mapComposableArrows₂ — Mathlib

English

Compatibility relation δ_eq' for a morphism between short complexes in a diagram of five arrows.

Русский

Соотношение совместимости δ_eq' для морфизма между короткими комплексами в диаграмме с пятью стрелками.

LaTeX

$$δ_eq' hS i j hij$$

Lean4

/-- The map between the exact sequences `S₁.X₁.homology i ⟶ S₁.X₂.homology i ⟶ S₁.X₃.homology i`
and `S₂.X₁.homology i ⟶ S₂.X₂.homology i ⟶ S₂.X₃.homology i` that is induced by `φ : S₁ ⟶ S₂`. -/
@[simp]
noncomputable def mapComposableArrows₂ (i : ι) : composableArrows₂ S₁ i ⟶ composableArrows₂ S₂ i :=
  homMk₂ (homologyMap φ.τ₁ i) (homologyMap φ.τ₂ i) (homologyMap φ.τ₃ i)
    (by
      dsimp
      simp only [← homologyMap_comp, φ.comm₁₂])
    (by
      dsimp [Precomp.map]
      simp only [← homologyMap_comp, φ.comm₂₃])

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