Theorems · Definition · ring theory

GroupLike.valEquiv

{R : Type u_2} →
  {A : Type u_3} →
    [inst : CommSemiring R] →
      [inst_1 : AddCommMonoid A] →
        [inst_2 : Module R A] → [inst_3 : Coalgebra R A] → GroupLike R A ≃ Subtype (IsGroupLikeElem R)

Identity equivalence between GroupLike R A and {a : A // IsGroupLikeElem R a}.

Defined in: Mathlib.RingTheory.Coalgebra.GroupLike
Cited by: 3 results in Mathlib
Foundations: Depth 10 from the axioms · uses no axioms
Assumes: CommSemiring AddCommMonoid Module Coalgebra

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Cites9

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Modulestatement and proof · cited by 20,661
AddCommMonoidstatement and proof · cited by 12,281
CommSemiringstatement and proof · cited by 10,911
Equivstatement · cited by 8,337
Coalgebrastatement and proof · cited by 112
IsGroupLikeElemstatement and proof · cited by 39
GroupLikestatement and proof · cited by 19
GroupLike.valproof · cited by 16
GroupLike.isGroupLikeElem_valproof · cited by 1

Cited by3

Results whose statement or proof uses this declaration.

GroupLike.valEquiv_apply_coestatement and proof · cited by 0
linearIndep_groupLikeValproof · cited by 0
GroupLike.val_valEquiv_symm_applystatement and proof · cited by 0