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Theorems · Definition · category theory

CategoryTheory.MorphismProperty.HasCardinalLT

{C : Type u} → [inst : CategoryTheory.Category.{v, u} C] → CategoryTheory.MorphismProperty C → Cardinal.{w} → Prop

The property that the subtype of arrows satisfying a property P : MorphismProperty C is of cardinality < κ.

Defined in
Mathlib.CategoryTheory.MorphismProperty.HasCardinalLT
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.

CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.Diagram.ext · cited by 2Diagram.extCategoryTheory.IsCardinalFiltered.exists_cardinal_directed.Diagram.mk.inj · cited by 1mk.injCategoryTheory.IsCardinalFiltered.exists_cardinal_directed.Diagram.mk.noConfusion · cited by 1mk.noConfusionCategoryTheory.IsCardinalFiltered.exists_cardinal_directed.Diagram.casesOn · cited by 0Diagram.casesOnCategoryTheory.MorphismProperty.hasCardinalLT_ofHoms · cited by 0MorphismProperty.hasCardi…CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.Diagram.hW · cited by 0Diagram.hWCategoryTheory.IsCardinalFiltered.exists_cardinal_directed.Diagram.noConfusion · cited by 0Diagram.noConfusionCategoryTheory.IsCardinalFiltered.exists_cardinal_directed.Diagram.noConfusionType · cited by 0Diagram.noConfusionTypeCategoryTheory.IsCardinalFiltered.exists_cardinal_directed.Diagram.recOn · cited by 0Diagram.recOnCategoryTheory.IsCardinalFiltered.exists_cardinal_directed.Diagram.mk.injEq · cited by 0mk.injEqCategoryTheory.IsCardinalFiltered.exists_cardinal_directed.Diagram.mk.sizeOf_spec · cited by 0mk.sizeOf_specCategoryTheory.MorphismProperty.HasCardinalLT.iSup · cited by 0HasCardinalLT.iSupCategoryTheory.MorphismProperty.HasCardinalLT.sup · cited by 0HasCardinalLT.supCategoryTheory.Category · cited by 32673CategoryTheory.CategorySet.Elem · cited by 7166Set.ElemCardinal · cited by 2598CardinalCategoryTheory.MorphismProperty · cited by 2179CategoryTheory.MorphismPr…HasCardinalLT · cited by 99HasCardinalLTCategoryTheory.MorphismProperty.toSet · cited by 26MorphismProperty.toSetMorphismProperty.HasCardinalLTCITED BYCITES

Cites6

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

Cited by13

Results whose statement or proof uses this declaration.