Theorems · Definition · field theory
InfiniteGalois.mulEquivToLimit
(k : Type u_3) →
(K : Type u_4) →
[inst : Field k] →
[inst_1 : Field K] →
[inst_2 : Algebra k K] →
[IsGalois k K] →
Gal(K/k) ≃* ↑(ProfiniteGrp.limit (InfiniteGalois.asProfiniteGaloisGroupFunctor k K)).toProfinite.toTopalgEquivToLimit as a MulEquiv.
- Defined in
- Mathlib.FieldTheory.Galois.Profinite
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CategoryTheory.Functor.objstatement · cited by 19,642
- Algebrastatement and proof · cited by 11,388
- Oppositestatement · cited by 8,081
- Fieldstatement and proof · cited by 7,404
- TopCat.carrierstatement and proof · cited by 3,184
- TopCatstatement · cited by 1,889
- AlgEquivstatement · cited by 1,681
- MulEquivstatement · cited by 1,142
- TotallyDisconnectedSpacestatement · cited by 295
- CompHausLike.toTopstatement and proof · cited by 258
- IsGaloisstatement and proof · cited by 149
Cited by4
Results whose statement or proof uses this declaration.
- InfiniteGalois.isOpen_mulEquivToLimit_image_fixingSubgroupstatement and proof · cited by 1
- InfiniteGalois.continuousMulEquivToLimitproof · cited by 0
- InfiniteGalois.mulEquivToLimit_symm_continuousstatement and proof · cited by 0
- InfiniteGalois.mulEquivToLimit.congr_simpstatement and proof · cited by 0