Theorems · Theorem · category theory
CategoryTheory.isCodetector_def
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] (G : C),
CategoryTheory.IsCodetector G ↔
∀ ⦃X Y : C⦄ (f : X ⟶ Y),
(∀ (h : X ⟶ G), ∃! h', CategoryTheory.CategoryStruct.comp f h' = h) → CategoryTheory.IsIso f- Defined in
- Mathlib.CategoryTheory.Generator.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses propext
- 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
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
- CategoryTheory.IsIsostatement and proof · cited by 1,156
- ExistsUniquestatement and proof · cited by 268
- CategoryTheory.ObjectProperty.singletonproof · cited by 20
- CategoryTheory.IsCodetectorstatement and proof · cited by 14
- CategoryTheory.ObjectProperty.singleton_iffproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- CategoryTheory.IsCodetector.defproof · cited by 1
- CategoryTheory.isCodetector_iff_reflectsIsomorphisms_yoneda_objproof · cited by 0