isTriangulated_of_precomp — Mathlib

English

If H ≅ F ⋙ G is triangulated, then G is triangulated given F is triangulated and F.mapArrow.EssSurj.

Русский

Если H ≅ F ⋙ G трангулирован, то G трангулирован при условии, что F трангулирован и F.mapArrow.EssSurj.

LaTeX

$$isTriangulated_of_precomp F G$$

Lean4

theorem isTriangulated_of_precomp [(F ⋙ G).IsTriangulated] [F.IsTriangulated] [F.mapArrow.EssSurj] : G.IsTriangulated
    where
  map_distinguished T
    hT := by
    obtain ⟨T', hT', ⟨e⟩⟩ := F.mem_mapTriangle_essImage_of_distinguished T hT
    exact
      isomorphic_distinguished _ ((F ⋙ G).map_distinguished T' hT') _
        (G.mapTriangle.mapIso e.symm ≪≫ (mapTriangleCompIso F G).symm.app _)

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