Spectrum

Introduction The point of stability is that fibre and cofibre sequences become the same data. In a stable category one can build a long exact sequence in either direction and the choice is forced — there is no “missing” octahedral axiom to postulate, no shift functor whose square has to be remembered. Cones are functorial; mapping fibres glue. The triangulated structure on the homotopy category is a theorem, not a definition. ...