  In this article, we give an explicit construction of the derived moduli stack
of Harder-Narasimhan filtrations on a connected projective scheme over an
algebraically closed field k of characteristic 0 by using methods by Behrend,
Ciocan-Fontanine, Hwang and Rose. Moreover, we describe the derived deformation
theory of a filtered sheave on a connected projective scheme over k and compare
our construction with a construction by Di Natale.
