Commit 2024-06-05 19:32 ef633564
View on Github →feat(CategoryTheory/Triangulated): the long exact sequence of a homological functor (#11805)
Assuming F : C ⥤ A is a homological functor (from a pretriangulated category to an abelian category), we show that any distinguished triangle leads to a long exact sequence (assuming n₀ + 1 = n₁):
... ⟶ (F.shift n₀).obj T.obj₁ ⟶ (F.shift n₀).obj T.obj₂ ⟶ (F.shift n₀).obj T.obj₃ ⟶ (F.shift n₁).obj T.obj₁ ⟶ ...