Theorems · Theorem · ring theory
MonoidAlgebra.antipode_single
∀ {R : Type u_1} {A : Type u_2} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : HopfAlgebra R A] {G : Type u_3}
[inst_3 : Group G] (g : G) (a : A),
(HopfAlgebraStruct.antipode R) (MonoidAlgebra.single g a) =
MonoidAlgebra.single g⁻¹ ((HopfAlgebraStruct.antipode R) a)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
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- MonoidAlgebrastatement · cited by 590
- Finsupp.sumproof · cited by 481
- MonoidAlgebra.singlestatement and proof · cited by 253
- Finsupp.sum_single_indexproof · cited by 130
- HopfAlgebrastatement and proof · cited by 59
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