Theorems · Definition · category theory

CategoryTheory.CategoryOfElements.costructuredArrowYonedaEquivalence

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    (F : CategoryTheory.Functor Cᵒᵖ (Type v)) → F.Elementsᵒᵖ ≌ CategoryTheory.CostructuredArrow CategoryTheory.yoneda F

The equivalence F.Elementsᵒᵖ ≅ (yoneda, F) given by yoneda lemma.

Defined in: Mathlib.CategoryTheory.Elements
Cited by: 9 results in Mathlib
Foundations: Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category

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

Cites19

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
CategoryTheory.Functor.objproof · cited by 19,642
CategoryTheory.Functorstatement and proof · cited by 16,252
Oppositestatement and proof · cited by 8,081
CategoryTheory.Functor.compproof · cited by 6,529
Opposite.unopproof · cited by 2,231
CategoryTheory.Iso.reflproof · cited by 727
CategoryTheory.Equivalencestatement · cited by 601
CategoryTheory.CostructuredArrowstatement and proof · cited by 536
CategoryTheory.yonedastatement and proof · cited by 351
CategoryTheory.Functor.rightOpproof · cited by 214
CategoryTheory.CostructuredArrow.leftproof · cited by 202

Cited by12

Results whose statement or proof uses this declaration.

CategoryTheory.Limits.isFiltered_costructuredArrow_yoneda_of_preservesFiniteLimitsproof · cited by 2
CategoryTheory.Presheaf.isColimitTautologicalCoconeproof · cited by 2
CategoryTheory.CategoryOfElements.costructuredArrowYonedaEquivalenceFunctorProjstatement and proof · cited by 2
CategoryTheory.CategoryOfElements.costructuredArrowYonedaEquivalenceInverseπstatement and proof · cited by 2
CategoryTheory.CategoryOfElements.costructuredArrowYonedaEquivalenceFunctorProj_hom_appstatement · cited by 0
CategoryTheory.CategoryOfElements.costructuredArrowYonedaEquivalenceFunctorProj_inv_appstatement · cited by 0
CategoryTheory.CategoryOfElements.costructuredArrowYonedaEquivalenceInverseπ_hom_appstatement · cited by 0
CategoryTheory.CategoryOfElements.costructuredArrowYonedaEquivalenceInverseπ_inv_appstatement · cited by 0
CategoryTheory.CategoryOfElements.costructuredArrowYonedaEquivalence_counitIsostatement and proof · cited by 0
CategoryTheory.CategoryOfElements.costructuredArrowYonedaEquivalence_functorstatement and proof · cited by 0
CategoryTheory.CategoryOfElements.costructuredArrowYonedaEquivalence_inversestatement and proof · cited by 0
CategoryTheory.CategoryOfElements.costructuredArrowYonedaEquivalence_unitIsostatement and proof · cited by 0