Theorems · Definition · category theory

CategoryTheory.Localization.SmallHom.comp

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {W : CategoryTheory.MorphismProperty C} →
      {X Y Z : C} →
        [inst_1 : CategoryTheory.Localization.HasSmallLocalizedHom W X Y] →
          [inst_2 : CategoryTheory.Localization.HasSmallLocalizedHom W Y Z] →
            [inst_3 : CategoryTheory.Localization.HasSmallLocalizedHom W X Z] →
              CategoryTheory.Localization.SmallHom W X Y →
                CategoryTheory.Localization.SmallHom W Y Z → CategoryTheory.Localization.SmallHom W X Z

The composition on SmallHom W.

Defined in

Mathlib.CategoryTheory.Localization.SmallHom

Cited by

11 results in Mathlib

Foundations

Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Localization.HasSmallLocalizedHomCategoryTheory.Localization.HasSmallLocalizedHomCategoryTheory.Localization.HasSmallLocalizedHom