A preliminary version of a paper with A. Pultr entitled "Free Quillen factorization systems" is available (as a pdf file) from my home page at http://www.math.yorku.ca/Who/Faculty/Tholen/research.html The abstract follows. Regards, Walter Tholen. Abstract. The notion of Quillen factorization system is obtained by strengthening the left and right lifting properties in a Quillen model category to the unique diagonalization property. An equivalent description of this notion is given in terms of a double factorization system which decomposes each arrow uniquely into three factors. The free category with Quillen factorization system over a given category is described. 19-Aug-2002 17:43:21 -0300,6577;000000000000-00000000