (Localization.Away (1 : R))) := by
   cases R; exact localization_unit_isIso _
@@ -45,23 +39,11 @@ theorem IsLocalization.epi {R : Type _} [CommRing R] (M : Submonoid R) (S : Type
 #align is_localization.epi IsLocalization.epi
 -/
 
-/- warning: localization.epi -> Localization.epi is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))), CategoryTheory.Epi.{u1, succ u1} CommRingCat.{u1} CommRingCat.largeCategory.{u1} (CommRingCat.of.{u1} R _inst_1) (CommRingCat.of.{u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (Localization.commRing.{u1} R _inst_1 M)) (CommRingCat.ofHom.{u1} R (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) _inst_1 (Localization.commRing.{u1} R _inst_1 M) (algebraMap.{u1, u1} R (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (CommRing.toRing.{u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (Localization.commRing.{u1} R _inst_1 M))) (Localization.algebra.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) M R (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))), CategoryTheory.Epi.{u1, succ u1} CommRingCat.{u1} instCommRingCatLargeCategory.{u1} (CommRingCat.of.{u1} R _inst_1) (CommRingCat.of.{u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommRingLocalizationToCommMonoid.{u1} R _inst_1 M)) (CommRingCat.ofHom.{u1} R (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) _inst_1 (Localization.instCommRingLocalizationToCommMonoid.{u1} R _inst_1 M) (algebraMap.{u1, u1} R (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) M)) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) M R (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))
-Case conversion may be inaccurate. Consider using '#align localization.epi Localization.epiₓ'. -/
 instance Localization.epi {R : Type _} [CommRing R] (M : Submonoid R) :
     Epi (CommRingCat.ofHom <| algebraMap R <| Localization M) :=
   IsLocalization.epi M _
 #align localization.epi Localization.epi
 
-/- warning: localization.epi' -> Localization.epi' is a dubious translation:
-lean 3 declaration is
-  forall {R : CommRingCat.{u1}} (M : Submonoid.{u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) (MulZeroOneClass.toMulOneClass.{u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) (NonAssocSemiring.toMulZeroOneClass.{u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) (NonAssocRing.toNonAssocSemiring.{u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) (Ring.toNonAssocRing.{u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) (CommRing.toRing.{u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) (CommRingCat.commRing.{u1} R))))))), CategoryTheory.Epi.{u1, succ u1} CommRingCat.{u1} CommRingCat.largeCategory.{u1} R (CommRingCat.of.{u1} (Localization.{u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) (CommRing.toCommMonoid.{u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) (CommRingCat.commRing.{u1} R)) M) (Localization.commRing.{u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) (CommRingCat.commRing.{u1} R) M)) (CommRingCat.ofHom.{u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) (Localization.{u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) (CommRing.toCommMonoid.{u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) (CommRingCat.commRing.{u1} R)) M) (CommRingCat.commRing.{u1} R) (Localization.commRing.{u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) (CommRingCat.commRing.{u1} R) M) (algebraMap.{u1, u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) (Localization.{u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) (CommRing.toCommMonoid.{u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) (CommRingCat.commRing.{u1} R)) M) (CommRing.toCommSemiring.{u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) (CommRingCat.commRing.{u1} R)) (Ring.toSemiring.{u1} (Localization.{u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) (CommRing.toCommMonoid.{u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) (CommRingCat.commRing.{u1} R)) M) (CommRing.toRing.{u1} (Localization.{u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) (CommRing.toCommMonoid.{u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) (CommRingCat.commRing.{u1} R)) M) (Localization.commRing.{u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) (CommRingCat.commRing.{u1} R) M))) (Localization.algebra.{u1, u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) (CommRing.toCommSemiring.{u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) (CommRingCat.commRing.{u1} R)) M (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) (CommRing.toCommSemiring.{u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) (CommRingCat.commRing.{u1} R)) (Algebra.id.{u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) (CommRing.toCommSemiring.{u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) (CommRingCat.commRing.{u1} R))))))
-but is expected to have type
-  forall {R : CommRingCat.{u1}} (M : Submonoid.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (MulZeroOneClass.toMulOneClass.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (NonAssocSemiring.toMulZeroOneClass.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (Semiring.toNonAssocSemiring.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommSemiring.toSemiring.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRing.toCommSemiring.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRingCat.instCommRingα_1.{u1} R))))))), CategoryTheory.Epi.{u1, succ u1} CommRingCat.{u1} instCommRingCatLargeCategory.{u1} R (CommRingCat.of.{u1} (Localization.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRing.toCommMonoid.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRingCat.instCommRingα_1.{u1} R)) M) (Localization.instCommRingLocalizationToCommMonoid.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRingCat.instCommRingα_1.{u1} R) M)) (CommRingCat.ofHom.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (Localization.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRing.toCommMonoid.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRingCat.instCommRingα_1.{u1} R)) M) (CommRingCat.instCommRingα_1.{u1} R) (Localization.instCommRingLocalizationToCommMonoid.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRingCat.instCommRingα_1.{u1} R) M) (algebraMap.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (Localization.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRing.toCommMonoid.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRingCat.instCommRingα_1.{u1} R)) M) (CommRing.toCommSemiring.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRingCat.instCommRingα_1.{u1} R)) (CommSemiring.toSemiring.{u1} (Localization.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRing.toCommMonoid.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRingCat.instCommRingα_1.{u1} R)) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRing.toCommSemiring.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRingCat.instCommRingα_1.{u1} R)) M)) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRing.toCommSemiring.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRingCat.instCommRingα_1.{u1} R)) M (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRing.toCommSemiring.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRingCat.instCommRingα_1.{u1} R)) (Algebra.id.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRing.toCommSemiring.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRingCat.instCommRingα_1.{u1} R))))))
-Case conversion may be inaccurate. Consider using '#align localization.epi' Localization.epi'ₓ'. -/
 instance Localization.epi' {R : CommRingCat} (M : Submonoid R) :
     @Epi CommRingCat _ R _ (CommRingCat.ofHom <| algebraMap R <| Localization M : _) := by cases R;
   exact IsLocalization.epi M _
Diff
@@ -34,10 +34,8 @@ instance localization_unit_isIso (R : CommRingCat) :
 <too large>
 Case conversion may be inaccurate. Consider using '#align localization_unit_is_iso' localization_unit_isIso'ₓ'. -/
 instance localization_unit_isIso' (R : CommRingCat) :
-    @IsIso CommRingCat _ R _ (CommRingCat.ofHom <| algebraMap R (Localization.Away (1 : R))) :=
-  by
-  cases R
-  exact localization_unit_isIso _
+    @IsIso CommRingCat _ R _ (CommRingCat.ofHom <| algebraMap R (Localization.Away (1 : R))) := by
+  cases R; exact localization_unit_isIso _
 #align localization_unit_is_iso' localization_unit_isIso'
 
 #print IsLocalization.epi /-
@@ -65,9 +63,7 @@ but is expected to have type
   forall {R : CommRingCat.{u1}} (M : Submonoid.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (MulZeroOneClass.toMulOneClass.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (NonAssocSemiring.toMulZeroOneClass.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (Semiring.toNonAssocSemiring.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommSemiring.toSemiring.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRing.toCommSemiring.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRingCat.instCommRingα_1.{u1} R))))))), CategoryTheory.Epi.{u1, succ u1} CommRingCat.{u1} instCommRingCatLargeCategory.{u1} R (CommRingCat.of.{u1} (Localization.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRing.toCommMonoid.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRingCat.instCommRingα_1.{u1} R)) M) (Localization.instCommRingLocalizationToCommMonoid.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRingCat.instCommRingα_1.{u1} R) M)) (CommRingCat.ofHom.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (Localization.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRing.toCommMonoid.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRingCat.instCommRingα_1.{u1} R)) M) (CommRingCat.instCommRingα_1.{u1} R) (Localization.instCommRingLocalizationToCommMonoid.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRingCat.instCommRingα_1.{u1} R) M) (algebraMap.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (Localization.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRing.toCommMonoid.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRingCat.instCommRingα_1.{u1} R)) M) (CommRing.toCommSemiring.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRingCat.instCommRingα_1.{u1} R)) (CommSemiring.toSemiring.{u1} (Localization.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRing.toCommMonoid.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRingCat.instCommRingα_1.{u1} R)) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRing.toCommSemiring.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRingCat.instCommRingα_1.{u1} R)) M)) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRing.toCommSemiring.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRingCat.instCommRingα_1.{u1} R)) M (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRing.toCommSemiring.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRingCat.instCommRingα_1.{u1} R)) (Algebra.id.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRing.toCommSemiring.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRingCat.instCommRingα_1.{u1} R))))))
 Case conversion may be inaccurate. Consider using '#align localization.epi' Localization.epi'ₓ'. -/
 instance Localization.epi' {R : CommRingCat} (M : Submonoid R) :
-    @Epi CommRingCat _ R _ (CommRingCat.ofHom <| algebraMap R <| Localization M : _) :=
-  by
-  cases R
+    @Epi CommRingCat _ R _ (CommRingCat.ofHom <| algebraMap R <| Localization M : _) := by cases R;
   exact IsLocalization.epi M _
 #align localization.epi' Localization.epi'
 
Diff
@@ -23,28 +23,22 @@ import Mathbin.RingTheory.Ideal.LocalRing
 open CategoryTheory
 
 /- warning: localization_unit_is_iso -> localization_unit_isIso is a dubious translation:
-lean 3 declaration is
-  forall (R : CommRingCat.{u1}), CategoryTheory.IsIso.{u1, succ u1} CommRingCat.{u1} CommRingCat.largeCategory.{u1} (CommRingCat.of.{u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) (CommRingCat.commRing.{u1} R)) (CommRingCat.of.{u1} (Localization.Away.{u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) (CommRing.toCommMonoid.{u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) (CommRingCat.commRing.{u1} R)) (OfNat.ofNat.{u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) 1 (OfNat.mk.{u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) 1 (One.one.{u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) (AddMonoidWithOne.toOne.{u1} (coeSort.{succ (succ u1), succ 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 Case conversion may be inaccurate. Consider using '#align localization_unit_is_iso localization_unit_isIsoₓ'. -/
 instance localization_unit_isIso (R : CommRingCat) :
     IsIso (CommRingCat.ofHom <| algebraMap R (Localization.Away (1 : R))) :=
   IsIso.of_iso (IsLocalization.atOne R (Localization.Away (1 : R))).toRingEquiv.toCommRingCatIso
 #align localization_unit_is_iso localization_unit_isIso
 
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(CommMonoid.toMonoid.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRing.toCommMonoid.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRingCat.instCommRingα_1.{u1} R))) (OfNat.ofNat.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) 1 (One.toOfNat1.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (Semiring.toOne.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommSemiring.toSemiring.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRing.toCommSemiring.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRingCat.instCommRingα_1.{u1} R))))))) (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRing.toCommSemiring.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRingCat.instCommRingα_1.{u1} R)) (Algebra.id.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRing.toCommSemiring.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRingCat.instCommRingα_1.{u1} R))))))
-Case conversion may be inaccurate. Consider using '#align localization_unit_is_iso' localization_unit_is_iso'ₓ'. -/
-instance localization_unit_is_iso' (R : CommRingCat) :
+/- warning: localization_unit_is_iso' -> localization_unit_isIso' is a dubious translation:
+<too large>
+Case conversion may be inaccurate. Consider using '#align localization_unit_is_iso' localization_unit_isIso'ₓ'. -/
+instance localization_unit_isIso' (R : CommRingCat) :
     @IsIso CommRingCat _ R _ (CommRingCat.ofHom <| algebraMap R (Localization.Away (1 : R))) :=
   by
   cases R
   exact localization_unit_isIso _
-#align localization_unit_is_iso' localization_unit_is_iso'
+#align localization_unit_is_iso' localization_unit_isIso'
 
 #print IsLocalization.epi /-
 theorem IsLocalization.epi {R : Type _} [CommRing R] (M : Submonoid R) (S : Type _) [CommRing S]
Diff
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Andrew Yang
 
 ! This file was ported from Lean 3 source module algebra.category.Ring.instances
-! leanprover-community/mathlib commit a7c017d750512a352b623b1824d75da5998457d0
+! leanprover-community/mathlib commit 38df578a6450a8c5142b3727e3ae894c2300cae0
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.RingTheory.Ideal.LocalRing
 
 /-!
 # Ring-theoretic results in terms of categorical languages
+
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
 -/
 
 
Diff
@@ -19,11 +19,23 @@ import Mathbin.RingTheory.Ideal.LocalRing
 
 open CategoryTheory
 
+/- warning: localization_unit_is_iso -> localization_unit_isIso is a dubious translation:
+lean 3 declaration is
+  forall (R : CommRingCat.{u1}), CategoryTheory.IsIso.{u1, succ u1} CommRingCat.{u1} CommRingCat.largeCategory.{u1} (CommRingCat.of.{u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) (CommRingCat.commRing.{u1} R)) (CommRingCat.of.{u1} (Localization.Away.{u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) (CommRing.toCommMonoid.{u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) (CommRingCat.commRing.{u1} R)) (OfNat.ofNat.{u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) 1 (OfNat.mk.{u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) 1 (One.one.{u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) (AddMonoidWithOne.toOne.{u1} (coeSort.{succ (succ u1), succ 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+but is expected to have type
+  forall (R : CommRingCat.{u1}), CategoryTheory.IsIso.{u1, succ u1} CommRingCat.{u1} instCommRingCatLargeCategory.{u1} (CommRingCat.of.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRingCat.instCommRingα_1.{u1} R)) (CommRingCat.of.{u1} (Localization.Away.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRing.toCommMonoid.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRingCat.instCommRingα_1.{u1} R)) (OfNat.ofNat.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) 1 (One.toOfNat1.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (Semiring.toOne.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommSemiring.toSemiring.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRing.toCommSemiring.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRingCat.instCommRingα_1.{u1} R))))))) (Localization.instCommRingLocalizationToCommMonoid.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRingCat.instCommRingα_1.{u1} R) (Submonoid.powers.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommMonoid.toMonoid.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRing.toCommMonoid.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRingCat.instCommRingα_1.{u1} R))) (OfNat.ofNat.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) 1 (One.toOfNat1.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (Semiring.toOne.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommSemiring.toSemiring.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRing.toCommSemiring.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRingCat.instCommRingα_1.{u1} R))))))))) (CommRingCat.ofHom.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (Localization.Away.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRing.toCommMonoid.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRingCat.instCommRingα_1.{u1} R)) (OfNat.ofNat.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) 1 (One.toOfNat1.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (Semiring.toOne.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommSemiring.toSemiring.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRing.toCommSemiring.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRingCat.instCommRingα_1.{u1} R))))))) (CommRingCat.instCommRingα_1.{u1} R) (Localization.instCommRingLocalizationToCommMonoid.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRingCat.instCommRingα_1.{u1} R) (Submonoid.powers.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommMonoid.toMonoid.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRing.toCommMonoid.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRingCat.instCommRingα_1.{u1} R))) (OfNat.ofNat.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) 1 (One.toOfNat1.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (Semiring.toOne.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommSemiring.toSemiring.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRing.toCommSemiring.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRingCat.instCommRingα_1.{u1} R)))))))) (algebraMap.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (Localization.Away.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRing.toCommMonoid.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRingCat.instCommRingα_1.{u1} R)) (OfNat.ofNat.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) 1 (One.toOfNat1.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (Semiring.toOne.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommSemiring.toSemiring.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRing.toCommSemiring.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRingCat.instCommRingα_1.{u1} R))))))) (CommRing.toCommSemiring.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRingCat.instCommRingα_1.{u1} R)) (CommSemiring.toSemiring.{u1} (Localization.Away.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRing.toCommMonoid.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRingCat.instCommRingα_1.{u1} R)) (OfNat.ofNat.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) 1 (One.toOfNat1.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (Semiring.toOne.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommSemiring.toSemiring.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRing.toCommSemiring.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRingCat.instCommRingα_1.{u1} R))))))) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRing.toCommSemiring.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRingCat.instCommRingα_1.{u1} R)) (Submonoid.powers.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommMonoid.toMonoid.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRing.toCommMonoid.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRingCat.instCommRingα_1.{u1} R))) (OfNat.ofNat.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) 1 (One.toOfNat1.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (Semiring.toOne.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommSemiring.toSemiring.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRing.toCommSemiring.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRingCat.instCommRingα_1.{u1} R))))))))) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRing.toCommSemiring.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRingCat.instCommRingα_1.{u1} R)) (Submonoid.powers.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommMonoid.toMonoid.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRing.toCommMonoid.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRingCat.instCommRingα_1.{u1} R))) (OfNat.ofNat.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) 1 (One.toOfNat1.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (Semiring.toOne.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommSemiring.toSemiring.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRing.toCommSemiring.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRingCat.instCommRingα_1.{u1} R))))))) (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRing.toCommSemiring.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRingCat.instCommRingα_1.{u1} R)) (Algebra.id.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRing.toCommSemiring.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRingCat.instCommRingα_1.{u1} R))))))
+Case conversion may be inaccurate. Consider using '#align localization_unit_is_iso localization_unit_isIsoₓ'. -/
 instance localization_unit_isIso (R : CommRingCat) :
     IsIso (CommRingCat.ofHom <| algebraMap R (Localization.Away (1 : R))) :=
   IsIso.of_iso (IsLocalization.atOne R (Localization.Away (1 : R))).toRingEquiv.toCommRingCatIso
 #align localization_unit_is_iso localization_unit_isIso
 
+/- warning: localization_unit_is_iso' -> localization_unit_is_iso' is a dubious translation:
+lean 3 declaration is
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(CommMonoid.toMonoid.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRing.toCommMonoid.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRingCat.instCommRingα_1.{u1} R))) (OfNat.ofNat.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) 1 (One.toOfNat1.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (Semiring.toOne.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommSemiring.toSemiring.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRing.toCommSemiring.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRingCat.instCommRingα_1.{u1} R))))))))) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u1, u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRing.toCommSemiring.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRingCat.instCommRingα_1.{u1} R)) (Submonoid.powers.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommMonoid.toMonoid.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRing.toCommMonoid.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRingCat.instCommRingα_1.{u1} R))) (OfNat.ofNat.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) 1 (One.toOfNat1.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (Semiring.toOne.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommSemiring.toSemiring.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRing.toCommSemiring.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRingCat.instCommRingα_1.{u1} R))))))) (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRing.toCommSemiring.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRingCat.instCommRingα_1.{u1} R)) (Algebra.id.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRing.toCommSemiring.{u1} (CategoryTheory.Bundled.α.{u1, u1} CommRing.{u1} R) (CommRingCat.instCommRingα_1.{u1} R))))))
+Case conversion may be inaccurate. Consider using '#align localization_unit_is_iso' localization_unit_is_iso'ₓ'. -/
 instance localization_unit_is_iso' (R : CommRingCat) :
     @IsIso CommRingCat _ R _ (CommRingCat.ofHom <| algebraMap R (Localization.Away (1 : R))) :=
   by
@@ -31,16 +43,30 @@ instance localization_unit_is_iso' (R : CommRingCat) :
   exact localization_unit_isIso _
 #align localization_unit_is_iso' localization_unit_is_iso'
 
+#print IsLocalization.epi /-
 theorem IsLocalization.epi {R : Type _} [CommRing R] (M : Submonoid R) (S : Type _) [CommRing S]
     [Algebra R S] [IsLocalization M S] : Epi (CommRingCat.ofHom <| algebraMap R S) :=
   ⟨fun T f₁ f₂ => @IsLocalization.ringHom_ext R _ M S _ _ T _ _ _ _⟩
 #align is_localization.epi IsLocalization.epi
+-/
 
+/- warning: localization.epi -> Localization.epi is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))), CategoryTheory.Epi.{u1, succ u1} CommRingCat.{u1} CommRingCat.largeCategory.{u1} (CommRingCat.of.{u1} R _inst_1) (CommRingCat.of.{u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (Localization.commRing.{u1} R _inst_1 M)) (CommRingCat.ofHom.{u1} R (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) _inst_1 (Localization.commRing.{u1} R _inst_1 M) (algebraMap.{u1, u1} R (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (CommRing.toRing.{u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (Localization.commRing.{u1} R _inst_1 M))) (Localization.algebra.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) M R (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (M : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))), CategoryTheory.Epi.{u1, succ u1} CommRingCat.{u1} instCommRingCatLargeCategory.{u1} (CommRingCat.of.{u1} R _inst_1) (CommRingCat.of.{u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommRingLocalizationToCommMonoid.{u1} R _inst_1 M)) (CommRingCat.ofHom.{u1} R (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) _inst_1 (Localization.instCommRingLocalizationToCommMonoid.{u1} R _inst_1 M) (algebraMap.{u1, u1} R (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} (Localization.{u1} R (CommRing.toCommMonoid.{u1} R _inst_1) M) (Localization.instCommSemiringLocalizationToCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) M)) (Localization.instAlgebraLocalizationToCommMonoidToSemiringInstCommSemiringLocalizationToCommMonoid.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) M R (CommRing.toCommSemiring.{u1} R _inst_1) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))
+Case conversion may be inaccurate. Consider using '#align localization.epi Localization.epiₓ'. -/
 instance Localization.epi {R : Type _} [CommRing R] (M : Submonoid R) :
     Epi (CommRingCat.ofHom <| algebraMap R <| Localization M) :=
   IsLocalization.epi M _
 #align localization.epi Localization.epi
 
+/- warning: localization.epi' -> Localization.epi' is a dubious translation:
+lean 3 declaration is
+  forall {R : CommRingCat.{u1}} (M : Submonoid.{u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) (MulZeroOneClass.toMulOneClass.{u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) (NonAssocSemiring.toMulZeroOneClass.{u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) (NonAssocRing.toNonAssocSemiring.{u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) (Ring.toNonAssocRing.{u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) (CommRing.toRing.{u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) (CommRingCat.commRing.{u1} R))))))), CategoryTheory.Epi.{u1, succ u1} CommRingCat.{u1} CommRingCat.largeCategory.{u1} R (CommRingCat.of.{u1} (Localization.{u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) (CommRing.toCommMonoid.{u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) (CommRingCat.commRing.{u1} R)) M) (Localization.commRing.{u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) (CommRingCat.commRing.{u1} R) M)) (CommRingCat.ofHom.{u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) (Localization.{u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) (CommRing.toCommMonoid.{u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) (CommRingCat.commRing.{u1} R)) M) (CommRingCat.commRing.{u1} R) (Localization.commRing.{u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) (CommRingCat.commRing.{u1} R) M) (algebraMap.{u1, u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) (Localization.{u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) (CommRing.toCommMonoid.{u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) (CommRingCat.commRing.{u1} R)) M) (CommRing.toCommSemiring.{u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) (CommRingCat.commRing.{u1} R)) (Ring.toSemiring.{u1} (Localization.{u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) (CommRing.toCommMonoid.{u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) (CommRingCat.commRing.{u1} R)) M) (CommRing.toRing.{u1} (Localization.{u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) (CommRing.toCommMonoid.{u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) (CommRingCat.commRing.{u1} R)) M) (Localization.commRing.{u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) (CommRingCat.commRing.{u1} R) M))) (Localization.algebra.{u1, u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) (CommRing.toCommSemiring.{u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) (CommRingCat.commRing.{u1} R)) M (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) (CommRing.toCommSemiring.{u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) (CommRingCat.commRing.{u1} R)) (Algebra.id.{u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) (CommRing.toCommSemiring.{u1} (coeSort.{succ (succ u1), succ (succ u1)} CommRingCat.{u1} Type.{u1} CommRingCat.hasCoeToSort.{u1} R) (CommRingCat.commRing.{u1} R))))))
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+Case conversion may be inaccurate. Consider using '#align localization.epi' Localization.epi'ₓ'. -/
 instance Localization.epi' {R : CommRingCat} (M : Submonoid R) :
     @Epi CommRingCat _ R _ (CommRingCat.ofHom <| algebraMap R <| Localization M : _) :=
   by
@@ -48,21 +74,27 @@ instance Localization.epi' {R : CommRingCat} (M : Submonoid R) :
   exact IsLocalization.epi M _
 #align localization.epi' Localization.epi'
 
+#print CommRingCat.isLocalRingHom_comp /-
 instance CommRingCat.isLocalRingHom_comp {R S T : CommRingCat} (f : R ⟶ S) (g : S ⟶ T)
     [IsLocalRingHom g] [IsLocalRingHom f] : IsLocalRingHom (f ≫ g) :=
   isLocalRingHom_comp _ _
 #align CommRing.is_local_ring_hom_comp CommRingCat.isLocalRingHom_comp
+-/
 
+#print isLocalRingHom_of_iso /-
 theorem isLocalRingHom_of_iso {R S : CommRingCat} (f : R ≅ S) : IsLocalRingHom f.Hom :=
   {
     map_nonunit := fun a ha => by
       convert f.inv.is_unit_map ha
       rw [CategoryTheory.Iso.hom_inv_id_apply] }
 #align is_local_ring_hom_of_iso isLocalRingHom_of_iso
+-/
 
+#print isLocalRingHom_of_isIso /-
 -- see Note [lower instance priority]
 instance (priority := 100) isLocalRingHom_of_isIso {R S : CommRingCat} (f : R ⟶ S) [IsIso f] :
     IsLocalRingHom f :=
   isLocalRingHom_of_iso (asIso f)
 #align is_local_ring_hom_of_is_iso isLocalRingHom_of_isIso
+-/
 
Diff
@@ -4,12 +4,12 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Andrew Yang
 
 ! This file was ported from Lean 3 source module algebra.category.Ring.instances
-! leanprover-community/mathlib commit c1918ac18519732d5bdfa2b6917c016c4d6a8148
+! leanprover-community/mathlib commit a7c017d750512a352b623b1824d75da5998457d0
 ! 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.RingTheory.Localization.Away
+import Mathbin.RingTheory.Localization.Away.Basic
 import Mathbin.RingTheory.Ideal.LocalRing
 
 /-!
Diff
@@ -21,7 +21,7 @@ open CategoryTheory
 
 instance localization_unit_isIso (R : CommRingCat) :
     IsIso (CommRingCat.ofHom <| algebraMap R (Localization.Away (1 : R))) :=
-  IsIso.of_iso (IsLocalization.atOne R (Localization.Away (1 : R))).toRingEquiv.toCommRingIso
+  IsIso.of_iso (IsLocalization.atOne R (Localization.Away (1 : R))).toRingEquiv.toCommRingCatIso
 #align localization_unit_is_iso localization_unit_isIso
 
 instance localization_unit_is_iso' (R : CommRingCat) :

Changes in mathlib4

mathlib3
mathlib4
chore: banish Type _ and Sort _ (#6499)

We remove all possible occurences of Type _ and Sort _ in favor of Type* and Sort*.

This has nice performance benefits.

Diff
@@ -27,12 +27,12 @@ instance localization_unit_isIso' (R : CommRingCat) :
   exact localization_unit_isIso _
 #align localization_unit_is_iso' localization_unit_isIso'
 
-theorem IsLocalization.epi {R : Type _} [CommRing R] (M : Submonoid R) (S : Type _) [CommRing S]
+theorem IsLocalization.epi {R : Type*} [CommRing R] (M : Submonoid R) (S : Type _) [CommRing S]
     [Algebra R S] [IsLocalization M S] : Epi (CommRingCat.ofHom <| algebraMap R S) :=
   ⟨fun {T} _ _ => @IsLocalization.ringHom_ext R _ M S _ _ T _ _ _ _⟩
 #align is_localization.epi IsLocalization.epi
 
-instance Localization.epi {R : Type _} [CommRing R] (M : Submonoid R) :
+instance Localization.epi {R : Type*} [CommRing R] (M : Submonoid R) :
     Epi (CommRingCat.ofHom <| algebraMap R <| Localization M) :=
   IsLocalization.epi M _
 #align localization.epi Localization.epi
chore: script to replace headers with #align_import statements (#5979)

Open in Gitpod

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

Diff
@@ -2,16 +2,13 @@
 Copyright (c) 2021 Andrew Yang. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Andrew Yang
-
-! This file was ported from Lean 3 source module algebra.category.Ring.instances
-! leanprover-community/mathlib commit a7c017d750512a352b623b1824d75da5998457d0
-! 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.RingTheory.Localization.Away.Basic
 import Mathlib.RingTheory.Ideal.LocalRing
 
+#align_import algebra.category.Ring.instances from "leanprover-community/mathlib"@"a7c017d750512a352b623b1824d75da5998457d0"
+
 /-!
 # Ring-theoretic results in terms of categorical languages
 -/
chore: tidy various files (#4304)

Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com> Co-authored-by: Chris Hughes <chrishughes24@gmail.com>

Diff
@@ -24,11 +24,11 @@ instance localization_unit_isIso (R : CommRingCat) :
   IsIso.of_iso (IsLocalization.atOne R (Localization.Away (1 : R))).toRingEquiv.toCommRingCatIso
 #align localization_unit_is_iso localization_unit_isIso
 
-instance localization_unit_is_iso' (R : CommRingCat) :
+instance localization_unit_isIso' (R : CommRingCat) :
     @IsIso CommRingCat _ R _ (CommRingCat.ofHom <| algebraMap R (Localization.Away (1 : R))) := by
   cases R
   exact localization_unit_isIso _
-#align localization_unit_is_iso' localization_unit_is_iso'
+#align localization_unit_is_iso' localization_unit_isIso'
 
 theorem IsLocalization.epi {R : Type _} [CommRing R] (M : Submonoid R) (S : Type _) [CommRing S]
     [Algebra R S] [IsLocalization M S] : Epi (CommRingCat.ofHom <| algebraMap R S) :=
feat: port Algebra.Category.Ring.Instances (#4185)

Dependencies 8 + 617

618 files ported (98.7%)
248546 lines ported (98.8%)
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The unported dependencies are