TITLE: Adams Spectral Sequence for Triangulated Categories
QUESTION [6 upvotes]: We have the Adams SS with 
$$ E_2^{p,q} = Ext^{p,q} _{E^*(E)}([S,E],[S,E]) $$
where $E$ is the Eilenberg-Maclane Spectrum yielding $\mathbb{Z}/p$ coefficients.
I was wondering if there is a SS for arbitrary compactly generated triangulated categories of which this is special case. 
More specifically I am curious if we assume our category to have enough projectives (or injectives) can we avoid invoking the smash product? I am new to Stable Homotopy theory and think of smash products as black box. It would be really delightful if I could replace having a smash product by having enough projectives or something similar but algebraic.

REPLY [4 votes]: A general treatment of the Adams spectral sequence in the context of triangulated categories based on the work of Brinkmann and Christensen can be found here: http://arxiv.org/pdf/0801.1344.
No monoidal structure is necessary (although, in applications, you might use a monoidal structure to define a homological ideal).