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Theorems · Inductive type · category theory

CategoryTheory.MorphismProperty.HasLeftCalculusOfFractions

{C : Type u_1} → [inst : CategoryTheory.Category.{v_1, u_1} C] → CategoryTheory.MorphismProperty C → Prop

A multiplicative morphism property W has left calculus of fractions if any right fraction can be turned into a left fraction and that two morphisms that can be equalized by precomposition with a morphism in W can also be equalized by postcomposition with a morphism in W.

Defined in
Mathlib.CategoryTheory.Localization.CalculusOfFractions
Cited by
71 results in Mathlib
Foundations
Depth 3 from the axioms · uses no axioms
Assumes
CategoryTheory.Category
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CategoryTheory.MorphismProperty.LeftFraction.Localization.Q · cited by 21Localization.QCategoryTheory.Localization.exists_leftFraction · cited by 14Localization.exists_leftF…CategoryTheory.Localization.Preadditive.add' · cited by 14Preadditive.add'CategoryTheory.MorphismProperty.LeftFraction.Localization.homMk · cited by 9Localization.homMkCategoryTheory.MorphismProperty.LeftFraction.Localization.Qinv · cited by 9Localization.QinvCategoryTheory.Localization.exists_leftFraction₂ · cited by 7Localization.exists_leftF…CategoryTheory.MorphismProperty.RightFraction.exists_leftFraction · cited by 7RightFraction.exists_left…CategoryTheory.Localization.Preadditive.add · cited by 7Preadditive.addCategoryTheory.Localization.Preadditive.add'_eq · cited by 7Preadditive.add'_eqCategoryTheory.MorphismProperty.LeftFraction.comp₀ · cited by 5LeftFraction.comp₀CategoryTheory.Localization.essSurj_mapArrow · cited by 4Localization.essSurj_mapA…CategoryTheory.MorphismProperty.LeftFraction.map_eq_iff · cited by 4LeftFraction.map_eq_iffCategoryTheory.MorphismProperty.LeftFraction.Localization.Qiso · cited by 4Localization.QisoCategoryTheory.MorphismProperty.HasLeftCalculusOfFractions.exists_leftFraction · cited by 3HasLeftCalculusOfFraction…CategoryTheory.MorphismProperty.HasLeftCalculusOfFractions.ext · cited by 3HasLeftCalculusOfFraction…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.MorphismProperty · cited by 2179CategoryTheory.MorphismPr…MorphismProperty.HasLeftCalcu…CITED BYCITES

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