Theorems · Theorem · category theory

CategoryTheory.Triangulated.TStructure.descTruncGT.congr_simp

∀ {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) {X Y : C} (f f_1 : X ⟶ Y),
  f = f_1 →
    ∀ (n₀ n₁ n₁_1 : ℤ) (e_n₁ : n₁ = n₁_1) (h : n₀ + 1 = n₁) [inst_6 : t.IsGE Y n₁],
      t.descTruncGT f n₀ n₁ h = t.descTruncGT f_1 n₀ n₁_1 ⋯

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.PretriangulatedCategoryTheory.Triangulated.TStructure.IsGE