Theorems · Theorem · ring theory
AlgHom.toLinearMap_injective
∀ {R : Type u} {A : Type v} {B : Type w} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Semiring B]
[inst_3 : Algebra R A] [inst_4 : Algebra R B], Function.Injective AlgHom.toLinearMap- Defined in
- Mathlib.Algebra.Algebra.Hom
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 24 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.
- 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
- AlgHomstatement and proof · cited by 3,236
- AlgHom.toLinearMapstatement and proof · cited by 254
- AlgHom.extproof · cited by 170
- LinearMap.congr_funproof · cited by 96
Cited by17
Results whose statement or proof uses this declaration.
- Algebra.TensorProduct.extproof · cited by 26
- TrivSqZeroExt.algHom_ext'proof · cited by 3
- DirectSum.algHom_ext'proof · cited by 3
- TrivSqZeroExt.algHom_extproof · cited by 2
- PiTensorProduct.algHom_extproof · cited by 1
- BialgHom.map_comp_comulAlgHomproof · cited by 1
- SkewMonoidAlgebra.algHom_extproof · cited by 1
- AlgHom.eq_piEvalAlgHomproof · cited by 1
- GradedAlgHom.coe_linearMap_injectiveproof · cited by 0
- AlgHom.comp_convMul_distribproof · cited by 0
- AlgHom.antipode_id_cancelproof · cited by 0
- AlgHom.counitAlgHom_comp_antipodeAlgHomproof · cited by 0