Mathlib Map

Theorems · Theorem · category theory

CategoryTheory.isFiltered_of_isCardinalFiltered

∀ (J : Type u) [inst : CategoryTheory.Category.{v, u} J] (κ : Cardinal.{w}) [hκ : Fact κ.IsRegular]
  [CategoryTheory.IsCardinalFiltered J κ], CategoryTheory.IsFiltered J
Defined in
Mathlib.CategoryTheory.Presentable.IsCardinalFiltered
Cited by
18 results in Mathlib
Foundations
Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryFactCategoryTheory.IsCardinalFiltered

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CategoryTheory.IsGrothendieckAbelian.exists_isIso_of_functor_from_monoOver · cited by 2IsGrothendieckAbelian.exi…CategoryTheory.CardinalDirectedPoset.isCardinalPresentable_of_hasCardinalLT_of_le · cited by 2CardinalDirectedPoset.isC…CategoryTheory.IsCardinalPresentable.exists_eq_of_isColimit' · cited by 2IsCardinalPresentable.exi…HasCardinalLT.isCardinalPresentable · cited by 1HasCardinalLT.isCardinalP…CategoryTheory.IsCardinalFiltered.exists_cardinal_directed · cited by 1IsCardinalFiltered.exists…CategoryTheory.IsGrothendieckAbelian.IsPresentable.injectivity₀ · cited by 1IsPresentable.injectivity₀CategoryTheory.IsGrothendieckAbelian.IsPresentable.surjectivity · cited by 1IsPresentable.surjectivityCategoryTheory.IsCardinalFiltered.exists_cardinal_directed.final_functor · cited by 1exists_cardinal_directed.…CategoryTheory.isCardinalFiltered_aleph0_iff · cited by 1CategoryTheory.isCardinal…CategoryTheory.IsCardinalPresentable.exists_eq_of_isColimit · cited by 1IsCardinalPresentable.exi…CategoryTheory.Functor.Accessible.Limits.isColimitMapCocone · cited by 1Limits.isColimitMapCoconeCategoryTheory.IsCardinalFiltered.multicoequalizer · cited by 0IsCardinalFiltered.multic…CategoryTheory.IsCardinalFiltered.nonempty · cited by 0IsCardinalFiltered.nonemp…CategoryTheory.IsCardinalFiltered.of_final · cited by 0IsCardinalFiltered.of_fin…CategoryTheory.Retract.isCardinalPresentable · cited by 0Retract.isCardinalPresent…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorFact · cited by 2726FactCardinal · cited by 2598CardinalCategoryTheory.Arrow · cited by 713CategoryTheory.ArrowCategoryTheory.SmallCategory · cited by 480CategoryTheory.SmallCateg…Fact.out · cited by 328Fact.outCardinal.IsRegular · cited by 282Cardinal.IsRegularCategoryTheory.IsFiltered · cited by 210CategoryTheory.IsFilteredCategoryTheory.FinCategory · cited by 107CategoryTheory.FinCategoryHasCardinalLT · cited by 99HasCardinalLTCategoryTheory.IsCardinalFiltered · cited by 69CategoryTheory.IsCardinal…Cardinal.IsRegular.aleph0_le · cited by 22IsRegular.aleph0_leCategoryTheory.IsCardinalFiltered.cocone · cited by 5IsCardinalFiltered.coconeHasCardinalLT.of_le · cited by 5HasCardinalLT.of_leCategoryTheory.isFiltered_of_…CITED BYCITES

Cites16

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

Cited by19

Results whose statement or proof uses this declaration.