http://www.ncatlab.org/nlab/show/stable+(infinity,1)-category
http://www.ncatlab.org/nlab/show/Stable+Infinity-Categories
http://ncatlab.org/nlab/show/stable+%28infinity%2C1%29-topos the entry relates to sheaves of spectra
http://mathoverflow.net/questions/74386/how-should-i-think-of-the-infty-category-of-spectra
http://mathoverflow.net/questions/59270/is-the-infty-category-of-stable-infty-categories-stable
arXiv:1004.3087 Monoidal Infinity Category of Complexes from Tannakian Viewpoint from arXiv Front: math.AT by Hiroshi Fukuyama, Isamu Iwanari In this paper we prove that a morphism between schemes or stacks naturally corresponds to a symmetric monoidal functor between stable infinity-categories of quasi-coherent complexes. It can be viewed as a derived analogue of Tannaka duality. As a consequence, we deduce that an algebraic stack satisfying a certain condition can be recovered from the stable infinity-category of quasi-coherent complexes with tensor operation.
nLab page on Stable infinity-category