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Theorems · Theorem · ring theory

IsGroupLikeElem.one

∀ {R : Type u_1} {A : Type u_2} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Bialgebra R A],
  IsGroupLikeElem R 1

In a bialgebra, 1 is a group-like element.

Defined in
Mathlib.RingTheory.Bialgebra.GroupLike
Cited by
0 results in Mathlib
Foundations
Depth 58 from the axioms · uses propext, Quot.sound
Assumes
CommSemiringSemiringBialgebra
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

groupLikeSubmonoid · cited by 1groupLikeSubmonoidSemiring · cited by 13802SemiringCommSemiring · cited by 10911CommSemiringBialgebra · cited by 160BialgebraIsGroupLikeElem · cited by 39IsGroupLikeElemBialgebra.counit_one · cited by 6Bialgebra.counit_oneBialgebra.comul_one · cited by 6Bialgebra.comul_oneIsGroupLikeElem.oneCITED BYCITES

Cites6

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

Cited by1

Results whose statement or proof uses this declaration.