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Theorems · Definition · category theory

CategoryTheory.coyoneda

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] → CategoryTheory.Functor Cᵒᵖ (CategoryTheory.Functor C (Type v₁))

The co-Yoneda embedding, as a functor from Cᵒᵖ into co-presheaves on C.

Defined in
Mathlib.CategoryTheory.Yoneda
Cited by
208 results in Mathlib
Foundations
Depth 27 from the axioms, rests on 163 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.Presheaf.IsSheaf · cited by 991Presheaf.IsSheafCategoryTheory.IsCardinalPresentable · cited by 39CategoryTheory.IsCardinal…CategoryTheory.isSheaf_iff_isSheaf_of_type · cited by 30CategoryTheory.isSheaf_if…CategoryTheory.Functor.leftAdjointObjIsDefined · cited by 16Functor.leftAdjointObjIsD…CategoryTheory.Functor.functorHom · cited by 16Functor.functorHomCategoryTheory.MonoidalCategory.DayConvolution.corepresentableBy · cited by 10DayConvolution.corepresen…CategoryTheory.coyonedaEquiv · cited by 9CategoryTheory.coyonedaEq…CategoryTheory.Functor.partialLeftAdjointObj · cited by 9Functor.partialLeftAdjoin…CategoryTheory.Functor.cocones · cited by 9Functor.coconesCategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitor · cited by 9DayConvolutionUnit.leftUn…CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitor · cited by 9DayConvolutionUnit.rightU…CategoryTheory.Presheaf.isSheaf_of_iso_iff · cited by 8Presheaf.isSheaf_of_iso_i…CategoryTheory.Functor.op_comp_isSheaf · cited by 8Functor.op_comp_isSheafCategoryTheory.Functor.partialLeftAdjointHomEquiv · cited by 7Functor.partialLeftAdjoin…AlgebraicGeometry.Scheme.pointSmallEtale · cited by 7Scheme.pointSmallEtaleCategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorOpposite · cited by 8081OppositeCategoryTheory.yoneda · cited by 351CategoryTheory.yonedaCategoryTheory.Functor.flip · cited by 320Functor.flipCategoryTheory.coyonedaCITED BYCITES

Cites5

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

Cited by328

Results whose statement or proof uses this declaration.