Mathlib Map

Theorems · Definition · group theory

SubAddAction.ofFixingAddSubgroup_equivariantMap

(M : Type u_1) →
  {α : Type u_2} →
    [inst : AddGroup M] →
      [inst_1 : AddAction M α] →
        (s : Set α) → ↥(SubAddAction.ofFixingAddSubgroup M s) →ₑ[⇑(fixingAddSubgroup M s).subtype] α

The identity map of the SubAddAction of the fixingAddSubgroup into the ambient set, as an equivariant map.

Defined in
Mathlib.GroupTheory.GroupAction.SubMulAction.OfFixingSubgroup
Cited by
2 results in Mathlib
Foundations
Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddGroupAddAction
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

SubAddAction.ofFixingAddSubgroupEmpty_equivariantMap_bijective · cited by 1SubAddAction.ofFixingAddS…SubAddAction.ofFixingAddSubgroup_equivariantMap_injective · cited by 1SubAddAction.ofFixingAddS…DFunLike.coe · cited by 62936DFunLike.coeSet · cited by 53352SetAddGroup · cited by 4410AddGroupAddSubgroup · cited by 3232AddSubgroupAddMonoidHom · cited by 3230AddMonoidHomAddAction · cited by 820AddActionSubAddAction · cited by 86SubAddActionAddActionHom · cited by 82AddActionHomAddSubgroup.subtype · cited by 82AddSubgroup.subtypefixingAddSubgroup · cited by 50fixingAddSubgroupSubAddAction.ofFixingAddSubgroup · cited by 32SubAddAction.ofFixingAddS…SubAddAction.ofFixingAddSubgr…CITED BYCITES

Cites11

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.