Theorems · Definition · category theory
CategoryTheory.Functor.RepresentableBy.ofIsoObj
{C : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} C] →
{F : CategoryTheory.Functor Cᵒᵖ (Type w)} → {X Y : C} → F.RepresentableBy X → (Y ≅ X) → F.RepresentableBy YTransport RepresentableBy along an isomorphism of the object.
- Defined in
- Mathlib.CategoryTheory.Yoneda
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 19 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.
Cites8
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
- CategoryTheory.Isostatement and proof · cited by 3,963
- Equiv.transproof · cited by 337
- CategoryTheory.Functor.RepresentableBystatement and proof · cited by 51
- CategoryTheory.Functor.RepresentableBy.homEquivproof · cited by 35
- CategoryTheory.Iso.homToEquivproof · cited by 6
Cited by5
Results whose statement or proof uses this declaration.
- CategoryTheory.Functor.RepresentableBy.equivOfIsoObjproof · cited by 2
- CategoryTheory.Functor.IsRepresentedBy.of_isoObjproof · cited by 1
- CategoryTheory.Functor.RepresentableBy.ofIsoObj_homEquivstatement and proof · cited by 1
- CategoryTheory.Functor.RepresentableBy.equivOfIsoObj_applystatement · cited by 0
- CategoryTheory.Functor.RepresentableBy.equivOfIsoObj_symm_applystatement · cited by 0