  We propose a generalization of Quillen's exact category -- arithmetic exact
category and we discuss conditions on such categories under which one can
establish the notion of Harder-Narasimhan filtrations and Harder-Narsimhan
polygons. Furthermore, we show the functoriality of Harder-Narasimhan
filtrations (indexed by $\mathbb R$), which can not be stated in the classical
setting of Harder and Narasimhan's formalism.
