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