Theorems · Theorem · ring theory
HopfAlgebra.mul_antipode_lTensor_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.lTensor A (HopfAlgebraStruct.antipode R)) (CoalgebraStruct.comul a)) =
(algebraMap R A) (CoalgebraStruct.counit a)- Defined in
- Mathlib.RingTheory.HopfAlgebra.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · 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
- RingHomstatement · cited by 10,189
- Algebra.algebraMapstatement · cited by 4,706
- TensorProductstatement · cited by 2,545
- LinearMap.lTensorstatement · cited by 203
- CoalgebraStruct.comulstatement · cited by 118
- CoalgebraStruct.counitstatement · cited by 108
- LinearMap.congr_funproof · cited by 96
Cited by1
Results whose statement or proof uses this declaration.
- IsGroupLikeElem.mul_antipode_cancelproof · cited by 1