Theorems · Definition · category theory
CategoryTheory.MorphismProperty.IsStableUnderInfiniteComposition
{C : Type u} → [inst : CategoryTheory.Category.{v, u} C] → CategoryTheory.MorphismProperty C → PropA class of morphisms W : MorphismProperty C is stable under infinite composition
if for any functor F : ℕ ⥤ C such that F.obj n ⟶ F.obj (n + 1) is in W for any n : ℕ,
the map F.obj 0 ⟶ c.pt is in W for any colimit cocone c : Cocone F.
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- Foundations
- Depth 22 from the axioms · uses propext
- Assumes
- CategoryTheory.Category
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- CategoryTheory.Categorystatement and proof · cited by 32,673
- CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
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