Theorems · Definition · category theory

CategoryTheory.Triangulated.TStructure.IsGE.casesOn

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Preadditive C] →
      [inst_2 : CategoryTheory.Limits.HasZeroObject C] →
        [inst_3 : CategoryTheory.HasShift C ℤ] →
          [inst_4 : ∀ (n : ℤ), (CategoryTheory.shiftFunctor C n).Additive] →
            [inst_5 : CategoryTheory.Pretriangulated C] →
              {t : CategoryTheory.Triangulated.TStructure C} →
                {X : C} →
                  {n : ℤ} →
                    {motive : t.IsGE X n → Sort u} → (t_1 : t.IsGE X n) → ((ge : t.ge n X) → motive ⋯) → motive t_1

Defined in

Mathlib.CategoryTheory.Triangulated.TStructure.Basic

Cited by

2 results in Mathlib

Foundations

Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.Limits.HasZeroObjectCategoryTheory.HasShiftCategoryTheory.Functor.AdditiveCategoryTheory.Pretriangulated