Theorems · Definition · category theory
CategoryTheory.CardinalDirectedPoset.isColimitCocone
{κ : Cardinal.{u}} →
[inst : Fact κ.IsRegular] → (J : CategoryTheory.CardinalDirectedPoset κ) → CategoryTheory.Limits.IsColimit J.coconeAny object J : CardinalDirectedPoset κ is a colimit
of its subsets that are of cardinality < κ and have a terminal object.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Fact
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Factstatement and proof · cited by 2,726
- Cardinalstatement and proof · cited by 2,598
- CategoryTheory.ObjectProperty.FullSubcategory.objstatement · cited by 1,316
- CategoryTheory.Limits.IsColimitstatement · cited by 773
- Cardinal.IsRegularstatement and proof · cited by 282
- PartOrdEmbstatement · cited by 68
- PartOrdEmb.carrierstatement · cited by 61
- PartOrdEmb.isCardinalFilteredstatement · cited by 25
- CategoryTheory.CardinalDirectedPosetstatement and proof · cited by 24
- CategoryTheory.CardinalDirectedPoset.functorOfPredicateSetstatement · cited by 6
- CategoryTheory.CardinalDirectedPoset.PropSetstatement and proof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- CategoryTheory.CardinalFilteredPoset.isColimitCoconeproof · cited by 0