Theorems · Theorem · ring theory
Bialgebra.counit_algebraMap
∀ {R : Type u} {A : Type v} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Bialgebra R A] (r : R),
CoalgebraStruct.counit ((algebraMap R A) r) = r- Defined in
- Mathlib.RingTheory.Bialgebra.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 42 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Bialgebrastatement and proof · cited by 160
- CoalgebraStruct.counitstatement · cited by 108
- AlgHom.commutesproof · cited by 96
- Bialgebra.counitAlgHomproof · cited by 23
Cited by2
Results whose statement or proof uses this declaration.
- Bialgebra.algebraMap_injectiveproof · cited by 1
- Bialgebra.counit_surjectiveproof · cited by 0