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Theorems · Definition · category theory

CategoryTheory.CategoryOfElements.fromCostructuredArrow

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

The reverse direction of the equivalence F.Elementsᵒᵖ ≅ (yoneda, F), given by CategoryTheory.yonedaEquiv.

Defined in
Mathlib.CategoryTheory.Elements
Cited by
7 results in Mathlib
Foundations
Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.Category
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

CategoryTheory.CategoryOfElements.costructuredArrowYonedaEquivalence · cited by 9CategoryOfElements.costru…CategoryTheory.CategoryOfElements.fromCostructuredArrow_map_coe · cited by 0CategoryOfElements.fromCo…CategoryTheory.CategoryOfElements.fromCostructuredArrow_obj_fst · cited by 0CategoryOfElements.fromCo…CategoryTheory.CategoryOfElements.fromCostructuredArrow_obj_mk · cited by 0CategoryOfElements.fromCo…CategoryTheory.CategoryOfElements.fromCostructuredArrow_obj_snd · cited by 0CategoryOfElements.fromCo…CategoryTheory.CategoryOfElements.costructuredArrowYonedaEquivalence_counitIso · cited by 0CategoryOfElements.costru…CategoryTheory.CategoryOfElements.costructuredArrowYonedaEquivalence_inverse · cited by 0CategoryOfElements.costru…CategoryTheory.CategoryOfElements.costructuredArrowYonedaEquivalence_unitIso · cited by 0CategoryOfElements.costru…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorOpposite · cited by 8081OppositeOpposite.unop · cited by 2231Opposite.unopQuiver.Hom.op · cited by 1948Hom.opQuiver.Hom.unop · cited by 903Hom.unopCategoryTheory.Comma.left · cited by 886Comma.leftCategoryTheory.CostructuredArrow · cited by 536CategoryTheory.Costructur…CategoryTheory.CommaMorphism.left · cited by 526CommaMorphism.leftCategoryTheory.Comma.hom · cited by 490Comma.homCategoryTheory.yoneda · cited by 351CategoryTheory.yonedaEquiv.toFun · cited by 279Equiv.toFunCategoryTheory.Functor.Elements · cited by 141Functor.ElementsCategoryTheory.yonedaEquiv · cited by 42CategoryTheory.yonedaEquivCategoryOfElements.fromCostru…CITED BYCITES

Cites15

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Cited by8

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