Theorems · Theorem · category theory
CategoryTheory.Functor.RepresentableBy.isRepresentedBy
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {F : CategoryTheory.Functor Cᵒᵖ (Type w)} {X : C}
(R : F.RepresentableBy X), F.IsRepresentedBy (R.homEquiv (CategoryTheory.CategoryStruct.id X))- Defined in
- Mathlib.CategoryTheory.RepresentedBy
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 32 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.
Cites28
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.Functor.mapproof · cited by 8,698
- Equivstatement · cited by 8,337
- Oppositestatement and proof · cited by 8,081
- CategoryTheory.Iso.homproof · cited by 7,684
- CategoryTheory.Functor.compproof · cited by 6,529
- CategoryTheory.CategoryStruct.idstatement and proof · cited by 6,235
- CategoryTheory.ConcreteCategory.homproof · cited by 4,022
Cited by2
Results whose statement or proof uses this declaration.
- CategoryTheory.Functor.IsRepresentedBy.iff_exists_representableByproof · cited by 2
- CategoryTheory.Functor.IsRepresentedBy.of_isRepresentableproof · cited by 1