Theorems · Theorem · group theory
fixingSubgroup_fixedPoints_gc
∀ (M : Type u_1) (α : Type u_2) [inst : Group M] [inst_1 : MulAction M α], GaloisConnection (⇑OrderDual.toDual ∘ fixingSubgroup M) ((fun P => MulAction.fixedPoints (↥P) α) ∘ ⇑OrderDual.ofDual)
The Galois connection between fixing subgroups and fixed points of a group action
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Equivstatement · cited by 8,337
- Set.Elemproof · cited by 7,166
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- MulActionstatement and proof · cited by 1,294
- OrderDualstatement and proof · cited by 927
- OrderDual.toDualstatement and proof · cited by 481
- OrderDual.ofDualstatement and proof · cited by 400
- GaloisConnectionstatement · cited by 253
- fixingSubgroupstatement and proof · cited by 83
Cited by7
Results whose statement or proof uses this declaration.
- fixingSubgroup_emptyproof · cited by 2
- fixingSubgroup_antitoneproof · cited by 1
- fixingSubgroup_unionproof · cited by 1
- fixedPoints_subgroup_antitoneproof · cited by 0
- fixedPoints_subgroup_iSupproof · cited by 0
- fixedPoints_subgroup_supproof · cited by 0
- fixingSubgroup_iUnionproof · cited by 0