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Theorems · Inductive type · category theory

CategoryTheory.PreGaloisCategory.PointedGaloisObject

{C : Type u₁} →
  [inst : CategoryTheory.Category.{u₂, u₁} C] →
    [CategoryTheory.GaloisCategory C] → CategoryTheory.Functor C FintypeCat → Type (max u₁ u₂ w)

A pointed Galois object is a Galois object with a fixed point of its fiber.

Defined in
Mathlib.CategoryTheory.Galois.Prorepresentability
Cited by
34 results in Mathlib
Foundations
Depth 12 from the axioms · uses propext
Assumes
CategoryTheory.CategoryCategoryTheory.GaloisCategory

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CategoryTheory.PreGaloisCategory.PointedGaloisObject.obj · cited by 29PointedGaloisObject.objCategoryTheory.PreGaloisCategory.PointedGaloisObject.pt · cited by 16PointedGaloisObject.ptCategoryTheory.PreGaloisCategory.PointedGaloisObject.Hom.val · cited by 11Hom.valCategoryTheory.PreGaloisCategory.AutGalois.π · cited by 9AutGalois.πCategoryTheory.PreGaloisCategory.PointedGaloisObject.Hom · cited by 7PointedGaloisObject.HomCategoryTheory.PreGaloisCategory.PointedGaloisObject.incl · cited by 6PointedGaloisObject.inclCategoryTheory.PreGaloisCategory.autGaloisSystem · cited by 6PreGaloisCategory.autGalo…CategoryTheory.PreGaloisCategory.endEquivAutGalois_π · cited by 3PreGaloisCategory.endEqui…CategoryTheory.PreGaloisCategory.endEquivAutGalois · cited by 3PreGaloisCategory.endEqui…CategoryTheory.PreGaloisCategory.PointedGaloisObject.cocone · cited by 2PointedGaloisObject.coconeCategoryTheory.PreGaloisCategory.endEquivSectionsFibers · cited by 2PreGaloisCategory.endEqui…CategoryTheory.PreGaloisCategory.PointedGaloisObject.Hom.ext · cited by 2Hom.extCategoryTheory.PreGaloisCategory.PointedGaloisObject.comp_val · cited by 1PointedGaloisObject.comp_…CategoryTheory.PreGaloisCategory.PointedGaloisObject.hom_ext · cited by 1PointedGaloisObject.hom_e…CategoryTheory.PreGaloisCategory.PointedGaloisObject.isColimit · cited by 1PointedGaloisObject.isCol…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorFinite · cited by 3029FiniteFintypeCat · cited by 217FintypeCatCategoryTheory.GaloisCategory · cited by 88CategoryTheory.GaloisCate…PreGaloisCategory.PointedGalo…CITED BYCITES

Cites5

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Cited by58

Results whose statement or proof uses this declaration.