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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.

CategoryTheory.coyoneda · cited by 208CategoryTheory.coyonedaCategoryTheory.uliftYoneda · cited by 84CategoryTheory.uliftYonedaCategoryTheory.shrinkYoneda · cited by 64CategoryTheory.shrinkYone…CategoryTheory.yonedaEquiv · cited by 42CategoryTheory.yonedaEquivCategoryTheory.GrothendieckTopology.yoneda · cited by 37GrothendieckTopology.yone…CategoryTheory.shrinkYonedaObjObjEquiv · cited by 35CategoryTheory.shrinkYone…CategoryTheory.OverPresheafAux.YonedaCollection · cited by 24OverPresheafAux.YonedaCol…CategoryTheory.OverPresheafAux.OverArrows · cited by 23OverPresheafAux.OverArrowsCategoryTheory.OverPresheafAux.YonedaCollection.fst · cited by 23YonedaCollection.fstCategoryTheory.OverPresheafAux.yonedaCollectionPresheaf · cited by 21OverPresheafAux.yonedaCol…CategoryTheory.OverPresheafAux.OverArrows.val · cited by 19OverArrows.valCategoryTheory.OverPresheafAux.YonedaCollection.snd · cited by 18YonedaCollection.sndCategoryTheory.OverPresheafAux.restrictedYonedaObj · cited by 17OverPresheafAux.restricte…CategoryTheory.MorphismProperty.presheaf · cited by 17MorphismProperty.presheafCategoryTheory.shrinkYonedaEquiv · cited by 15CategoryTheory.shrinkYone…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorOpposite · cited by 8081OppositeOpposite.unop · cited by 2231Opposite.unopQuiver.Hom.unop · cited by 903Hom.unopTypeCat.ofHom · cited by 389TypeCat.ofHomCategoryTheory.yonedaCITED BYCITES

Cites9

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

Cited by542

Results whose statement or proof uses this declaration.

Showing the 200 most cited of 542.