Theorems · Theorem · category theory

CategoryTheory.Triangulated.TStructure.eTruncLTGEIsoGELT_hom_naturality

∀ {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) {X Y : C}
  (f : X ⟶ Y),
  CategoryTheory.CategoryStruct.comp ((t.eTruncLT.obj b).map ((t.eTruncGE.obj a).map f))
      ((t.eTruncLTGEIsoGELT a b).hom.app Y) =
    CategoryTheory.CategoryStruct.comp ((t.eTruncLTGEIsoGELT a b).hom.app X)
      ((t.eTruncGE.obj a).map ((t.eTruncLT.obj b).map f))

Defined in

Mathlib.CategoryTheory.Triangulated.TStructure.ETrunc

Cited by

2 results in Mathlib

Foundations

Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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