Theorems · Definition · category theory
CategoryTheory.Quiv.homEquivOfIso
{V W : CategoryTheory.Quiv} → (e : V ≅ W) → {X Y : ↑V} → (X ⟶ Y) ≃ (e.hom.obj X ⟶ e.hom.obj Y)An isomorphism of quivers defines an equivalence on hom types.
- Defined in
- Mathlib.CategoryTheory.Category.Quiv
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement and proof · cited by 32,603
- Equivstatement · cited by 8,337
- CategoryTheory.Iso.homstatement and proof · cited by 7,684
- CategoryTheory.Iso.invproof · cited by 6,514
- CategoryTheory.Isostatement and proof · cited by 3,963
- Prefunctor.objstatement and proof · cited by 1,241
- Prefunctor.mapproof · cited by 952
- CategoryTheory.Bundled.αstatement and proof · cited by 736
- Quiverstatement · cited by 405
- CategoryTheory.Quivstatement and proof · cited by 21
- Quiver.homOfEqproof · cited by 21
Cited by2
Results whose statement or proof uses this declaration.
- CategoryTheory.Quiv.homEquivOfIso_symm_applystatement and proof · cited by 0
- CategoryTheory.Quiv.homEquivOfIso_applystatement and proof · cited by 0