Theorems · Theorem · category theory
CategoryTheory.ObjectProperty.isDetecting_iff_isSeparating
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {P : CategoryTheory.ObjectProperty C}
[CategoryTheory.Limits.HasEqualizers C] [CategoryTheory.Balanced C], P.IsDetecting ↔ P.IsSeparating- Defined in
- Mathlib.CategoryTheory.Generator.Basic
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- Foundations
- Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound
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- CategoryTheory.Categorystatement and proof · cited by 32,673
- CategoryTheory.ObjectPropertystatement and proof · cited by 798
- CategoryTheory.Balancedstatement and proof · cited by 61
- CategoryTheory.Limits.HasEqualizersstatement and proof · cited by 60
- CategoryTheory.ObjectProperty.IsSeparatingstatement · cited by 41
- CategoryTheory.ObjectProperty.IsDetectingstatement · cited by 20
- CategoryTheory.ObjectProperty.IsSeparating.isDetectingproof · cited by 4
- CategoryTheory.ObjectProperty.IsDetecting.isSeparatingproof · cited by 3
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