Title: Comparing homotopy categories Author: David Blanc e-mail: blanc@math.haifa.ac.il Address: Department of Mathematics University of Haifa 31905 Haifa Israel AMS Classification: Primary: 55U35; Secondary: 55P65, 55Q35, 18G55 Abstract: Given a suitable functor T:C -> D between model categories, we define a long exact sequence relating the homotopy groups of any X in C with those of TX, and use this to describe an obstruction theory for lifting an object G in D to C. Examples include finding spaces with given homology or homotopy groups.