Theorems · Theorem · ring theory

HopfAlgebra.mul_antipode_rTensor_comul_apply

∀ {R : Type u} {A : Type v} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : HopfAlgebra R A] (a : A),
  (LinearMap.mul' R A) ((LinearMap.rTensor A (HopfAlgebraStruct.antipode R)) (CoalgebraStruct.comul a)) =
    (algebraMap R A) (CoalgebraStruct.counit a)

Defined in

Mathlib.RingTheory.HopfAlgebra.Basic

Cited by

2 results in Mathlib

Foundations

Depth 61 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringSemiringHopfAlgebra