Simplicial model category structures on the category of chain functors (Q859461)

The notion of chain functor has been introduced in a series of papers by the first author [\textit{F. W. Bauer}, Homology Homotopy Appl. 1, 95--116 (1999; Zbl 0921.55007) and ibid. 3, 55--85 (2001; Zbl 0978.55009)] and with the second author [\textit{T. Datuashvili}, J. Algebra Appl. 5, No. 4, 379--401 (2006; Zbl 1116.55003) and Topology Appl. 131, 101--128 (2003; Zbl 1027.55018)] to provide a tool for the study of various generalised homology theories analogous and complementary to that of spectra. In this paper the problem of giving the category of chain functors a simplicial model category structure is attacked. The category of chain functors is not tensored for fairly simple reasons, so only an approximation to the simplicial model category structure is possible.