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Timeline for triangulated vs. dg/A-infinity

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Oct 17, 2009 at 15:03 comment added Urs Schreiber It might be I still don't exactly see what precisely the question is, but just for the record: more on the pre-triangulated dg-story is here: ncatlab.org/nlab/show/pretriangulated+dg-category
Oct 17, 2009 at 12:12 comment added Greg Stevenson Although that is a very helpful response - I had forgotten that I did also ask about it in my actual answer and I think this makes it very clear what is going on.
Oct 17, 2009 at 12:03 comment added Greg Stevenson Thanks Urs, although I was actually asking about the notion of pre-triangulated category in the sense that suspension is not necessarily invertible but one has compatible left and right triangulated structures. This class of categories then includes triangulated categories, abelian categories (and quasi-abelian categories if memory serves) as well as additive closed model categories (well at least their homotopy categories). These categories turn out to be a good place to do torsion theory. I was wondering if they had a homotopy coherent analogue?
Oct 17, 2009 at 11:43 history answered Urs Schreiber CC BY-SA 2.5