Theorems · Definition · category theory

CategoryTheory.PreGaloisCategory.endEquivSectionsFibers

{C : Type u₁} →
  [inst : CategoryTheory.Category.{u₂, u₁} C] →
    [inst_1 : CategoryTheory.GaloisCategory C] →
      (F : CategoryTheory.Functor C FintypeCat) →
        [CategoryTheory.PreGaloisCategory.FiberFunctor F] →
          CategoryTheory.End F ≃
            ↑((CategoryTheory.PreGaloisCategory.PointedGaloisObject.incl F).comp (F.comp FintypeCat.incl)).sections

The endomorphisms of F are isomorphic to the limit over the fibers of F on all Galois objects.

Defined in

Mathlib.CategoryTheory.Galois.Prorepresentability

Cited by

2 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.GaloisCategoryCategoryTheory.PreGaloisCategory.FiberFunctor