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Theorems · Definition · category theory

CategoryTheory.CardinalDirectedPoset

(κ : Cardinal.{u}) → [Fact κ.IsRegular] → Type (u + 1)

The category of κ-filtered partially ordered types, with morphisms given by order embeddings.

Defined in
Mathlib.CategoryTheory.Presentable.CardinalDirectedPoset
Cited by
24 results in Mathlib
Foundations
Depth 22 from the axioms · uses propext, Quot.sound
Assumes
Fact

Around this declaration

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

CategoryTheory.CardinalDirectedPoset.functorOfPredicateSet · cited by 6CardinalDirectedPoset.fun…CategoryTheory.CardinalDirectedPoset.PropSetWithTop · cited by 5CardinalDirectedPoset.Pro…CategoryTheory.CardinalDirectedPoset.withTop · cited by 5CardinalDirectedPoset.wit…CategoryTheory.CardinalDirectedPoset.PropSet · cited by 3CardinalDirectedPoset.Pro…CategoryTheory.CardinalDirectedPoset.isCardinalPresentable_iff · cited by 3CardinalDirectedPoset.isC…CategoryTheory.CardinalDirectedPoset.coconeOfPredicateSet · cited by 2CardinalDirectedPoset.coc…CategoryTheory.CardinalDirectedPoset.Hom.injective · cited by 2Hom.injectiveCategoryTheory.CardinalDirectedPoset.Hom.le_iff_le · cited by 2Hom.le_iff_leCategoryTheory.CardinalDirectedPoset.isCardinalPresentable_iff' · cited by 2CardinalDirectedPoset.isC…CategoryTheory.CardinalDirectedPoset.isCardinalPresentable_of_hasCardinalLT_of_le · cited by 2CardinalDirectedPoset.isC…CategoryTheory.CardinalDirectedPoset.propSetWithTop_pair · cited by 2CardinalDirectedPoset.pro…CategoryTheory.CardinalDirectedPoset.coconeWithTop · cited by 1CardinalDirectedPoset.coc…CategoryTheory.CardinalDirectedPoset.exists_mem_propSetWithTop · cited by 1CardinalDirectedPoset.exi…CategoryTheory.CardinalDirectedPoset.hasCardinalLTWithTerminal · cited by 1CardinalDirectedPoset.has…CategoryTheory.CardinalDirectedPoset.isColimitCocone · cited by 1CardinalDirectedPoset.isC…Fact · cited by 2726FactCardinal · cited by 2598CardinalCategoryTheory.ObjectProperty.FullSubcategory · cited by 726ObjectProperty.FullSubcat…Cardinal.IsRegular · cited by 282Cardinal.IsRegularPartOrdEmb.isCardinalFiltered · cited by 25PartOrdEmb.isCardinalFilt…CategoryTheory.CardinalDirect…CITED BYCITES

Cites5

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

Cited by54

Results whose statement or proof uses this declaration.