Theorems · Theorem · category theory
CategoryTheory.ObjectProperty.retractClosure_eq_self
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (P : CategoryTheory.ObjectProperty C)
[P.IsStableUnderRetracts], P.retractClosure = P- Cited by
- 6 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- le_antisymmproof · cited by 2,068
- CategoryTheory.ObjectPropertystatement and proof · cited by 798
- CategoryTheory.Retractproof · cited by 34
- CategoryTheory.ObjectProperty.retractClosurestatement and proof · cited by 22
- CategoryTheory.ObjectProperty.IsStableUnderRetractsstatement and proof · cited by 12
- CategoryTheory.ObjectProperty.le_retractClosureproof · cited by 5
- CategoryTheory.ObjectProperty.prop_of_retractproof · cited by 2
Cited by6
Results whose statement or proof uses this declaration.
- CategoryTheory.ObjectProperty.retractClosure_le_iffproof · cited by 3
- CategoryTheory.ObjectProperty.retractClosure_retractClosureproof · cited by 2
- CategoryTheory.ObjectProperty.retractClosure_botproof · cited by 1
- CategoryTheory.ObjectProperty.triangEnvelopeIter_zeroproof · cited by 1
- CategoryTheory.ObjectProperty.retractClosure_topproof · cited by 0