English
If G is an additive functor, then the image of the triangulated structure is triangulated: G.mapHomotopyCategory (up ℤ) preserves triangulated structure.
Русский
Если G аддитивный функтор, то образ треугольной структуры через G сохраняет трiангулированность.
LaTeX
$$$ (G.mapHomotopyCategory (ComplexShape.up \\mathbb{Z})).IsTriangulated$$$
Lean4
noncomputable instance : Pretriangulated (HomotopyCategory C (ComplexShape.up ℤ))
where
distinguishedTriangles := Pretriangulated.distinguishedTriangles C
isomorphic_distinguished := Pretriangulated.isomorphic_distinguished
contractible_distinguished := Pretriangulated.contractible_distinguished
distinguished_cocone_triangle := Pretriangulated.distinguished_cocone_triangle
rotate_distinguished_triangle := Pretriangulated.rotate_distinguished_triangle
complete_distinguished_triangle_morphism := Pretriangulated.complete_distinguished_triangle_morphism
