Theorems · Theorem · ring theory

HopfAlgebra.antipode_comp_mul_comp_comm

∀ {R : Type u_1} {A : Type u_2} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : HopfAlgebra R A],
  HopfAlgebraStruct.antipode R ∘ₗ LinearMap.mul' R A ∘ₗ ↑(TensorProduct.comm R A A) =
    LinearMap.mul' R A ∘ₗ TensorProduct.map (HopfAlgebraStruct.antipode R) (HopfAlgebraStruct.antipode R)

Defined in

Mathlib.RingTheory.HopfAlgebra.Convolution

Cited by

1 results in Mathlib

Foundations

Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringSemiringHopfAlgebra