Theorems · Definition · ring theory
BialgHom.toCoalgHom
{R : Type u_1} →
{A : Type u_2} →
{B : Type u_3} →
[inst : CommSemiring R] →
[inst_1 : Semiring A] →
[inst_2 : Algebra R A] →
[inst_3 : Semiring B] →
[inst_4 : Algebra R B] →
[inst_5 : CoalgebraStruct R A] → [inst_6 : CoalgebraStruct R B] → (A →ₐc[R] B) → A →ₗc[R] B- Defined in
- Mathlib.RingTheory.Bialgebra.Hom
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- CoalgebraStructstatement and proof · cited by 230
- BialgHomstatement and proof · cited by 190
- CoalgHomstatement · cited by 105
Cited by14
Results whose statement or proof uses this declaration.
- BialgHom.toAlgHomproof · cited by 38
- CategoryTheory.Iso.toBialgEquivproof · cited by 4
- CategoryTheory.Iso.toHopfAlgEquivproof · cited by 4
- BialgHom.map_mul'statement · cited by 0
- BialgHom.map_one'statement · cited by 0
- BialgHom.map_smul_of_towerproof · cited by 0
- AddMonoidAlgebra.bialgEquivOfSubsingletonproof · cited by 0
- Bialgebra.toCoalgHom_mulBialgHomstatement and proof · cited by 0
- HopfAlgebra.ofSurjectivestatement and proof · cited by 0
- BialgHom.toCoalgHom_applystatement · cited by 0
- BialgHom.toLinearMap_convMulstatement · cited by 0
- BialgHom.toLinearMap_convPowstatement · cited by 0