Theorems · Definition · category theory

CategoryTheory.MorphismProperty.LeftFraction.ofInv

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    {W : CategoryTheory.MorphismProperty C} → {X Y : C} → (s : Y ⟶ X) → W s → W.LeftFraction X Y

The left fraction from X to Y given by a morphism s : Y ⟶ X such that W s.

Defined in: Mathlib.CategoryTheory.Localization.CalculusOfFractions
Cited by: 9 results in Mathlib
Foundations: Depth 5 from the axioms · uses no axioms
Assumes: CategoryTheory.Category

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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 and proof · cited by 32,603
CategoryTheory.CategoryStruct.idproof · cited by 6,235
CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
CategoryTheory.MorphismProperty.LeftFractionstatement · cited by 67

Cited by10

Results whose statement or proof uses this declaration.

CategoryTheory.MorphismProperty.LeftFraction.Localization.Qinvproof · cited by 9
CategoryTheory.MorphismProperty.LeftFraction.Localization.Q_map_comp_Qinvproof · cited by 2
CategoryTheory.MorphismProperty.LeftFraction.map_hom_ofInv_idstatement · cited by 1
CategoryTheory.MorphismProperty.LeftFraction.map_ofInv_hom_idstatement · cited by 1
CategoryTheory.MorphismProperty.LeftFraction.map_hom_ofInv_id_assocstatement and proof · cited by 0
CategoryTheory.MorphismProperty.LeftFraction.map_ofInv_hom_id_assocstatement and proof · cited by 0
CategoryTheory.MorphismProperty.LeftFraction.ofInv_Y'statement and proof · cited by 0
CategoryTheory.MorphismProperty.LeftFraction.ofInv_fstatement and proof · cited by 0
CategoryTheory.MorphismProperty.LeftFraction.ofInv_sstatement and proof · cited by 0
CategoryTheory.MorphismProperty.LeftFraction.ofInv.congr_simpstatement and proof · cited by 0