Theorems · Theorem · ring theory
HopfAlgebra.counit_comp_antipode
∀ {R : Type u} {A : Type v} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : HopfAlgebra R A],
CoalgebraStruct.counit ∘ₗ HopfAlgebraStruct.antipode R = CoalgebraStruct.counit- Defined in
- Mathlib.RingTheory.HopfAlgebra.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- 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
- LinearMap.compstatement · cited by 1,642
- LinearMap.extproof · cited by 844
- CoalgebraStruct.counitstatement · cited by 108
- HopfAlgebrastatement and proof · cited by 59
- HopfAlgebraStruct.antipodestatement · cited by 38
- HopfAlgebra.counit_antipodeproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- AlgHom.counitAlgHom_comp_antipodeAlgHomproof · cited by 0