Theorems · Inductive type · category theory
CategoryTheory.MorphismProperty.IsStableUnderTransfiniteComposition
{C : Type u} → [inst : CategoryTheory.Category.{v, u} C] → CategoryTheory.MorphismProperty C → PropA class of morphisms W : MorphismProperty C is stable under transfinite composition
if it is multiplicative and stable under transfinite composition of any shape
(in a certain universe).
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 3 from the axioms · uses no axioms
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement · cited by 32,673
- CategoryTheory.MorphismPropertystatement · cited by 2,179
Cited by8
Results whose statement or proof uses this declaration.
- CategoryTheory.MorphismProperty.transfiniteCompositions_lestatement and proof · cited by 1
- CategoryTheory.MorphismProperty.IsStableUnderTransfiniteComposition.shrinkstatement and proof · cited by 1
- CategoryTheory.MorphismProperty.transfiniteCompositions_le_iffstatement and proof · cited by 0
- CategoryTheory.MorphismProperty.IsStableUnderTransfiniteComposition.casesOnstatement and proof · cited by 0
- CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.mem_incl_appstatement and proof · cited by 0
- CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.mem_mapstatement and proof · cited by 0
- CategoryTheory.MorphismProperty.IsStableUnderTransfiniteComposition.recOnstatement and proof · cited by 0
- CategoryTheory.MorphismProperty.IsStableUnderTransfiniteComposition.shrink₀statement and proof · cited by 0