Theorems · Theorem · category theory
CategoryTheory.Subobject.eq_of_isDetecting
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] [CategoryTheory.Limits.HasPullbacks C]
{𝒢 : CategoryTheory.ObjectProperty C},
𝒢.IsDetecting →
∀ {X : C} (P Q : CategoryTheory.Subobject X), (∀ (G : C), 𝒢 G → ∀ {f : G ⟶ X}, P.Factors f ↔ Q.Factors f) → P = Q- Defined in
- Mathlib.CategoryTheory.Generator.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 45 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.ObjectPropertystatement and proof · cited by 798
- CategoryTheory.Limits.HasPullbacksstatement and proof · cited by 439
- CategoryTheory.Subobjectstatement and proof · cited by 385
- inf_commproof · cited by 139
- CategoryTheory.Subobject.Factorsstatement and proof · cited by 56
- CategoryTheory.ObjectProperty.IsDetectingstatement and proof · cited by 20
- CategoryTheory.Subobject.inf_eq_of_isDetectingproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.wellPowered_of_isDetectingproof · cited by 2