Harder-Narasimhan categories

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.