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Theorems · Definition · category theory

CategoryTheory.Functor.sectionsFunctor

(J : Type u) →
  [inst : CategoryTheory.Category.{v, u} J] →
    CategoryTheory.Functor (CategoryTheory.Functor J (Type w)) (Type (max u w))

The functor which sends a functor to types to its sections.

Defined in
Mathlib.CategoryTheory.Types.Basic
Cited by
8 results in Mathlib
Foundations
Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.Category

Around this declaration

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

CategoryTheory.PreGaloisCategory.endEquivAutGalois · cited by 3PreGaloisCategory.endEqui…CategoryTheory.sectionsFunctorNatIsoCoyoneda · cited by 2CategoryTheory.sectionsFu…CategoryTheory.sheafHomSectionsEquiv · cited by 1CategoryTheory.sheafHomSe…CategoryTheory.Functor.sectionsEquivHom_naturality_symm · cited by 1Functor.sectionsEquivHom_…CategoryTheory.sectionsFunctorNatIsoCoyoneda_hom_app_hom_apply_app_hom_apply · cited by 0CategoryTheory.sectionsFu…CategoryTheory.sectionsFunctorNatIsoCoyoneda_inv_app_hom_apply_coe · cited by 0CategoryTheory.sectionsFu…CategoryTheory.Limits.Types.limNatIsoSectionsFunctor · cited by 0Types.limNatIsoSectionsFu…CategoryTheory.Sheaf.ΓObjEquivSections_naturality · cited by 0Sheaf.ΓObjEquivSections_n…CategoryTheory.Sheaf.ΓNatIsoSectionsFunctor · cited by 0Sheaf.ΓNatIsoSectionsFunc…CategoryTheory.Functor.sectionsEquivHom_naturality · cited by 0Functor.sectionsEquivHom_…CategoryTheory.Functor.sectionsFunctor_map · cited by 0Functor.sectionsFunctor_m…CategoryTheory.Functor.sectionsFunctor_obj · cited by 0Functor.sectionsFunctor_o…CategoryTheory.Sheaf.ΓObjEquivSections_naturality_symm · cited by 0Sheaf.ΓObjEquivSections_n…DFunLike.coe · cited by 62936DFunLike.coeCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.NatTrans.app · cited by 7406NatTrans.appSet.Elem · cited by 7166Set.ElemCategoryTheory.ConcreteCategory.hom · cited by 4022ConcreteCategory.homTypeCat.ofHom · cited by 389TypeCat.ofHomCategoryTheory.Functor.sections · cited by 140Functor.sectionsFunctor.sectionsFunctorCITED BYCITES

Cites9

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

Cited by13

Results whose statement or proof uses this declaration.