Theorems · Definition · category theory
CategoryTheory.shrinkYoneda
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
[CategoryTheory.LocallySmall.{w, v, u} C] → CategoryTheory.Functor C (CategoryTheory.Functor Cᵒᵖ (Type w))The Yoneda embedding C ⥤ Cᵒᵖ ⥤ Type w for a locally w-small category C.
- Defined in
- Mathlib.CategoryTheory.ShrinkYoneda
- Cited by
- 64 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homproof · cited by 32,603
- CategoryTheory.Functor.objproof · cited by 19,642
- CategoryTheory.Functorstatement · cited by 16,252
- CategoryTheory.Functor.mapproof · cited by 8,698
- Oppositestatement · cited by 8,081
- CategoryTheory.yonedaproof · cited by 351
- CategoryTheory.LocallySmallstatement and proof · cited by 242
- CategoryTheory.FunctorToTypes.shrinkproof · cited by 9
- CategoryTheory.FunctorToTypes.shrinkMapproof · cited by 3
Cited by95
Results whose statement or proof uses this declaration.
- CategoryTheory.shrinkYonedaObjObjEquivstatement · cited by 35
- CategoryTheory.shrinkCoyonedaproof · cited by 23
- CategoryTheory.shrinkYonedaEquivstatement and proof · cited by 15
- CategoryTheory.Sieve.shrinkFunctorstatement and proof · cited by 14
- CategoryTheory.GrothendieckTopology.Point.ofIsCofiltered.fiberproof · cited by 9
- CategoryTheory.GrothendieckTopology.Point.ofIsCofiltered.fiberMkproof · cited by 9
- CategoryTheory.shrinkYoneda_map_app_shrinkYonedaObjObjEquiv_symmstatement · cited by 6
- CategoryTheory.Presieve.shrinkFunctorHomEquivstatement · cited by 5
- CategoryTheory.GrothendieckTopology.pointBotproof · cited by 5
- CategoryTheory.Presheaf.coconeCompShrinkYonedaHomEquivstatement and proof · cited by 5
- CategoryTheory.Presheaf.coconePtToShrinkYonedastatement and proof · cited by 5
- CategoryTheory.shrinkYoneda_obj_map_shrinkYonedaObjObjEquiv_symmstatement · cited by 5