Theorems · Definition · category theory

CategoryTheory.PreGaloisCategory.toAutHomeo

{C : Type u₁} →
  [inst : CategoryTheory.Category.{u₂, u₁} C] →
    (F : CategoryTheory.Functor C FintypeCat) →
      [inst_1 : CategoryTheory.GaloisCategory C] →
        (G : Type u_1) →
          [inst_2 : Group G] →
            [inst_3 : (X : C) → MulAction G (F.obj X).obj] →
              [CategoryTheory.PreGaloisCategory.FiberFunctor F] →
                [inst_5 : TopologicalSpace G] →
                  [inst_6 : IsTopologicalGroup G] →
                    [inst_7 : CompactSpace G] →
                      [CategoryTheory.PreGaloisCategory.IsFundamentalGroup F G] → G ≃ₜ CategoryTheory.Aut F

If G is a fundamental group for F, it is canonically homeomorphic to Aut F.

Defined in

Mathlib.CategoryTheory.Galois.IsFundamentalgroup

Cited by

1 results in Mathlib

Foundations

Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.GaloisCategoryGroupMulActionCategoryTheory.PreGaloisCategory.FiberFunctorTopologicalSpaceIsTopologicalGroupCompactSpaceCategoryTheory.PreGaloisCategory.IsFundamentalGroup