Theorems · Theorem · category theory

CategoryTheory.Triangulated.TStructure.natTransTruncLEOfLE_trans_app_assoc

∀ {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) (a b c : ℤ) (hab : a ≤ b) (hbc : b ≤ c) (X : C) {Z : C}
  (h : (t.truncLE c).obj X ⟶ Z),
  CategoryTheory.CategoryStruct.comp ((t.natTransTruncLEOfLE a b hab).app X)
      (CategoryTheory.CategoryStruct.comp ((t.natTransTruncLEOfLE b c hbc).app X) h) =
    CategoryTheory.CategoryStruct.comp ((t.natTransTruncLEOfLE a c ⋯).app X) h

Defined in

Mathlib.CategoryTheory.Triangulated.TStructure.TruncLEGT

Cited by

0 results in Mathlib

Foundations

Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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