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Dec 15, 2015 at 18:19 vote accept Dmitri Pavlov
Dec 15, 2015 at 18:19 comment added Dmitri Pavlov Indeed, Bousfield's notion of a homotopy factorization system combined with t-structures provides one answer to the question. I didn't know that Bousfield already developed such a theory way back in 1975.
Dec 15, 2015 at 14:28 history edited fosco CC BY-SA 3.0
removed unessential and already linked explanation
Dec 15, 2015 at 14:21 history answered fosco CC BY-SA 3.0