Theorems · Definition · category theory
CategoryTheory.MorphismProperty.HasCardinalLT
{C : Type u} → [inst : CategoryTheory.Category.{v, u} C] → CategoryTheory.MorphismProperty C → Cardinal.{w} → PropThe property that the subtype of arrows satisfying a property P : MorphismProperty C
is of cardinality < κ.
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
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
- Set.Elemproof · cited by 7,166
- Cardinalstatement and proof · cited by 2,598
- CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
- HasCardinalLTproof · cited by 99
- CategoryTheory.MorphismProperty.toSetproof · cited by 26
Cited by13
Results whose statement or proof uses this declaration.
- CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.Diagram.extproof · cited by 2
- CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.Diagram.mk.injstatement and proof · cited by 1
- CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.Diagram.mk.noConfusionstatement and proof · cited by 1
- CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.Diagram.casesOnstatement and proof · cited by 0
- CategoryTheory.MorphismProperty.hasCardinalLT_ofHomsstatement · cited by 0
- CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.Diagram.hWstatement · cited by 0
- CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.Diagram.recOnstatement and proof · cited by 0
- CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.Diagram.mk.injEqstatement and proof · cited by 0
- CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.Diagram.mk.sizeOf_specstatement and proof · cited by 0
- CategoryTheory.MorphismProperty.HasCardinalLT.iSupstatement and proof · cited by 0