Theorems · Theorem · group theory
fixingAddSubgroup_fixedPoints_gc
∀ (M : Type u_1) (α : Type u_2) [inst : AddGroup M] [inst_1 : AddAction M α],
GaloisConnection (⇑OrderDual.toDual ∘ fixingAddSubgroup M)
((fun P => AddAction.fixedPoints (↥P) α) ∘ ⇑OrderDual.ofDual)- 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
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- OrderDualstatement and proof · cited by 927
- AddActionstatement and proof · cited by 820
- OrderDual.toDualstatement and proof · cited by 481
- OrderDual.ofDualstatement and proof · cited by 400
- GaloisConnectionstatement · cited by 253
- fixingAddSubgroupstatement and proof · cited by 50
Cited by7
Results whose statement or proof uses this declaration.
- fixingAddSubgroup_antitoneproof · cited by 1
- fixingAddSubgroup_emptyproof · cited by 1
- fixingAddSubgroup_unionproof · cited by 1
- fixedPoints_addSubgroup_antitoneproof · cited by 0
- fixedPoints_addSubgroup_iSupproof · cited by 0
- fixingAddSubgroup_iUnionproof · cited by 0
- fixedPoints_addSubgroup_supproof · cited by 0