Theorems · Theorem · ring theory
Bialgebra.counit_one
∀ {R : Type u} {A : Type v} {inst : CommSemiring R} {inst_1 : Semiring A} [self : Bialgebra R A],
CoalgebraStruct.counit 1 = 1The counit on a bialgebra preserves 1.
- Defined in
- Mathlib.RingTheory.Bialgebra.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Quot.sound
- Assumes
- Bialgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Bialgebrastatement and proof · cited by 160
- CoalgebraStruct.counitstatement · cited by 108
Cited by7
Results whose statement or proof uses this declaration.
- Bialgebra.counitAlgHomproof · cited by 23
- AddMonoidAlgebra.isGroupLikeElem_single_oneproof · cited by 5
- MonoidAlgebra.isGroupLikeElem_single_oneproof · cited by 3
- IsGroupLikeElem.of_mul_eq_oneproof · cited by 2
- HopfAlgebra.counit_antipodeproof · cited by 1
- HopfAlgebra.antipode_oneproof · cited by 1
- IsGroupLikeElem.oneproof · cited by 0