Mike Barr's recent paper Absolute Homology (TAC 14,pp53-59) contains a very nice result. Strikingly, it is of a completely basic nature, yet seems new. Similarly, his book Acyclic Models concerns concepts partly formulated fifty yeas ago and supposedly old hat, yet demonstrates new simplifications. The point is that the foundations of homological algebra are not rigidly fixed, since new fundamental insights can be made explicit to guide teaching and research. It appears that the same is true of the foundations of homotopical algebra as well ! The recent book Homotopy Limit Functors on Model Categories and Homotopical Categories (AMS Surveys and monographs 13) by Dwyer, Hirschhorn, Kan, and Smith describes itself as "an unsuccessful attempt to give an updated account of Quillen's closed model categories". But it seems to have achieved a big simplification, in basic complications like saturation and hammock calculation. It may serve as a text for a renewed seminar for nonspecialists which tries to finally understand these matters. 25-Feb-2005 16:54:17 -0400,4056;000000000000-00000000