Theorems · Inductive type · category theory
CategoryTheory.MorphismProperty.LeftFraction
{C : Type u_1} →
[inst : CategoryTheory.Category.{v_1, u_1} C] → CategoryTheory.MorphismProperty C → C → C → Type (max u_1 v_1)A left fraction from X : C to Y : C for W : MorphismProperty C consists of the
datum of an object Y' : C and maps f : X ⟶ Y' and s : Y ⟶ Y' such that W s.
- Cited by
- 67 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 by103
Results whose statement or proof uses this declaration.
- CategoryTheory.MorphismProperty.LeftFraction.Y'statement and proof · cited by 57
- CategoryTheory.MorphismProperty.LeftFraction.fstatement and proof · cited by 52
- CategoryTheory.MorphismProperty.LeftFraction.sstatement and proof · cited by 51
- CategoryTheory.MorphismProperty.LeftFraction.mapstatement and proof · cited by 43
- CategoryTheory.MorphismProperty.LeftFraction.hsstatement and proof · cited by 20
- CategoryTheory.MorphismProperty.LeftFractionRelstatement and proof · cited by 18
- CategoryTheory.MorphismProperty.LeftFraction.map_comp_map_sstatement and proof · cited by 16
- CategoryTheory.Localization.exists_leftFractionstatement and proof · cited by 14
- CategoryTheory.MorphismProperty.LeftFraction₂.sndstatement · cited by 14
- CategoryTheory.MorphismProperty.LeftFraction₂.fststatement · cited by 12
- CategoryTheory.MorphismProperty.LeftFraction₂.addstatement · cited by 10
- CategoryTheory.MorphismProperty.LeftFraction.Localization.Hom.mkstatement and proof · cited by 10