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Theorems · Theorem · ring theory

HopfAlgebra.antipode_mul_antidistrib

∀ {R : Type u_1} {A : Type u_2} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : HopfAlgebra R A] (a b : A),
  (HopfAlgebraStruct.antipode R) (a * b) = (HopfAlgebraStruct.antipode R) b * (HopfAlgebraStruct.antipode R) a
Defined in
Mathlib.RingTheory.HopfAlgebra.Convolution
Cited by
2 results in Mathlib
Foundations
Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommSemiringSemiringHopfAlgebra
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HopfAlgebra.antipode_mul · cited by 0HopfAlgebra.antipode_mulHopfAlgebra.antipode_mul_distrib · cited by 0HopfAlgebra.antipode_mul_…DFunLike.coe · cited by 62936DFunLike.coeRingHom.id · cited by 18349RingHom.idSemiring · cited by 13802SemiringCommSemiring · cited by 10911CommSemiringLinearMap · cited by 10215LinearMapTensorProduct · cited by 2545TensorProductTensorProduct.tmul · cited by 1182TensorProduct.tmulHopfAlgebra · cited by 59HopfAlgebraHopfAlgebraStruct.antipode · cited by 38HopfAlgebraStruct.antipodeHopfAlgebra.antipode_comp_mul_comp_comm · cited by 1HopfAlgebra.antipode_comp…HopfAlgebra.antipode_mul_anti…CITED BYCITES

Cites10

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Cited by2

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