Theorems · Definition · category theory
CategoryTheory.Functor.representableBy
{C : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} C] →
(F : CategoryTheory.Functor Cᵒᵖ (Type v)) → [hF : F.IsRepresentable] → F.RepresentableBy F.reprXA chosen term in F.RepresentableBy (reprX F) when F.IsRepresentable holds.
- Defined in
- Mathlib.CategoryTheory.Yoneda
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext, Classical.choice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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.Functorstatement and proof · cited by 16,252
- Oppositestatement and proof · cited by 8,081
- Nonempty.someproof · cited by 340
- CategoryTheory.Functor.RepresentableBystatement · cited by 51
- CategoryTheory.Functor.IsRepresentablestatement and proof · cited by 24
- CategoryTheory.Functor.reprXstatement · cited by 6
Cited by12
Results whose statement or proof uses this declaration.
- CategoryTheory.Functor.partialRightAdjointHomEquivproof · cited by 7
- CategoryTheory.Functor.reprxproof · cited by 4
- CategoryTheory.Functor.uliftYonedaReprXIsoproof · cited by 3
- CategoryTheory.Functor.partialRightAdjointHomEquiv_compproof · cited by 1
- CategoryTheory.Functor.partialRightAdjointHomEquiv_comp_symmproof · cited by 1
- CategoryTheory.Functor.IsRepresentedBy.of_isRepresentableproof · cited by 1
- CategoryTheory.Functor.isLeftAdjoint_of_rightAdjointObjIsDefined_eq_topproof · cited by 1
- CategoryTheory.Functor.reprWproof · cited by 1
- CategoryTheory.isRepresentable_of_natIsoproof · cited by 0
- CategoryTheory.Functor.uliftYonedaReprXIso_hom_appproof · cited by 0
- CategoryTheory.Functor.RepresentableBy.isoReprXproof · cited by 0
- CategoryTheory.Functor.reprW_hom_appproof · cited by 0