Theorems · Theorem · ring theory
IsGroupLikeElem.mul
∀ {R : Type u_1} {A : Type u_2} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Bialgebra R A] {a b : A},
IsGroupLikeElem R a → IsGroupLikeElem R b → IsGroupLikeElem R (a * b)Group-like elements in a bialgebra are stable under multiplication.
- Defined in
- Mathlib.RingTheory.Bialgebra.GroupLike
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- CommSemiringstatement and proof · cited by 10,911
- mul_oneproof · cited by 3,885
- TensorProduct.tmulproof · cited by 1,182
- Bialgebrastatement and proof · cited by 160
- IsGroupLikeElemstatement and proof · cited by 39
- IsGroupLikeElem.comul_eq_tmul_selfproof · cited by 13
- IsGroupLikeElem.counit_eq_oneproof · cited by 9
- Bialgebra.counit_mulproof · cited by 2
- Bialgebra.comul_mulproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- groupLikeSubmonoidproof · cited by 1