Theorems · Theorem · category theory

CategoryTheory.Triangulated.TStructure.truncGELTToLTGE_app_pentagon

∀ {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) [inst_6 : CategoryTheory.IsTriangulated C] (a b : ℤ) (X : C),
  CategoryTheory.CategoryStruct.comp ((t.truncGEπ a).app ((t.truncLT b).obj X))
      (CategoryTheory.CategoryStruct.comp ((t.truncGELTToLTGE a b).app X) ((t.truncLTι b).app ((t.truncGE a).obj X))) =
    CategoryTheory.CategoryStruct.comp ((t.truncLTι b).app X) ((t.truncGEπ a).app X)

Defined in

Mathlib.CategoryTheory.Triangulated.TStructure.TruncLTGE

Cited by

2 results in Mathlib

Foundations

Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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