Theorems · Definition · ring theory
Bialgebra.counitAlgHom
(R : Type u) → (A : Type v) → [inst : CommSemiring R] → [inst_1 : Semiring A] → [inst_2 : Bialgebra R A] → A →ₐ[R] R
counitAlgHom R A is the counit of the R-bialgebra A, as an R-algebra map.
- Defined in
- Mathlib.RingTheory.Bialgebra.Basic
- Cited by
- 23 results in Mathlib
- Foundations
- Depth 41 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- CommSemiringstatement and proof · cited by 10,911
- AlgHomstatement · cited by 3,236
- Bialgebrastatement and proof · cited by 160
- CoalgebraStruct.counitproof · cited by 108
- AlgHom.ofLinearMapproof · cited by 11
- Bialgebra.counit_oneproof · cited by 6
- Bialgebra.counit_mulproof · cited by 2
Cited by28
Results whose statement or proof uses this declaration.
- BialgHom.ofAlgHomstatement and proof · cited by 9
- Bialgebra.counitBialgHomproof · cited by 4
- BialgEquiv.ofAlgEquivstatement and proof · cited by 3
- Bialgebra.counitAlgHom_applystatement and proof · cited by 3
- BialgEquiv.ofAlgEquiv_applystatement and proof · cited by 2
- Bialgebra.counit_algebraMapproof · cited by 2
- Bialgebra.Quotient.counitAlgHomproof · cited by 2
- CommAlgCat.one_op_of_unop_homstatement · cited by 0
- Bialgebra.TensorProduct.counitAlgHom_defstatement · cited by 0
- Bialgebra.TensorProduct.counit_eq_algHom_toLinearMapstatement · cited by 0
- BialgHom.ofAlgHom_applystatement and proof · cited by 0
- MonoidAlgebra.counitAlgHom_comp_mapRingHomstatement and proof · cited by 0