Theorems · Theorem · ring theory
BialgHom.coe_linearMap_injective
∀ {R : Type u_1} {A : Type u_2} {B : Type u_3} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Semiring B]
[inst_3 : Algebra R A] [inst_4 : Algebra R B] [inst_5 : CoalgebraStruct R A] [inst_6 : CoalgebraStruct R B],
Function.Injective fun x => ↑x- Defined in
- Mathlib.RingTheory.Bialgebra.Hom
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement · cited by 10,215
- CoalgebraStructstatement and proof · cited by 230
- BialgHomstatement · cited by 190
- SemilinearMapClass.semilinearMapstatement · cited by 80
- CoalgHom.coe_linearMap_injectiveproof · cited by 3
- BialgHom.coe_coalgHom_injectiveproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- BialgHom.ext_of_ringproof · cited by 1