Theorems · Theorem · category theory
CategoryTheory.MorphismProperty.precomp_iff
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (W : CategoryTheory.MorphismProperty C)
{W' : CategoryTheory.MorphismProperty C} [W.RespectsLeft W'] [W.HasOfPrecompProperty W'] {X Y Z : C} (f : X ⟶ Y)
(g : Y ⟶ Z), W' f → (W (CategoryTheory.CategoryStruct.comp f g) ↔ W g)- Cited by
- 5 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement · cited by 17,999
- CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
- CategoryTheory.MorphismProperty.RespectsLeftstatement and proof · cited by 6
- CategoryTheory.MorphismProperty.HasOfPrecompPropertystatement and proof · cited by 6
- CategoryTheory.MorphismProperty.RespectsLeft.precompproof · cited by 5
- CategoryTheory.MorphismProperty.of_precompproof · cited by 5
Cited by5
Results whose statement or proof uses this declaration.
- CategoryTheory.ObjectProperty.isLocal_iff_isIso_mapproof · cited by 2
- CategoryTheory.ObjectProperty.localEpi_mem_range_iff_epiproof · cited by 1
- CategoryTheory.ObjectProperty.isColocal_iff_isIso_mapproof · cited by 1