Theorems · Theorem · category theory
CategoryTheory.ObjectProperty.EssentiallySmall.exists_small_le
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (P : CategoryTheory.ObjectProperty C)
[CategoryTheory.ObjectProperty.EssentiallySmall.{w, v, u} P],
∃ Q, ∃ (_ : CategoryTheory.ObjectProperty.Small.{w, v, u} Q), Q ≤ P ∧ P ≤ Q.isoClosure- Cited by
- 7 results in Mathlib
- Foundations
- Depth 25 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
- Set.rangeproof · cited by 4,705
- CategoryTheory.Isoproof · cited by 3,963
- CategoryTheory.Iso.symmproof · cited by 993
- CategoryTheory.ObjectPropertystatement and proof · cited by 798
- CategoryTheory.Iso.transproof · cited by 566
- Nonempty.someproof · cited by 340
- CategoryTheory.ObjectProperty.isoClosurestatement and proof · cited by 61
- CategoryTheory.ObjectProperty.Smallstatement and proof · cited by 30
- CategoryTheory.ObjectProperty.EssentiallySmallstatement and proof · cited by 26
- small_of_surjectiveproof · cited by 11
- CategoryTheory.ObjectProperty.EssentiallySmall.exists_small_le'proof · cited by 4
Cited by7
Results whose statement or proof uses this declaration.
- CategoryTheory.ObjectProperty.exists_equivalence_iffproof · cited by 1
- CommRingCat.essentiallySmall_of_finiteTypeproof · cited by 1
- CommRingCat.essentiallySmall_of_localizationAwayproof · cited by 1
- CategoryTheory.HasCardinalFilteredGenerator.exists_small_generatorproof · cited by 1
- CategoryTheory.ObjectProperty.essentiallySmall_op_iffproof · cited by 1
- CategoryTheory.ObjectProperty.EssentiallySmall.exists_smallproof · cited by 0
- CategoryTheory.ObjectProperty.isEssentiallySmall_limitsClosureproof · cited by 0