instReflectsIsomorphismsActionFintypeCatAutFunctorFunctorToAction

English

For IsGalois X, Aut X action carrier is pretransitive; hence connectivity is preserved.

Русский

Для IsGalois X, действие Aut X сохраняет связность оболочки.

LaTeX

$$$\\forall X\\ [IsGalois X] \\Rightarrow MulAction.IsPretransitive(Aut X, ((functorToAction F).obj X).V)$$$

Lean4

instance : Functor.ReflectsIsomorphisms (functorToAction F) where
  reflects f
    _ :=
    have : IsIso (F.map f) := (forget₂ _ FintypeCat).map_isIso ((functorToAction F).map f)
    isIso_of_reflects_iso f F

Похожие утверждения