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I have added a remark to stable derivator about why the homotopy category of such acquires one triangulation and not the “negative” triangulation, a potentially confusing point (at least, to me).
This remark would probably fit better at stable (∞,1)-category, since the “negating one morphism” operation makes more sense there than in a derivator. But currently that page doesn’t actually describe the construction of the triangulation, which is necessary for the remark to make sense, whereas the page stable derivator does.
I have added a pointer to introductory notes by Yonatan Harpaz on stable $\infty$-categories. These are notes a kindly prepared for our group seminar last week.
Briefly added pointer to formalization of the enrichment over spectra by Gepner-Haugseng, but then my battery died (this here from my phone)
I have added some missing op’s to the section Stabilization and localization of presheaf $(\infty,1)$-categories, and updated the statement of Proposition 2 (it’s even a sufficient condition for stable + presentable).
for ease of reference, I have copied over the discussion of the Schwede-Shipley result also to stable infinity-category – Stabilization and localization
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