galoisCoinsertionIntermediateFieldSubgroup

English

Dual notion to Galois insertion giving a coinsertion between the same two functors.

Русский

Двойственная концепция к Galо insertion даёт Coinsertion между теми же двумя отображениями.

LaTeX

$$galoisCoinsertionIntermediateFieldSubgroup$$

Lean4

/-- The Galois correspondence as a `GaloisCoinsertion`. -/
def galoisCoinsertionIntermediateFieldSubgroup [FiniteDimensional F E] [IsGalois F E] :
    GaloisCoinsertion
      (OrderDual.toDual ∘ (IntermediateField.fixingSubgroup : IntermediateField F E → Subgroup (E ≃ₐ[F] E)))
      ((IntermediateField.fixedField : Subgroup (E ≃ₐ[F] E) → IntermediateField F E) ∘ OrderDual.toDual) :=
  OrderIso.toGaloisCoinsertion intermediateFieldEquivSubgroup

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