  The notion of Harder-Narasimhan filtration was firstly introduced by Harder
and Narasimhan in the setting of vector bundles on a non-singular projective
curve. Curiously, analogous constructions have been discovered in other
branches of mathematics which motivate categorical constructions of
Harder-Narasimhan filtration. In this article, we introduce a categorical
construction of Harder-Narasimhan filtration via slope function method which
does not need the additive condition in degree function. We also give a method
to prove the existence and uniqueness theorem of the Harder-Narasimhan
filtration intrinsically from a set E and a admissible collection of subsets of
E, which does not need sub-quotient structure.
