Theorems · Definition · category theory

CategoryTheory.Localization.SmallShiftedHom.comp

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {W : CategoryTheory.MorphismProperty C} →
      {M : Type w'} →
        [inst_1 : AddMonoid M] →
          [inst_2 : CategoryTheory.HasShift C M] →
            [W.IsCompatibleWithShift M] →
              {X Y Z : C} →
                {a b c : M} →
                  [inst_4 : CategoryTheory.Localization.HasSmallLocalizedShiftedHom W M X Y] →
                    [inst_5 : CategoryTheory.Localization.HasSmallLocalizedShiftedHom W M Y Z] →
                      [inst_6 : CategoryTheory.Localization.HasSmallLocalizedShiftedHom W M X Z] →
                        [CategoryTheory.Localization.HasSmallLocalizedShiftedHom W M Z Z] →
                          CategoryTheory.Localization.SmallShiftedHom W X Y a →
                            CategoryTheory.Localization.SmallShiftedHom W Y Z b →
                              b + a = c → CategoryTheory.Localization.SmallShiftedHom W X Z c

The composition on SmallShiftedHom W.

Defined in

Mathlib.CategoryTheory.Localization.SmallShiftedHom

Cited by

12 results in Mathlib

Foundations

Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryAddMonoidCategoryTheory.HasShiftCategoryTheory.MorphismProperty.IsCompatibleWithShiftCategoryTheory.Localization.HasSmallLocalizedShiftedHomCategoryTheory.Localization.HasSmallLocalizedShiftedHomCategoryTheory.Localization.HasSmallLocalizedShiftedHomCategoryTheory.Localization.HasSmallLocalizedShiftedHom