Theorems · Theorem · group theory
fixingSubmonoid_fixedPoints_gc
∀ (M : Type u_1) (α : Type u_2) [inst : Monoid M] [inst_1 : MulAction M α], GaloisConnection (⇑OrderDual.toDual ∘ fixingSubmonoid M) ((fun P => MulAction.fixedPoints (↥P) α) ∘ ⇑OrderDual.ofDual)
The Galois connection between fixing submonoids and fixed points of a monoid action
- Cited by
- 6 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
- Monoidstatement and proof · cited by 3,887
- Submonoidstatement and proof · cited by 3,086
- 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
- MulAction.fixedPointsstatement and proof · cited by 41
Cited by6
Results whose statement or proof uses this declaration.
- fixedPoints_antitoneproof · cited by 0
- fixedPoints_submonoid_iSupproof · cited by 0
- fixedPoints_submonoid_supproof · cited by 0
- fixingSubmonoid_antitoneproof · cited by 0
- fixingSubmonoid_iUnionproof · cited by 0
- fixingSubmonoid_unionproof · cited by 0