Theorems · Theorem · ring theory
Bialgebra.counit_mul
∀ {R : Type u} {A : Type v} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Bialgebra R A] (a b : A),
CoalgebraStruct.counit (a * b) = CoalgebraStruct.counit a * CoalgebraStruct.counit b- Defined in
- Mathlib.RingTheory.Bialgebra.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 40 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- DFunLike.congr_funproof · cited by 288
- Bialgebrastatement and proof · cited by 160
- CoalgebraStruct.counitstatement · cited by 108
- Bialgebra.mul_compr₂_counitproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- Bialgebra.counitAlgHomproof · cited by 23
- HopfAlgebra.counit_antipodeproof · cited by 1
- IsGroupLikeElem.mulproof · cited by 0