According to the abstract of http://arxiv.org/abs/math/0108143 (Schwede & Shipley, Classification of Stable Model Categories), they deal with the case of stable model categories (=stable presentable (∞,1)-categories, I suppose) which have a set of generators, and show they are the same as model categories of functors from spectral-enriched categories.

According to the abstract of http://arxiv.org/abs/math/0108143 (Schwede & Shipley, Classification of Stable Model Categories), they deal with the case of stable model categories (=stable presentable (∞,1)-categories, I suppose) which have a set of compact generators, and show they are the same as model categories of functors from spectral-enriched categories.

(Edited, in the light of Reid's comment, to include the hypothesis of compact generators.)

According to the abstract of http://arxiv.org/abs/math/0108143 (Schwede & Shipley, Classification of Stable Model Categories, they deal with the case of stable model categories (=stable presentable (∞,1)-categories, I suppose) which have a set of generators, and show they are the same as model categories of functors from spectral-enriched categories.

According to the abstract of http://arxiv.org/abs/math/0108143 (Schwede & Shipley, Classification of Stable Model Categories), they deal with the case of stable model categories (=stable presentable (∞,1)-categories, I suppose) which have a set of generators, and show they are the same as model categories of functors from spectral-enriched categories.