Theorems · Inductive type · category theory
CategoryTheory.ObjectProperty.EssentiallySmall
{C : Type u} → [inst : CategoryTheory.Category.{v, u} C] → CategoryTheory.ObjectProperty C → PropA property of objects is essentially small relative to a universe w
if it is contained in the closure by isomorphisms of a small property.
- Cited by
- 26 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.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement · cited by 32,673
- CategoryTheory.ObjectPropertystatement · cited by 798
Cited by30
Results whose statement or proof uses this declaration.
- CategoryTheory.ObjectProperty.EssentiallySmall.exists_small_lestatement and proof · cited by 7
- CategoryTheory.HasCardinalFilteredGenerator.exists_generatorstatement · cited by 4
- CategoryTheory.ObjectProperty.EssentiallySmall.exists_small_le'statement and proof · cited by 4
- CategoryTheory.Adjunction.hasCardinalFilteredGeneratorproof · cited by 3
- CategoryTheory.ObjectProperty.EssentiallySmall.of_lestatement and proof · cited by 3
- CategoryTheory.exists_equivalence_iff_of_locallySmallstatement · cited by 2
- CategoryTheory.EssentiallySmall.of_functorstatement and proof · cited by 1
- CategoryTheory.HasCardinalFilteredGenerator.exists_small_generatorproof · cited by 1
- CategoryTheory.IsCardinalFilteredGenerator.of_isDense_ιstatement and proof · cited by 1
- CategoryTheory.ObjectProperty.IsCardinalFilteredGenerator.essentiallyLarge_topstatement and proof · cited by 1
- CategoryTheory.essentiallySmall_iff_objectPropertyEssentiallySmallstatement and proof · cited by 1
- CategoryTheory.isCardinalFilteredGenerator_isCardinalPresentableproof · cited by 1