We introduce the concept of strict ample sequence in a fibered triangulated category and define the stability of the objects in a triangulated category. Then we construct the moduli space of (semi) stable objects by GIT construction.
"Moduli of stable objects in a triangulated category." J. Math. Soc. Japan 62 (2) 395 - 429, April, 2010. https://doi.org/10.2969/jmsj/06220395