Theorems · Inductive type · ring theory
HopfAlgebra
(R : Type u) → (A : Type v) → [CommSemiring R] → [Semiring A] → Type (max u v)
A Hopf algebra over a commutative (semi)ring R is a bialgebra over R equipped with an
R-linear endomorphism antipode satisfying the antipode axioms.
- Defined in
- Mathlib.RingTheory.HopfAlgebra.Basic
- Cited by
- 59 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
- Assumes
- CommSemiringSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement · cited by 13,802
- CommSemiringstatement · cited by 10,911
Cited by86
Results whose statement or proof uses this declaration.
- HopfAlgCat.ofstatement and proof · cited by 13
- CommHopfAlgCat.ofHomstatement and proof · cited by 11
- BialgEquiv.toHopfAlgIsostatement and proof · cited by 8
- HopfAlgCat.ofHomstatement and proof · cited by 5
- HopfAlgebra.antipodeAlgHomstatement and proof · cited by 5
- HopfAlgebra.sum_antipode_mul_eq_algebraMap_counitstatement and proof · cited by 3
- HopfAlgebra.sum_mul_antipode_eq_algebraMap_counitstatement and proof · cited by 3
- CommHopfAlgCat.isoMkstatement and proof · cited by 3
- GroupLike.toUnitsstatement and proof · cited by 3
- AddMonoidAlgebra.antipode_singlestatement and proof · cited by 3
- HopfAlgebra.antipode_mul_antidistribstatement and proof · cited by 2
- HopfAlgebra.mul_antipode_lTensor_comulstatement and proof · cited by 2