Theorems · Theorem · category theory
CategoryTheory.Yoneda.isIso
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {X Y : C} (f : X ⟶ Y)
[CategoryTheory.IsIso (CategoryTheory.yoneda.map f)], CategoryTheory.IsIso fIf yoneda.map f is an isomorphism, so was f.
- Defined in
- Mathlib.CategoryTheory.Yoneda
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Functor.objstatement · cited by 19,642
- CategoryTheory.Functorstatement · cited by 16,252
- CategoryTheory.Functor.mapstatement and proof · cited by 8,698
- Oppositestatement · cited by 8,081
- CategoryTheory.IsIsostatement and proof · cited by 1,156
- CategoryTheory.yonedastatement and proof · cited by 351
- CategoryTheory.isIso_of_fully_faithfulproof · cited by 7
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.