Theorems · Theorem · ring theory
HopfAlgebra.sum_antipode_mul_eq_smul
∀ {R : Type u} {A : Type v} {ι : Type u_1} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : HopfAlgebra R A]
{a : A} (repr : Coalgebra.Repr R a ι),
∑ i ∈ repr.index, (HopfAlgebraStruct.antipode R) (repr.left i) * repr.right i = CoalgebraStruct.counit a • 1- Defined in
- Mathlib.RingTheory.HopfAlgebra.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Quot.sound
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- DFunLike.coestatement and proof · 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
- Finset.sumstatement · cited by 5,195
- Algebra.algebraMapproof · cited by 4,706
- mul_oneproof · cited by 3,885
- Algebra.smul_defproof · cited by 287
- CoalgebraStruct.counitstatement and proof · cited by 108
- HopfAlgebrastatement and proof · cited by 59
- HopfAlgebraStruct.antipodestatement · cited by 38
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