Lurie's book, higher topos theory describes a new notion of a triangulated category, which is apparently much more natural than the usual definition. Obviously by now a great deal of work has been done on triangulated categories, has anyone translated any of this work into this new language?

That is should one go straight to his book, or become reasonably acquainted with triangulated categories first, in the hope that by then people will have become more familiar with that language by then?