Theorems · Definition · group theory
AddSubmonoid.pointwiseMulAction
{M : Type u_3} →
{A : Type u_4} → [inst : Monoid M] → [inst_1 : AddMonoid A] → [DistribMulAction M A] → MulAction M (AddSubmonoid A)The action on an additive submonoid corresponding to applying the action to every element.
This is available as an instance in the Pointwise locale.
- Cited by
- 23 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Monoidstatement and proof · cited by 3,887
- AddMonoidstatement and proof · cited by 2,864
- MulActionstatement · cited by 1,294
- AddSubmonoidstatement · cited by 1,178
- DistribMulActionstatement and proof · cited by 584
Cited by23
Results whose statement or proof uses this declaration.
- Ideal.pointwise_smul_toAddSubmonoidstatement · cited by 0
- AddSubmonoid.mem_inv_pointwise_smul_iffstatement · cited by 0
- AddSubmonoid.mem_inv_pointwise_smul_iff₀statement · cited by 0
- Submodule.pointwise_smul_toAddSubmonoidstatement · cited by 0
- AddSubmonoid.le_pointwise_smul_iffstatement · cited by 0
- AddSubmonoid.pointwise_isCentralScalarstatement · cited by 0
- AddSubmonoid.pointwise_smul_le_iffstatement · cited by 0
- AddSubmonoid.pointwise_smul_le_iff₀statement · cited by 0
- AddSubgroup.pointwise_smul_toAddSubmonoidstatement · cited by 0
- AddSubmonoid.pointwise_smul_le_pointwise_smul_iff₀statement · cited by 0
- AddSubmonoid.pointwise_smul_le_pointwise_smul_iffstatement · cited by 0
- AddSubmonoid.mem_pointwise_smul_iff_inv_smul_memstatement · cited by 0