There is a followup article, first in the 5-article series Derived Algebraic Geometry:
- Stable Infinity Categories, arXiv:math/0608228
In particular,
The theory of stable ∞-categories is not really new: most of the results presented here are well-known to experts. There exists a sizable literature on the subject in the setting of stable model categories (see, for example, [27]). The theory of stable model categories is essentially equivalent to the notion of a presentable stable ∞-category, which we discuss in §15.