Theorems · Definition · category theory
CategoryTheory.ObjectProperty.retractClosure
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] → CategoryTheory.ObjectProperty C → CategoryTheory.ObjectProperty CThe closure by retracts of a predicate on objects in a category.
- Cited by
- 22 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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
- CategoryTheory.ObjectPropertystatement and proof · cited by 798
- CategoryTheory.Retractproof · cited by 34
Cited by23
Results whose statement or proof uses this declaration.
- CategoryTheory.ObjectProperty.triangEnvelopeIterproof · cited by 12
- CategoryTheory.ObjectProperty.retractClosure_eq_selfstatement and proof · cited by 6
- CategoryTheory.ObjectProperty.monotone_retractClosurestatement and proof · cited by 6
- CategoryTheory.ObjectProperty.le_retractClosurestatement · cited by 5
- CategoryTheory.ObjectProperty.retractClosure_extensionProduct_retractClosure_retractClosurestatement and proof · cited by 4
- CategoryTheory.ObjectProperty.retractClosure_le_iffstatement · cited by 3
- CategoryTheory.ObjectProperty.retractClosure_retractClosurestatement and proof · cited by 2
- CategoryTheory.ObjectProperty.extensionProduct_retractClosure_retractClosure_lestatement and proof · cited by 2
- CategoryTheory.ObjectProperty.retractClosure_botstatement · cited by 1
- CategoryTheory.ObjectProperty.monotone'_triangEnvelopeIterproof · cited by 1
- CategoryTheory.ObjectProperty.triangEnvelopeIter_zerostatement and proof · cited by 1
- CategoryTheory.ObjectProperty.extensionProductIter_retractClosure_lestatement and proof · cited by 1