homologySequenceComposableArrows₅

English

The five-term (composable arrows) construction is exact when F is homological.

Русский

Пять последовательность компонуемых стрелок точна, если F гомологичен.

LaTeX

$$$\text{homologySequenceComposableArrows}_{5}$ is exact$$

Lean4

/-- The exact sequence with six terms starting from `(F.shift n₀).obj T.obj₁` until
`(F.shift n₁).obj T.obj₃` when `T` is a distinguished triangle and `F` a homological functor. -/
@[simp]
noncomputable def homologySequenceComposableArrows₅ : ComposableArrows A 5 :=
  mk₅ ((F.shift n₀).map T.mor₁) ((F.shift n₀).map T.mor₂) (F.homologySequenceδ T n₀ n₁ h) ((F.shift n₁).map T.mor₁)
    ((F.shift n₁).map T.mor₂)

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