Theorems · Theorem · category theory

CategoryTheory.PreGaloisCategory.autMulEquivAutGalois_symm_app

∀ {C : Type u₁} [inst : CategoryTheory.Category.{u₂, u₁} C] [inst_1 : CategoryTheory.GaloisCategory C]
  (F : CategoryTheory.Functor C FintypeCat) [inst_2 : CategoryTheory.PreGaloisCategory.FiberFunctor F]
  (x : CategoryTheory.PreGaloisCategory.AutGalois F) (A : C) [inst_3 : CategoryTheory.PreGaloisCategory.IsGalois A]
  (a : (F.obj A).obj),
  (CategoryTheory.ConcreteCategory.hom
        (((CategoryTheory.PreGaloisCategory.autMulEquivAutGalois F).symm { unop' := x }).hom.app A))
      a =
    (CategoryTheory.ConcreteCategory.hom
        (F.map ((CategoryTheory.PreGaloisCategory.AutGalois.π F { obj := A, pt := a, isGalois := ⋯ }) x).hom))
      a

Defined in

Mathlib.CategoryTheory.Galois.Prorepresentability

Cited by

1 results in Mathlib

Foundations

Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.GaloisCategoryCategoryTheory.PreGaloisCategory.FiberFunctorCategoryTheory.PreGaloisCategory.IsGalois