Theorems · Theorem · category theory
CategoryTheory.MorphismProperty.HasLeftCalculusOfFractions.exists_leftFraction
∀ {C : Type u_1} {inst : CategoryTheory.Category.{v_1, u_1} C} {W : CategoryTheory.MorphismProperty C}
[self : W.HasLeftCalculusOfFractions] ⦃X Y : C⦄ (φ : W.RightFraction X Y),
∃ ψ, CategoryTheory.CategoryStruct.comp φ.f ψ.s = CategoryTheory.CategoryStruct.comp φ.s ψ.f- Cited by
- 3 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.
Cites13
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 · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement · cited by 17,999
- CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
- CategoryTheory.MorphismProperty.HasLeftCalculusOfFractionsstatement and proof · cited by 71
- CategoryTheory.MorphismProperty.LeftFractionstatement · cited by 67
- CategoryTheory.MorphismProperty.LeftFraction.Y'statement · cited by 57
- CategoryTheory.MorphismProperty.LeftFraction.fstatement · cited by 52
- CategoryTheory.MorphismProperty.LeftFraction.sstatement · cited by 51
- CategoryTheory.MorphismProperty.RightFraction.sstatement · cited by 38
- CategoryTheory.MorphismProperty.RightFractionstatement · cited by 37
- CategoryTheory.MorphismProperty.RightFraction.fstatement · cited by 36
Cited by3
Results whose statement or proof uses this declaration.
- CategoryTheory.MorphismProperty.RightFraction.exists_leftFractionproof · cited by 7
- CategoryTheory.MorphismProperty.LeftFractionRel.transproof · cited by 2
- CategoryTheory.MorphismProperty.LeftFraction.comp₀_relproof · cited by 1