Theorems · Definition · group theory

MulAction.equivSubgroupOrbitsSetoidComap

{G : Type u} →
  {X : Type v} →
    [inst : Group G] →
      [inst_1 : MulAction G X] →
        (H : Subgroup G) →
          (ω : Quotient (MulAction.orbitRel G X)) →
            MulAction.orbitRel.Quotient ↥H ↑(MulAction.orbitRel.Quotient.orbit ω) ≃
              Quotient (Setoid.comap Subtype.val (MulAction.orbitRel (↥H) X))

A bijection between the quotient of the action of a subgroup H on an orbit, and a corresponding quotient expressed in terms of Setoid.comap Subtype.val.

Defined in: Mathlib.GroupTheory.GroupAction.Quotient
Cited by: 0 results in Mathlib
Foundations: Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Group MulAction

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Cites12

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

Setstatement · cited by 53,352
Equivstatement · cited by 8,337
Set.Elemstatement and proof · cited by 7,166
Groupstatement and proof · cited by 6,238
Set.preimagestatement and proof · cited by 4,946
Subgroupstatement and proof · cited by 3,593
MulActionstatement and proof · cited by 1,294
MulAction.orbitRelstatement and proof · cited by 114
MulAction.orbitRel.Quotientstatement and proof · cited by 28
Quotient.liftOn'proof · cited by 19
Setoid.comapstatement and proof · cited by 16
MulAction.orbitRel.Quotient.orbitstatement and proof · cited by 15

Cited by1

Results whose statement or proof uses this declaration.

MulAction.equivSubgroupOrbitsproof · cited by 0