Theorems · Inductive type · category theory
CategoryTheory.MorphismProperty.RespectsLeft
{C : Type u} →
[inst : CategoryTheory.CategoryStruct.{v, u} C] →
CategoryTheory.MorphismProperty C → CategoryTheory.MorphismProperty C → PropA morphism property P satisfies P.RespectsLeft Q if it is stable under
pre-composition with morphisms satisfying Q, i.e. whenever P holds for f
and Q holds for i then P holds for i ≫ f.
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 3 from the axioms · uses no axioms
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.MorphismPropertystatement · cited by 2,179
- CategoryTheory.CategoryStructstatement · cited by 343
Cited by10
Results whose statement or proof uses this declaration.
- CategoryTheory.MorphismProperty.RespectsLeft.precompstatement and proof · cited by 5
- CategoryTheory.MorphismProperty.precomp_iffstatement and proof · cited by 5
- CategoryTheory.MorphismProperty.RespectsLeft.sInfstatement and proof · cited by 1
- AlgebraicGeometry.QuasiCompactCover.exists_homstatement and proof · cited by 1
- CategoryTheory.MorphismProperty.RespectsIso.sInfproof · cited by 0
- CategoryTheory.MorphismProperty.RespectsLeft.casesOnstatement and proof · cited by 0
- CategoryTheory.MorphismProperty.RespectsLeft.recOnstatement and proof · cited by 0
- CategoryTheory.MorphismProperty.sourceLocalClosure.sourceLocalClosure_iff_of_respectsLeftstatement and proof · cited by 0
- CategoryTheory.MorphismProperty.Respects.casesOnstatement and proof · cited by 0
- CategoryTheory.MorphismProperty.Respects.recOnstatement and proof · cited by 0