Theorems · Definition · category theory
CategoryTheory.MorphismProperty.LeftFraction.f
{C : Type u_1} →
[inst : CategoryTheory.Category.{v_1, u_1} C] →
{W : CategoryTheory.MorphismProperty C} → {X Y : C} → (self : W.LeftFraction X Y) → X ⟶ self.Y'the numerator of a left fraction
- Cited by
- 52 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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.MorphismPropertystatement and proof · cited by 2,179
- CategoryTheory.MorphismProperty.LeftFractionstatement and proof · cited by 67
- CategoryTheory.MorphismProperty.LeftFraction.Y'statement · cited by 57
Cited by63
Results whose statement or proof uses this declaration.
- CategoryTheory.MorphismProperty.LeftFraction.mapproof · cited by 43
- CategoryTheory.MorphismProperty.LeftFractionRelproof · cited by 18
- CategoryTheory.MorphismProperty.LeftFraction.map_comp_map_sstatement and proof · cited by 16
- CategoryTheory.MorphismProperty.RightFraction.exists_leftFractionstatement · cited by 7
- CategoryTheory.Localization.exists_leftFraction₂proof · cited by 7
- CategoryTheory.Localization.Preadditive.add'_eqproof · cited by 7
- CategoryTheory.MorphismProperty.LeftFraction.map_comp_map_s_assocstatement and proof · cited by 6
- CategoryTheory.MorphismProperty.LeftFraction.opproof · cited by 6
- CategoryTheory.MorphismProperty.LeftFraction.comp₀proof · cited by 5
- CategoryTheory.MorphismProperty.LeftFraction.unopproof · cited by 5
- CategoryTheory.Localization.essSurj_mapArrowproof · cited by 4
- CategoryTheory.MorphismProperty.LeftFractionRel.unopproof · cited by 4