Theorems · Definition · category theory

CategoryTheory.Adjunction.IsTriangulated.casesOn

{C : Type u_1} →
  {D : Type u_2} →
    [inst : CategoryTheory.Category.{v_1, u_1} C] →
      [inst_1 : CategoryTheory.Category.{v_2, u_2} D] →
        [inst_2 : CategoryTheory.Limits.HasZeroObject C] →
          [inst_3 : CategoryTheory.Limits.HasZeroObject D] →
            [inst_4 : CategoryTheory.Preadditive C] →
              [inst_5 : CategoryTheory.Preadditive D] →
                [inst_6 : CategoryTheory.HasShift C ℤ] →
                  [inst_7 : CategoryTheory.HasShift D ℤ] →
                    [inst_8 : ∀ (n : ℤ), (CategoryTheory.shiftFunctor C n).Additive] →
                      [inst_9 : ∀ (n : ℤ), (CategoryTheory.shiftFunctor D n).Additive] →
                        [inst_10 : CategoryTheory.Pretriangulated C] →
                          [inst_11 : CategoryTheory.Pretriangulated D] →
                            {F : CategoryTheory.Functor C D} →
                              {G : CategoryTheory.Functor D C} →
                                {adj : F ⊣ G} →
                                  [inst_12 : F.CommShift ℤ] →
                                    [inst_13 : G.CommShift ℤ] →
                                      {motive : adj.IsTriangulated → Sort u} →
                                        (t : adj.IsTriangulated) →
                                          ((commShift : adj.CommShift ℤ) →
                                              (leftAdjoint_isTriangulated : F.IsTriangulated) →
                                                (rightAdjoint_isTriangulated : G.IsTriangulated) → motive ⋯) →
                                            motive t

Defined in

Mathlib.CategoryTheory.Triangulated.Adjunction

Cited by

0 results in Mathlib

Foundations

Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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