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Theorems · Definition · category theory

CategoryTheory.uliftYoneda

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

Variant of the Yoneda embedding which allows a raise in the universe level for the category of types.

Defined in
Mathlib.CategoryTheory.Yoneda
Cited by
84 results in Mathlib
Foundations
Depth 27 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.

SSet.stdSimplex · cited by 499SSet.stdSimplexCategoryTheory.uliftYonedaEquiv · cited by 34CategoryTheory.uliftYoned…CategoryTheory.uliftCoyoneda · cited by 22CategoryTheory.uliftCoyon…CategoryTheory.Presheaf.restrictedULiftYoneda · cited by 15Presheaf.restrictedULiftY…CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence · cited by 7CategoryOfElements.costru…CategoryTheory.Presheaf.functorToRepresentables · cited by 7Presheaf.functorToReprese…CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.presheafHom · cited by 5compULiftYonedaIsoULiftYo…CategoryTheory.Presheaf.uliftYonedaAdjunction · cited by 5Presheaf.uliftYonedaAdjun…CategoryTheory.Presheaf.restrictedULiftYonedaHomEquiv' · cited by 4Presheaf.restrictedULiftY…CategoryTheory.GrothendieckTopology.uliftYonedaCompSheafToPresheaf · cited by 4GrothendieckTopology.ulif…CategoryTheory.Functor.FullyFaithful.compUliftYonedaCompWhiskeringLeft · cited by 4FullyFaithful.compUliftYo…CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan · cited by 4Presheaf.compULiftYonedaI…CategoryTheory.Sieve.uliftFunctorInclusion · cited by 3Sieve.uliftFunctorInclusi…CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.coconeApp · cited by 3compULiftYonedaIsoULiftYo…CategoryTheory.Presheaf.tautologicalCocone' · cited by 3Presheaf.tautologicalCoco…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorOpposite · cited by 8081OppositeCategoryTheory.Functor.comp · cited by 6529Functor.compCategoryTheory.yoneda · cited by 351CategoryTheory.yonedaCategoryTheory.Functor.whiskeringRight · cited by 221Functor.whiskeringRightCategoryTheory.uliftFunctor · cited by 58CategoryTheory.uliftFunct…CategoryTheory.uliftYonedaCITED BYCITES

Cites8

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

Cited by122

Results whose statement or proof uses this declaration.