Theorems · Theorem · category theory
CategoryTheory.ObjectProperty.is_iff
∀ {C : Type u} [inst : CategoryTheory.CategoryStruct.{v, u} C] (P : CategoryTheory.ObjectProperty C) (X : C),
P.Is X ↔ P X- Cited by
- 6 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.ObjectPropertystatement and proof · cited by 798
- CategoryTheory.CategoryStructstatement and proof · cited by 343
- CategoryTheory.ObjectProperty.Isstatement and proof · cited by 4
- CategoryTheory.ObjectProperty.Is.casesOnproof · cited by 1
Cited by6
Results whose statement or proof uses this declaration.
- CategoryTheory.isArtinianObject_iff_antitone_chain_conditionproof · cited by 4
- CategoryTheory.isNoetherianObject_iff_monotone_chain_conditionproof · cited by 4
- CategoryTheory.ObjectProperty.prop_of_isproof · cited by 1
- CategoryTheory.isArtinianObject_iff_not_strictAntiproof · cited by 1
- CategoryTheory.isNoetherianObject_iff_not_strictMonoproof · cited by 1
- CategoryTheory.ObjectProperty.is_of_propproof · cited by 0