Theorems · Definition · category theory

CategoryTheory.Functor.IsHomological.casesOn

{C : Type u_1} →
  {A : Type u_3} →
    [inst : CategoryTheory.Category.{v_1, u_1} C] →
      [inst_1 : CategoryTheory.HasShift C ℤ] →
        [inst_2 : CategoryTheory.Category.{v_3, u_3} A] →
          {F : CategoryTheory.Functor C A} →
            [inst_3 : CategoryTheory.Limits.HasZeroObject C] →
              [inst_4 : CategoryTheory.Preadditive C] →
                [inst_5 : ∀ (n : ℤ), (CategoryTheory.shiftFunctor C n).Additive] →
                  [inst_6 : CategoryTheory.Pretriangulated C] →
                    [inst_7 : CategoryTheory.Abelian A] →
                      {motive : F.IsHomological → Sort u} →
                        (t : F.IsHomological) →
                          ([toPreservesZeroMorphisms : F.PreservesZeroMorphisms] →
                              (exact :
                                  ∀ (T : CategoryTheory.Pretriangulated.Triangle C)
                                    (hT : T ∈ CategoryTheory.Pretriangulated.distinguishedTriangles),
                                    ((CategoryTheory.Pretriangulated.shortComplexOfDistTriangle T hT).map F).Exact) →
                                motive ⋯) →
                            motive t

Defined in

Mathlib.CategoryTheory.Triangulated.HomologicalFunctor

Cited by

0 results in Mathlib

Foundations

Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.HasShiftCategoryTheory.CategoryCategoryTheory.Limits.HasZeroObjectCategoryTheory.PreadditiveCategoryTheory.Functor.AdditiveCategoryTheory.PretriangulatedCategoryTheory.Abelian