nLab
spectral category

Spectral category is a category enriched in the symmetric monoidal category of spectra. Pretriangulated spectral categories are a model of stable $(\mathrm{\infty },1)$-categories.

• Stefan Schwede, Enhancements of triangulated categories, pdf
• Stefan Schwede, Brooke Shipley, Stable model categories are categories of modules, Topology 42:1 (2003) 103–153, MR2003g:55034

Background material on symmetric spectra is in

• Stefan Schwede, Symmetric spectra, book project in progress, beta version pdf