Theorems · Definition · category theory

CategoryTheory.Triangulated.SpectralObject.mapTriangulatedFunctor

{C : Type u_1} →
  {ι : Type u_2} →
    [inst : CategoryTheory.Category.{v_1, u_1} C] →
      [inst_1 : CategoryTheory.Category.{v_2, u_2} ι] →
        [inst_2 : CategoryTheory.Limits.HasZeroObject C] →
          [inst_3 : CategoryTheory.HasShift C ℤ] →
            [inst_4 : CategoryTheory.Preadditive C] →
              [inst_5 : ∀ (n : ℤ), (CategoryTheory.shiftFunctor C n).Additive] →
                [inst_6 : CategoryTheory.Pretriangulated C] →
                  {D : Type u_3} →
                    [inst_7 : CategoryTheory.Category.{v_3, u_3} D] →
                      [inst_8 : CategoryTheory.Limits.HasZeroObject D] →
                        [inst_9 : CategoryTheory.HasShift D ℤ] →
                          [inst_10 : CategoryTheory.Preadditive D] →
                            [inst_11 : ∀ (n : ℤ), (CategoryTheory.shiftFunctor D n).Additive] →
                              [inst_12 : CategoryTheory.Pretriangulated D] →
                                CategoryTheory.Triangulated.SpectralObject C ι →
                                  (F : CategoryTheory.Functor C D) →
                                    [inst_13 : F.CommShift ℤ] →
                                      [F.IsTriangulated] → CategoryTheory.Triangulated.SpectralObject D ι

The image of a spectral by a triangulated functor.

Defined in

Mathlib.CategoryTheory.Triangulated.SpectralObject

Cited by

3 results in Mathlib

Foundations

Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasZeroObjectCategoryTheory.HasShiftCategoryTheory.PreadditiveCategoryTheory.Functor.AdditiveCategoryTheory.PretriangulatedCategoryTheory.CategoryCategoryTheory.Limits.HasZeroObjectCategoryTheory.HasShiftCategoryTheory.PreadditiveCategoryTheory.Functor.AdditiveCategoryTheory.PretriangulatedCategoryTheory.Functor.CommShiftCategoryTheory.Functor.IsTriangulated