Theorems · Definition · ring theory
HopfAlgebraStruct.antipode
(R : Type u) →
{A : Type v} → {inst : CommSemiring R} → {inst_1 : Semiring A} → [self : HopfAlgebraStruct R A] → A →ₗ[R] AThe antipode of the Hopf algebra.
- Defined in
- Mathlib.RingTheory.HopfAlgebra.Basic
- Cited by
- 38 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Quot.sound
- Assumes
- HopfAlgebraStruct
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- 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
- HopfAlgebraStructstatement and proof · cited by 6
Cited by49
Results whose statement or proof uses this declaration.
- HopfAlgebra.antipodeAlgHomproof · cited by 5
- AddMonoidAlgebra.antipode_singlestatement and proof · cited by 3
- GroupLike.toUnitsproof · cited by 3
- HopfAlgebra.sum_antipode_mul_eq_algebraMap_counitstatement and proof · cited by 3
- HopfAlgebra.sum_mul_antipode_eq_algebraMap_counitstatement and proof · cited by 3
- IsGroupLikeElem.antipode_mul_cancelstatement and proof · cited by 2
- HopfAlgebra.antipode_mul_antidistribstatement · cited by 2
- HopfAlgebra.mul_antipode_lTensor_comulstatement · cited by 2
- HopfAlgebra.mul_antipode_rTensor_comulstatement · cited by 2
- HopfAlgebra.mul_antipode_rTensor_comul_applystatement · cited by 2
- LinearMap.id_mul_antipodestatement and proof · cited by 1
- Ideal.IsHopfIdeal.casesOnstatement and proof · cited by 1