Theorems · Definition · category theory
CategoryTheory.yoneda
{C : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} C] → CategoryTheory.Functor C (CategoryTheory.Functor Cᵒᵖ (Type v₁))The Yoneda embedding, as a functor from C into presheaves on C.
- Defined in
- Mathlib.CategoryTheory.Yoneda
- Cited by
- 351 results in Mathlib
- Foundations
- Depth 22 from the axioms, rests on 160 definitions · 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.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homproof · cited by 32,603
- CategoryTheory.Functor.objproof · cited by 19,642
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Functorstatement · cited by 16,252
- Oppositestatement and proof · cited by 8,081
- Opposite.unopproof · cited by 2,231
- Quiver.Hom.unopproof · cited by 903
- TypeCat.ofHomproof · cited by 389
Cited by542
Results whose statement or proof uses this declaration.
- CategoryTheory.coyonedaproof · cited by 208
- CategoryTheory.uliftYonedaproof · cited by 84
- CategoryTheory.shrinkYonedaproof · cited by 64
- CategoryTheory.yonedaEquivstatement and proof · cited by 42
- CategoryTheory.GrothendieckTopology.yonedaproof · cited by 37
- CategoryTheory.shrinkYonedaObjObjEquivproof · cited by 35
- CategoryTheory.OverPresheafAux.YonedaCollectionstatement and proof · cited by 24
- CategoryTheory.OverPresheafAux.OverArrowsstatement and proof · cited by 23
- CategoryTheory.OverPresheafAux.YonedaCollection.fststatement and proof · cited by 23
- CategoryTheory.OverPresheafAux.yonedaCollectionPresheafstatement and proof · cited by 21
- CategoryTheory.OverPresheafAux.OverArrows.valstatement and proof · cited by 19
- CategoryTheory.OverPresheafAux.YonedaCollection.sndstatement and proof · cited by 18
Showing the 200 most cited of 542.