Theorems · Definition · category theory
CategoryTheory.isCardinalPresentable
(C : Type u₁) →
[inst : CategoryTheory.Category.{v₁, u₁} C] →
(κ : Cardinal.{w}) → [Fact κ.IsRegular] → CategoryTheory.ObjectProperty CThe property of objects that are κ-presentable.
- Defined in
- Mathlib.CategoryTheory.Presentable.Basic
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.CategoryFact
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Factstatement and proof · cited by 2,726
- Cardinalstatement and proof · cited by 2,598
- CategoryTheory.ObjectPropertystatement · cited by 798
- Cardinal.IsRegularstatement and proof · cited by 282
- CategoryTheory.IsCardinalPresentableproof · cited by 39
Cited by22
Results whose statement or proof uses this declaration.
- CategoryTheory.ObjectProperty.IsCardinalFilteredGenerator.le_isCardinalPresentablestatement · cited by 8
- CategoryTheory.ObjectProperty.IsCardinalFilteredGenerator.of_le_isoClosurestatement and proof · cited by 4
- CategoryTheory.isCardinalPresentable_iffstatement · cited by 3
- CategoryTheory.ObjectProperty.IsStrongGenerator.isDense_colimitsCardinalClosure_ιstatement and proof · cited by 2
- CategoryTheory.ObjectProperty.colimitsCardinalClosure_le_isCardinalPresentablestatement and proof · cited by 2
- CategoryTheory.Adjunction.isCardinalFilteredGeneratorproof · cited by 1
- CategoryTheory.ObjectProperty.ColimitOfShape.isCardinalPresentablestatement and proof · cited by 1
- CategoryTheory.IsCardinalFilteredGenerator.of_isDense_ιstatement and proof · cited by 1
- CategoryTheory.IsCardinalLocallyPresentable.iff_exists_isStrongGeneratorstatement and proof · cited by 1
- CategoryTheory.ObjectProperty.IsCardinalFilteredGenerator.isPresentable_eq_retractClosurestatement and proof · cited by 1
- CategoryTheory.isCardinalFilteredGenerator_isCardinalPresentablestatement and proof · cited by 1
- CategoryTheory.ObjectProperty.IsCardinalFilteredGenerator.isoClosureproof · cited by 1