Harder–Narasimhan categories

Semistability and the Harder–Narasimhan filtration are important notions in algebraic and arithmetic geometry. Although these notions are associated to mathematical objects of quite different natures, their definition and the proofs of their existence are quite similar. We propose in this article a generalization of Quillen’s exact category and we discuss conditions on such categories under which one can define the notion of the Harder–Narasimhan filtrations and establish its functoriality.