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Nov 10, 2011 at 6:04 comment added Mike Crumley I'm afraid I stated the problem in more general terms than I intended to, but your reply will I believe nonetheless point me towards the answer I am looking for. Much appreciated.
Nov 10, 2011 at 6:03 vote accept Mike Crumley
Nov 7, 2011 at 21:53 comment added tj_ George, the question wasn't if there is an injective resolution with injective differentials, but if there is an injective resolution $I$ of a bounded complex $X$ (the extension in Mike's terminology) such that the maps $X_i \to I_i$ are injective.
Nov 6, 2011 at 21:18 history answered George C. Modoi CC BY-SA 3.0