Theorems · Inductive type · category theory
CategoryTheory.MorphismProperty.IsStableUnderComposition
{C : Type u} → [inst : CategoryTheory.Category.{v, u} C] → CategoryTheory.MorphismProperty C → PropA morphism property satisfies IsStableUnderComposition if the composition of
two such morphisms still falls in the class.
- Cited by
- 84 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 by107
Results whose statement or proof uses this declaration.
- CategoryTheory.MorphismProperty.comp_memstatement and proof · cited by 48
- CategoryTheory.MorphismProperty.Over.mapstatement and proof · cited by 26
- CategoryTheory.MorphismProperty.Under.mapstatement and proof · cited by 11
- CategoryTheory.MorphismProperty.Over.mapPullbackAdjstatement and proof · cited by 5
- AlgebraicGeometry.Scheme.smallPretopologystatement and proof · cited by 5
- AlgebraicGeometry.Scheme.Cover.pushforwardIsostatement and proof · cited by 4
- CategoryTheory.MorphismProperty.Over.mapCompstatement and proof · cited by 4
- CategoryTheory.MorphismProperty.Over.mapIdstatement and proof · cited by 4
- CategoryTheory.Span.compstatement and proof · cited by 4
- AlgebraicGeometry.Scheme.Cover.pullbackCoverOverPropstatement and proof · cited by 3
- AlgebraicGeometry.Scheme.Cover.pullbackCoverOverProp'statement and proof · cited by 3
- HomotopicalAlgebra.isCofibrant_of_cofibrationstatement and proof · cited by 3