Theorems · Theorem · category theory
CategoryTheory.ObjectProperty.IsDetecting.isIso_iff_of_mono
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {P : CategoryTheory.ObjectProperty C},
P.IsDetecting →
∀ {X Y : C} (f : X ⟶ Y) [CategoryTheory.Mono f],
CategoryTheory.IsIso f ↔
∀ (G : C),
P G →
Function.Surjective
⇑(CategoryTheory.ConcreteCategory.hom ((CategoryTheory.coyoneda.obj (Opposite.op G)).map f))- Defined in
- Mathlib.CategoryTheory.Generator.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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.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.ConcreteCategory.homstatement and proof · cited by 4,022
- TypeCat.Funstatement · cited by 1,307
- CategoryTheory.IsIsostatement and proof · cited by 1,156
- CategoryTheory.Monostatement and proof · cited by 893
Cited by1
Results whose statement or proof uses this declaration.