Theorems · Definition · ring theory
Bialgebra.comulAlgHom
(R : Type u) →
(A : Type v) →
[inst : CommSemiring R] → [inst_1 : Semiring A] → [inst_2 : Bialgebra R A] → A →ₐ[R] TensorProduct R A AcomulAlgHom R A is the comultiplication of the R-bialgebra A, as an R-algebra map.
- Defined in
- Mathlib.RingTheory.Bialgebra.Basic
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 79 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.
- Semiringstatement and proof · cited by 13,802
- CommSemiringstatement and proof · cited by 10,911
- AlgHomstatement · cited by 3,236
- TensorProductstatement · cited by 2,545
- Bialgebrastatement and proof · cited by 160
- CoalgebraStruct.comulproof · cited by 118
- AlgHom.ofLinearMapproof · cited by 11
- Bialgebra.comul_oneproof · cited by 6
- Bialgebra.comul_mulproof · cited by 2
Cited by25
Results whose statement or proof uses this declaration.
- BialgHom.ofAlgHomstatement and proof · cited by 9
- Bialgebra.comulAlgHom_applystatement and proof · cited by 4
- BialgEquiv.ofAlgEquivstatement and proof · cited by 3
- Bialgebra.comulBialgHomproof · cited by 3
- BialgEquiv.ofAlgEquiv_applystatement and proof · cited by 2
- Bialgebra.Quotient.comulAlgHomproof · cited by 2
- BialgHom.map_comp_comulAlgHomstatement and proof · cited by 1
- BialgEquiv.toLinearMap_ofAlgEquivstatement and proof · cited by 0
- AddMonoidAlgebra.comulAlgHom_comp_mapRingHomstatement and proof · cited by 0
- Bialgebra.TensorProduct.comulAlgHom_defstatement · cited by 0
- Bialgebra.TensorProduct.comul_eq_algHom_toLinearMapstatement · cited by 0
- MonoidAlgebra.comulAlgHom_comp_mapRingHomstatement and proof · cited by 0