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Theorems · Definition · category theory

CategoryTheory.isCardinalPresentable

(C : Type u₁) →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    (κ : Cardinal.{w}) → [Fact κ.IsRegular] → CategoryTheory.ObjectProperty C

The 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.

CategoryTheory.ObjectProperty.IsCardinalFilteredGenerator.le_isCardinalPresentable · cited by 8IsCardinalFilteredGenerat…CategoryTheory.ObjectProperty.IsCardinalFilteredGenerator.of_le_isoClosure · cited by 4IsCardinalFilteredGenerat…CategoryTheory.isCardinalPresentable_iff · cited by 3CategoryTheory.isCardinal…CategoryTheory.ObjectProperty.IsStrongGenerator.isDense_colimitsCardinalClosure_ι · cited by 2IsStrongGenerator.isDense…CategoryTheory.ObjectProperty.colimitsCardinalClosure_le_isCardinalPresentable · cited by 2ObjectProperty.colimitsCa…CategoryTheory.Adjunction.isCardinalFilteredGenerator · cited by 1Adjunction.isCardinalFilt…CategoryTheory.ObjectProperty.ColimitOfShape.isCardinalPresentable · cited by 1ColimitOfShape.isCardinal…CategoryTheory.IsCardinalFilteredGenerator.of_isDense_ι · cited by 1IsCardinalFilteredGenerat…CategoryTheory.IsCardinalLocallyPresentable.iff_exists_isStrongGenerator · cited by 1IsCardinalLocallyPresenta…CategoryTheory.ObjectProperty.IsCardinalFilteredGenerator.isPresentable_eq_retractClosure · cited by 1IsCardinalFilteredGenerat…CategoryTheory.isCardinalFilteredGenerator_isCardinalPresentable · cited by 1CategoryTheory.isCardinal…CategoryTheory.ObjectProperty.IsCardinalFilteredGenerator.isoClosure · cited by 1IsCardinalFilteredGenerat…CategoryTheory.isCardinalPresentable_monotone · cited by 1CategoryTheory.isCardinal…CategoryTheory.isClosedUnderColimitsOfShape_isCardinalPresentable · cited by 1CategoryTheory.isClosedUn…CategoryTheory.isCardinalPresentable.congr_simp · cited by 0isCardinalPresentable.con…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryFact · cited by 2726FactCardinal · cited by 2598CardinalCategoryTheory.ObjectProperty · cited by 798CategoryTheory.ObjectProp…Cardinal.IsRegular · cited by 282Cardinal.IsRegularCategoryTheory.IsCardinalPresentable · cited by 39CategoryTheory.IsCardinal…CategoryTheory.isCardinalPres…CITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by22

Results whose statement or proof uses this declaration.