finGaloisGroupFunctor — Mathlib

English

There is a multiplicative equivalence between G and the AlgEquiv automorphism group Aut_K(L) when L/K is finite Galois.

Русский

Существует мультипрокопийный эквивалент между G и Aut_K(L).

LaTeX

$$mulEquivAlgEquiv G K L$$

Lean4

/-- The functor from `FiniteGaloisIntermediateField` (ordered by reverse inclusion) to `FiniteGrp`,
mapping each `FiniteGaloisIntermediateField` `L` to `Gal (L/k)` -/
noncomputable def finGaloisGroupFunctor : (FiniteGaloisIntermediateField k K)ᵒᵖ ⥤ FiniteGrp
    where
  obj L := L.unop.finGaloisGroup
  map := finGaloisGroupMap
  map_id := finGaloisGroupMap.map_id
  map_comp := finGaloisGroupMap.map_comp

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