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[Merged by Bors] - feat(Algebra): add subsingleton of IsZero for AddCommGrpCat #32101

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[Merged by Bors] - feat(Algebra): add subsingleton of IsZero for AddCommGrpCat #32101

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4d7e1ed
add stupid lemma
Thmoas-Guan Nov 25, 2025
946e85a
use another proof
Thmoas-Guan Nov 25, 2025
7f6103e
fix first proof
Thmoas-Guan Nov 26, 2025
b306d5b
fix second proof
Thmoas-Guan Nov 26, 2025
f2de902
fix
Thmoas-Guan Nov 26, 2025
c18d678
fix indent
Thmoas-Guan Nov 26, 2025
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18 changes: 18 additions & 0 deletions Mathlib/Algebra/Category/Grp/Zero.lean
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Original file line number Diff line number Diff line change
Expand Up @@ -39,6 +39,15 @@ theorem isZero_of_subsingleton (G : GrpCat) [Subsingleton G] : IsZero G := by
instance : HasZeroObject GrpCat :=
⟨⟨of PUnit, isZero_of_subsingleton _⟩⟩

@[to_additive]
lemma subsingleton_of_isZero {G : GrpCat} (h : Limits.IsZero G) :
Subsingleton G :=
(h.iso (isZero_of_subsingleton <| .of PUnit)).groupIsoToMulEquiv.subsingleton

@[to_additive]
lemma isZero_iff_subsingleton {G : GrpCat} : Limits.IsZero G ↔ Subsingleton G :=
⟨fun h ↦ subsingleton_of_isZero h, fun _ ↦ isZero_of_subsingleton G⟩

end GrpCat

namespace CommGrpCat
Expand All @@ -56,4 +65,13 @@ theorem isZero_of_subsingleton (G : CommGrpCat) [Subsingleton G] : IsZero G := b
instance : HasZeroObject CommGrpCat :=
⟨⟨of PUnit, isZero_of_subsingleton _⟩⟩

@[to_additive]
lemma subsingleton_of_isZero {G : CommGrpCat} (h : Limits.IsZero G) :
Subsingleton G :=
(h.iso (isZero_of_subsingleton <| .of PUnit)).commGroupIsoToMulEquiv.subsingleton

@[to_additive]
lemma isZero_iff_subsingleton {G : CommGrpCat} : Limits.IsZero G ↔ Subsingleton G :=
⟨fun h ↦ subsingleton_of_isZero h, fun _ ↦ isZero_of_subsingleton G⟩

end CommGrpCat