Theorems · Theorem · category theory
CategoryTheory.isIso_iff_isIso_coyoneda_map
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {X Y : C} (f : X ⟶ Y),
CategoryTheory.IsIso f ↔ ∀ (c : C), CategoryTheory.IsIso ((CategoryTheory.coyoneda.map f.op).app c)- Defined in
- Mathlib.CategoryTheory.Yoneda
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 30 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.
Cites13
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.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Functorstatement · cited by 16,252
- CategoryTheory.Functor.mapstatement and proof · cited by 8,698
- Oppositestatement · cited by 8,081
- CategoryTheory.NatTrans.appstatement and proof · cited by 7,406
- Quiver.Hom.opstatement and proof · cited by 1,948
- CategoryTheory.IsIsostatement and proof · cited by 1,156
- CategoryTheory.coyonedastatement and proof · cited by 208
- CategoryTheory.bijective_iff_isIso_ofHomproof · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.Monoidal.Reflective.isIso_tfaeproof · cited by 0