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Oct 27, 2009 at 0:32 comment added Mike Shulman The paper of Hovey that I linked to includes a reference to the Christensen-Hovey paper, and to a number of others; I didn't want to give a huge list of references here. Thanks for the other link.
Oct 25, 2009 at 21:36 comment added D.-C. Cisinski I would also add the following references: J.D. Christensen and M. Hovey, Quillen model structures for relative homological algebra, Math. Proc. Camb. Phil. Soc. 133 (2002), no. 2, 231-293. The following paper should answer your questions 1) and 2) quite precisely. intlpress.com/HHA/v11/n1/a11
Oct 15, 2009 at 17:44 vote accept Kevin H. Lin
Oct 13, 2009 at 21:21 history answered Mike Shulman CC BY-SA 2.5