Homotopy Category of Chain Complexes - Generalization

Generalization

More generally, the homotopy category Ho C of a differential graded category C is defined to have the same objects as C, but morphisms are defined by . (This boils down to the homotopy of chain complexes if C is the category of complexes whose morphisms do not have to respect the differentials). If C has cones and shifts in a suitable sense, then Ho C is a triangulated category, too.