Mathlib Map

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
Assumes
CategoryTheory.CategoryCategoryTheory.LocallySmall

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CategoryTheory.shrinkYonedaObjObjEquiv · cited by 35CategoryTheory.shrinkYone…CategoryTheory.shrinkCoyoneda · cited by 23CategoryTheory.shrinkCoyo…CategoryTheory.shrinkYonedaEquiv · cited by 15CategoryTheory.shrinkYone…CategoryTheory.Sieve.shrinkFunctor · cited by 14Sieve.shrinkFunctorCategoryTheory.GrothendieckTopology.Point.ofIsCofiltered.fiber · cited by 9ofIsCofiltered.fiberCategoryTheory.GrothendieckTopology.Point.ofIsCofiltered.fiberMk · cited by 9ofIsCofiltered.fiberMkCategoryTheory.shrinkYoneda_map_app_shrinkYonedaObjObjEquiv_symm · cited by 6CategoryTheory.shrinkYone…CategoryTheory.Presieve.shrinkFunctorHomEquiv · cited by 5Presieve.shrinkFunctorHom…CategoryTheory.GrothendieckTopology.pointBot · cited by 5GrothendieckTopology.poin…CategoryTheory.Presheaf.coconeCompShrinkYonedaHomEquiv · cited by 5Presheaf.coconeCompShrink…CategoryTheory.Presheaf.coconePtToShrinkYoneda · cited by 5Presheaf.coconePtToShrink…CategoryTheory.shrinkYoneda_obj_map_shrinkYonedaObjObjEquiv_symm · cited by 5CategoryTheory.shrinkYone…CategoryTheory.Presieve.isSheafFor_iff_bijective_shrinkFunctor_ι_comp · cited by 4Presieve.isSheafFor_iff_b…CategoryTheory.Functor.Elements.coconeπOpCompShrinkYonedaObj · cited by 3Elements.coconeπOpCompShr…CategoryTheory.GrothendieckTopology.Point.shrinkYonedaCompPresheafFiberIso · cited by 3Point.shrinkYonedaCompPre…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.Functor.map · cited by 8698Functor.mapOpposite · cited by 8081OppositeCategoryTheory.yoneda · cited by 351CategoryTheory.yonedaCategoryTheory.LocallySmall · cited by 242CategoryTheory.LocallySma…CategoryTheory.FunctorToTypes.shrink · cited by 9FunctorToTypes.shrinkCategoryTheory.FunctorToTypes.shrinkMap · cited by 3FunctorToTypes.shrinkMapCategoryTheory.shrinkYonedaCITED BYCITES

Cites10

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

Cited by95

Results whose statement or proof uses this declaration.