English
Alternative formulation: isTriangulated_of_precomp_iso holds under weaker assumptions.
Русский
Альтернативная формулировка: isTriangulated_of_precomp_iso верна при менее строгих предпосылках.
LaTeX
$$isTriangulated_of_precomp_iso_again$$
Lean4
/-- The image of an octahedron by a triangulated functor. -/
@[simps]
def map :
Octahedron (by dsimp; rw [← F.map_comp, comm]) (F.map_distinguished _ h₁₂) (F.map_distinguished _ h₂₃)
(F.map_distinguished _ h₁₃)
where
m₁ := F.map h.m₁
m₃ := F.map h.m₃
comm₁ := by simpa using F.congr_map h.comm₁
comm₂ := by simpa using F.congr_map h.comm₂ =≫ (F.commShiftIso 1).hom.app X₁
comm₃ := by simpa using F.congr_map h.comm₃
comm₄ := by simpa using F.congr_map h.comm₄ =≫ (F.commShiftIso 1).hom.app X₂
mem :=
isomorphic_distinguished _ (F.map_distinguished _ h.mem) _
(Triangle.isoMk _ _ (Iso.refl _) (Iso.refl _) (Iso.refl _))
