Theorems · Definition · category theory

CategoryTheory.Triangulated.TStructure.Heart.casesOn

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} 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} →
                {H : Type u'} →
                  [inst_6 : CategoryTheory.Category.{v', u'} H] →
                    [inst_7 : CategoryTheory.Preadditive H] →
                      {motive : t.Heart H → Sort u_1} →
                        (t_1 : t.Heart H) →
                          ((ι : CategoryTheory.Functor H C) →
                              (additive_ι : ι.Additive) →
                                (full_ι : ι.Full) →
                                  (faithful_ι : ι.Faithful) →
                                    (essImage_eq_heart : ι.essImage = t.heart) →
                                      motive
                                        { ι := ι, additive_ι := additive_ι, full_ι := full_ι, faithful_ι := faithful_ι,
                                          essImage_eq_heart := essImage_eq_heart }) →
                            motive t_1

Defined in

Mathlib.CategoryTheory.Triangulated.TStructure.Heart

Cited by

0 results in Mathlib

Foundations

Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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