Theorems · Theorem · ring theory
LinearMap.toAddMonoidHom_injective
∀ {R : Type u_1} {S : Type u_5} {M : Type u_8} {M₃ : Type u_11} [inst : Semiring R] [inst_1 : Semiring S]
[inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₃] [inst_4 : Module R M] [inst_5 : Module S M₃] {σ : R →+* S},
Function.Injective LinearMap.toAddMonoidHom- Defined in
- Mathlib.Algebra.Module.LinearMap.Defs
- Cited by
- 10 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.
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- LinearMapstatement and proof · cited by 10,215
- RingHomstatement and proof · cited by 10,189
- AddMonoidHomstatement · cited by 3,230
- LinearMap.extproof · cited by 844
- DFunLike.congr_funproof · cited by 288
- LinearMap.toAddMonoidHomstatement and proof · cited by 101
Cited by10
Results whose statement or proof uses this declaration.
- MonoidAlgebra.lhom_ext'proof · cited by 21
- Finsupp.lhom_extproof · cited by 6
- Module.DirectLimit.hom_extproof · cited by 5
- LinearMap.pi_extproof · cited by 4
- Matrix.ext_linearMapproof · cited by 3
- Polynomial.lhom_ext'proof · cited by 3
- AddMonoidAlgebra.lhom_ext'proof · cited by 2
- DFinsupp.lhom_extproof · cited by 2
- SkewMonoidAlgebra.lhom_extproof · cited by 1
- CoalgHom.coe_addMonoidHom_injectiveproof · cited by 0