Theorems · Theorem · ring theory
IsGroupLikeElem.antipode
∀ {R : Type u_1} {A : Type u_2} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : HopfAlgebra R A] {a : A},
IsGroupLikeElem R a → IsGroupLikeElem R ((HopfAlgebraStruct.antipode R) a)- Defined in
- Mathlib.RingTheory.HopfAlgebra.GroupLike
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement · cited by 10,215
- HopfAlgebrastatement and proof · cited by 59
- IsGroupLikeElemstatement and proof · cited by 39
- HopfAlgebraStruct.antipodestatement · cited by 38
- IsGroupLikeElem.antipode_mul_cancelproof · cited by 2
- IsGroupLikeElem.of_mul_eq_oneproof · cited by 2
- IsGroupLikeElem.mul_antipode_cancelproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- IsGroupLikeElem.antipode_antipodeproof · cited by 0