Theorems · Definition · group theory
DistribSMul.toAddMonoidHom
{M : Type u_1} → (A : Type u_7) → [inst : AddZeroClass A] → [DistribSMul M A] → M → A →+ AEach element of the scalars defines an additive monoid homomorphism.
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- Assumes
- AddZeroClassDistribSMul
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.
- AddMonoidHomstatement · cited by 3,230
- AddZeroClassstatement and proof · cited by 1,237
- ZeroHomproof · cited by 161
- DistribSMulstatement and proof · cited by 117
- SMulZeroClass.toZeroHomproof · cited by 1
- DistribSMul.smul_addproof · cited by 1
Cited by30
Results whose statement or proof uses this declaration.
- Finset.smul_sumproof · cited by 88
- MulSemiringAction.toRingHomproof · cited by 23
- HasSum.const_smulproof · cited by 11
- AddSubmonoid.smulproof · cited by 11
- DistribMulAction.toAddMonoidEndproof · cited by 9
- AddSubmonoid.smul_mem_smulproof · cited by 8
- AddSubmonoid.smul_leproof · cited by 8
- MatrixModCat.toModuleCatObjproof · cited by 7
- List.smul_sumproof · cited by 3
- DistribSMul.toAddMonoidHom_applystatement and proof · cited by 3
- DistribMulAction.toAddEquivproof · cited by 3
- DistribMulAction.toAddMonoidEnd_applystatement · cited by 2