Theorems · Theorem · category theory

CategoryTheory.Pretriangulated.binaryBiproductData_bicone_fst

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasZeroObject C]
  [inst_2 : CategoryTheory.HasShift C ℤ] [inst_3 : CategoryTheory.Preadditive C]
  [inst_4 : ∀ (n : ℤ), (CategoryTheory.shiftFunctor C n).Additive] [hC : CategoryTheory.Pretriangulated C]
  (T : CategoryTheory.Pretriangulated.Triangle C) (hT : T ∈ CategoryTheory.Pretriangulated.distinguishedTriangles)
  (hT₀ : T.mor₃ = 0) (inr : T.obj₃ ⟶ T.obj₂)
  (inr_snd : CategoryTheory.CategoryStruct.comp inr T.mor₂ = CategoryTheory.CategoryStruct.id T.obj₃)
  (fst : T.obj₂ ⟶ T.obj₁)
  (total :
    CategoryTheory.CategoryStruct.comp fst T.mor₁ + CategoryTheory.CategoryStruct.comp T.mor₂ inr =
      CategoryTheory.CategoryStruct.id T.obj₂),
  (CategoryTheory.Pretriangulated.binaryBiproductData T hT hT₀ inr inr_snd fst total).bicone.fst = fst

Defined in

Mathlib.CategoryTheory.Triangulated.Pretriangulated

Cited by

0 results in Mathlib

Foundations

Depth 51 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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