Theorems · Theorem · category theory

CategoryTheory.Triangulated.TStructure.eTruncGEIsoGEGE_hom_inv_id_app

∀ {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) [inst_6 : CategoryTheory.IsTriangulated C] (a b : EInt) (hab : a ≤ b)
  (X : C),
  CategoryTheory.CategoryStruct.comp ((t.eTruncGE.obj b).map ((t.eTruncGEπ a).app X))
      ((t.eTruncGEIsoGEGE a b hab).inv.app X) =
    CategoryTheory.CategoryStruct.id ((t.eTruncGE.obj b).obj ((CategoryTheory.Functor.id C).obj X))

Defined in

Mathlib.CategoryTheory.Triangulated.TStructure.ETrunc

Cited by

1 results in Mathlib

Foundations

Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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