Theorems · Definition · group theory
AddSubgroup.pointwiseMulAction
{M : Type u_3} →
{A : Type u_4} → [inst : Monoid M] → [inst_1 : AddGroup A] → [DistribMulAction M A] → MulAction M (AddSubgroup A)The action on an additive subgroup corresponding to applying the action to every element.
This is available as an instance in the Pointwise locale.
- Defined in
- Mathlib.Algebra.GroupWithZero.Subgroup
- Cited by
- 24 results in Mathlib
- Foundations
- Depth 23 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.
- AddGroupstatement and proof · cited by 4,410
- Monoidstatement and proof · cited by 3,887
- AddSubgroupstatement · cited by 3,232
- MulActionstatement · cited by 1,294
- DistribMulActionstatement and proof · cited by 584
Cited by25
Results whose statement or proof uses this declaration.
- AddSubgroup.pointwise_smul_defstatement · cited by 1
- Ideal.pointwise_smul_toAddSubgroupstatement · cited by 0
- AddSubgroup.le_pointwise_smul_iffstatement · cited by 0
- Submodule.pointwise_smul_toAddSubgroupstatement · cited by 0
- AddSubgroup.le_pointwise_smul_iff₀statement · cited by 0
- AddSubgroup.smul_mem_pointwise_smulstatement · cited by 0
- AddSubgroup.smul_mem_pointwise_smul_iffstatement · cited by 0
- AddCommGroup.smul_top_eq_top_of_divisibleBy_intstatement · cited by 0
- AddSubgroup.pointwise_smul_le_iffstatement · cited by 0
- AddSubgroup.pointwise_smul_le_iff₀statement · cited by 0
- AddSubgroup.pointwise_smul_le_pointwise_smul_iffstatement · cited by 0
- AddSubgroup.pointwise_smul_le_pointwise_smul_iff₀statement · cited by 0