Triangulated Categories and Stable Model Categories
نویسنده
چکیده
X id → X → 0→ · For any morphism u : X → Y , there is an object Z (called a mapping cone of the morphism u) fitting into a distinguished triangle X u − → Y → Z → · Any triangle isomorphic to a distinguished triangle is distinguished. This means that if X u − → Y v − → Z w −→ X[1] is a distinguished triangle, and f : X → X, g : Y → Y , and h : Z → Z are isomorphisms, then X′ gu f −1 −−−−→ Y ′ hvg−1 −−−−→ Z′ f [1]wh−1 −−−−−−→ X′[1] is also a distinguished triangle. TR2 If X u − → Y v − → Z w −→ X[1] is a distinguished triangle, then so are the two rotated triangles
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