Mathlib Map

Theorems · Definition · category theory

CategoryTheory.PreGaloisCategory.PointedGaloisObject.Hom.val

{C : Type u₁} →
  [inst : CategoryTheory.Category.{u₂, u₁} C] →
    [inst_1 : CategoryTheory.GaloisCategory C] →
      {F : CategoryTheory.Functor C FintypeCat} →
        {A B : CategoryTheory.PreGaloisCategory.PointedGaloisObject F} → A.Hom B → (A.obj ⟶ B.obj)

The underlying homomorphism of C.

Defined in
Mathlib.CategoryTheory.Galois.Prorepresentability
Cited by
11 results in Mathlib
Foundations
Depth 14 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.autGaloisSystem · cited by 6PreGaloisCategory.autGalo…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.autGaloisSystem_map · cited by 1PreGaloisCategory.autGalo…CategoryTheory.PreGaloisCategory.autGaloisSystem_map_surjective · cited by 1PreGaloisCategory.autGalo…CategoryTheory.PreGaloisCategory.PointedGaloisObject.comp_val_assoc · cited by 0PointedGaloisObject.comp_…CategoryTheory.PreGaloisCategory.PointedGaloisObject.hom_ext_iff · cited by 0PointedGaloisObject.hom_e…CategoryTheory.PreGaloisCategory.PointedGaloisObject.id_val · cited by 0PointedGaloisObject.id_valCategoryTheory.PreGaloisCategory.PointedGaloisObject.incl_map · cited by 0PointedGaloisObject.incl_…CategoryTheory.PreGaloisCategory.PointedGaloisObject.Hom.comp · cited by 0Hom.compCategoryTheory.PreGaloisCategory.PointedGaloisObject.Hom.ext_iff · cited by 0Hom.ext_iffCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorFinite · cited by 3029FiniteFintypeCat · cited by 217FintypeCatCategoryTheory.GaloisCategory · cited by 88CategoryTheory.GaloisCate…CategoryTheory.PreGaloisCategory.PointedGaloisObject · cited by 34PreGaloisCategory.Pointed…CategoryTheory.PreGaloisCategory.PointedGaloisObject.obj · cited by 29PointedGaloisObject.objCategoryTheory.PreGaloisCategory.PointedGaloisObject.Hom · cited by 7PointedGaloisObject.HomHom.valCITED BYCITES

Cites9

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by12

Results whose statement or proof uses this declaration.