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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homproof · cited by 32,603
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.NatTrans.appproof · cited by 7,406
- Set.Elemproof · cited by 7,166
- CategoryTheory.ConcreteCategory.homproof · cited by 4,022
- TypeCat.ofHomproof · cited by 389
- CategoryTheory.Functor.sectionsproof · cited by 140
Cited by13
Results whose statement or proof uses this declaration.
- CategoryTheory.PreGaloisCategory.endEquivAutGaloisproof · cited by 3
- CategoryTheory.sectionsFunctorNatIsoCoyonedastatement · cited by 2
- CategoryTheory.sheafHomSectionsEquivproof · cited by 1
- CategoryTheory.Functor.sectionsEquivHom_naturality_symmstatement · cited by 1
- CategoryTheory.sectionsFunctorNatIsoCoyoneda_hom_app_hom_apply_app_hom_applystatement · cited by 0
- CategoryTheory.sectionsFunctorNatIsoCoyoneda_inv_app_hom_apply_coestatement · cited by 0
- CategoryTheory.Limits.Types.limNatIsoSectionsFunctorstatement · cited by 0
- CategoryTheory.Sheaf.ΓObjEquivSections_naturalitystatement · cited by 0
- CategoryTheory.Sheaf.ΓNatIsoSectionsFunctorstatement · cited by 0
- CategoryTheory.Functor.sectionsEquivHom_naturalitystatement and proof · cited by 0
- CategoryTheory.Functor.sectionsFunctor_mapstatement and proof · cited by 0
- CategoryTheory.Functor.sectionsFunctor_objstatement and proof · cited by 0