Theorems · Definition · field theory

InfiniteGalois.proj

{k : Type u_3} →
  {K : Type u_4} →
    [inst : Field k] →
      [inst_1 : Field K] →
        [inst_2 : Algebra k K] →
          (L : FiniteGaloisIntermediateField k K) →
            ↑(ProfiniteGrp.limit (InfiniteGalois.asProfiniteGaloisGroupFunctor k K)).toProfinite.toTop →*
              Gal(↥L.toIntermediateField/k)

The projection map from lim Gal(L/k) to a specific Gal(L/k).

Defined in: Mathlib.FieldTheory.Galois.Profinite
Cited by: 6 results in Mathlib
Foundations: Depth 157 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field Field Algebra

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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites18

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

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
MonoidHomstatement · cited by 3,629
TopCat.carrierstatement and proof · cited by 3,184
TopCatstatement · cited by 1,889
AlgEquivstatement · cited by 1,681
IntermediateFieldstatement · cited by 988
TotallyDisconnectedSpacestatement · cited by 295
CompHausLike.toTopstatement and proof · cited by 258
ProfiniteGrp.toProfinitestatement and proof · cited by 51

Cited by6

Results whose statement or proof uses this declaration.

InfiniteGalois.toAlgEquivAux_eq_proj_of_memstatement · cited by 2
InfiniteGalois.finGaloisGroupFunctor_map_proj_eq_projstatement · cited by 1
InfiniteGalois.proj_adjoin_singleton_valstatement · cited by 1
InfiniteGalois.proj_of_lestatement and proof · cited by 1
InfiniteGalois.toAlgEquivAux_eq_liftNormalstatement and proof · cited by 0
InfiniteGalois.mk_toAlgEquivAuxstatement and proof · cited by 0