Theorems · Theorem · category theory
CategoryTheory.ObjectProperty.IsDetecting.isSeparating
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {P : CategoryTheory.ObjectProperty C}
[CategoryTheory.Limits.HasEqualizers C], P.IsDetecting → P.IsSeparating- Defined in
- Mathlib.CategoryTheory.Generator.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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.Homproof · cited by 32,603
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.IsIsoproof · cited by 1,156
- CategoryTheory.ObjectPropertystatement and proof · cited by 798
- CategoryTheory.Limits.equalizer.ιproof · cited by 64
- CategoryTheory.Limits.HasEqualizersstatement and proof · cited by 60
- CategoryTheory.Limits.equalizerproof · cited by 60
- CategoryTheory.ObjectProperty.IsSeparatingstatement · cited by 41
- CategoryTheory.ObjectProperty.IsDetectingstatement and proof · cited by 20
- CategoryTheory.Limits.eq_of_epi_equalizerproof · cited by 6
- CategoryTheory.Limits.equalizer.existsUniqueproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- CategoryTheory.ObjectProperty.IsCodetecting.isCoseparatingproof · cited by 2
- CategoryTheory.IsDetector.isSeparatorproof · cited by 1
- CategoryTheory.ObjectProperty.isDetecting_iff_isSeparatingproof · cited by 0