Theorems · Theorem · category theory
CategoryTheory.Subobject.eq_of_le_of_isDetecting
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {𝒢 : CategoryTheory.ObjectProperty C},
𝒢.IsDetecting →
∀ {X : C} (P Q : CategoryTheory.Subobject X),
P ≤ Q → (∀ (G : C), 𝒢 G → ∀ {f : G ⟶ X}, Q.Factors f → P.Factors f) → P = Q- Defined in
- Mathlib.CategoryTheory.Generator.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 41 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.
Cites21
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.objproof · cited by 19,642
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Category.assocproof · cited by 6,433
- le_antisymmproof · cited by 2,068
- CategoryTheory.IsIsoproof · cited by 1,156
- CategoryTheory.ObjectPropertystatement and proof · cited by 798
- CategoryTheory.invproof · cited by 467
- CategoryTheory.cancel_monoproof · cited by 435
- CategoryTheory.Subobjectstatement and proof · cited by 385
- CategoryTheory.Subobject.underlyingproof · cited by 211
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.Subobject.inf_eq_of_isDetectingproof · cited by 1