Theorems · Definition · category theory

CategoryTheory.Localization.SmallHom.shift

{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 : C} →
                [inst_4 : CategoryTheory.Localization.HasSmallLocalizedHom W X Y] →
                  CategoryTheory.Localization.SmallHom W X Y →
                    (a : M) →
                      [inst_5 :
                          CategoryTheory.Localization.HasSmallLocalizedHom W ((CategoryTheory.shiftFunctor C a).obj X)
                            ((CategoryTheory.shiftFunctor C a).obj Y)] →
                        CategoryTheory.Localization.SmallHom W ((CategoryTheory.shiftFunctor C a).obj X)
                          ((CategoryTheory.shiftFunctor C a).obj Y)

Given f : SmallHom W X Y and a : M, this is the element in SmallHom W (X⟦a⟧) (Y⟦a⟧) obtained by shifting by a.

Defined in

Mathlib.CategoryTheory.Localization.SmallShiftedHom

Cited by

3 results in Mathlib

Foundations

Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryAddMonoidCategoryTheory.HasShiftCategoryTheory.MorphismProperty.IsCompatibleWithShiftCategoryTheory.Localization.HasSmallLocalizedHomCategoryTheory.Localization.HasSmallLocalizedHom