Theorems · Definition · category theory

CategoryTheory.Functor.mapTriangulatedSpectralObject

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroObject C] →
      [inst_2 : CategoryTheory.HasShift C ℤ] →
        [inst_3 : CategoryTheory.Preadditive C] →
          [inst_4 : ∀ (n : ℤ), (CategoryTheory.shiftFunctor C n).Additive] →
            [inst_5 : CategoryTheory.Pretriangulated C] →
              {D : Type u_3} →
                [inst_6 : CategoryTheory.Category.{v_3, u_3} D] →
                  [inst_7 : CategoryTheory.Limits.HasZeroObject D] →
                    [inst_8 : CategoryTheory.HasShift D ℤ] →
                      [inst_9 : CategoryTheory.Preadditive D] →
                        [inst_10 : ∀ (n : ℤ), (CategoryTheory.shiftFunctor D n).Additive] →
                          [inst_11 : CategoryTheory.Pretriangulated D] →
                            (F : CategoryTheory.Functor C D) →
                              [inst_12 : F.CommShift ℤ] →
                                [F.IsTriangulated] →
                                  (ι : Type u_4) →
                                    [inst_14 : CategoryTheory.Category.{v_4, u_4} ι] →
                                      CategoryTheory.Functor (CategoryTheory.Triangulated.SpectralObject C ι)
                                        (CategoryTheory.Triangulated.SpectralObject D ι)

The functor between categories of spectral objects that is induced by a triangulated functor.

Defined in

Mathlib.CategoryTheory.Triangulated.SpectralObject

Cited by

0 results in Mathlib

Foundations

Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroObjectCategoryTheory.HasShiftCategoryTheory.PreadditiveCategoryTheory.Functor.AdditiveCategoryTheory.PretriangulatedCategoryTheory.CategoryCategoryTheory.Limits.HasZeroObjectCategoryTheory.HasShiftCategoryTheory.PreadditiveCategoryTheory.Functor.AdditiveCategoryTheory.PretriangulatedCategoryTheory.Functor.CommShiftCategoryTheory.Functor.IsTriangulatedCategoryTheory.Category