Universal spaces for homotopy limits of modules over coaugmented functors. I (Q1811541)

After the introduction, the author gives the definitions and some facts about cofacial resolutions in section 2. Coaugmented functors are the standard source of cofacial resolutions. The concept of \(J\)-module is defined and is shown to be a source of trivial cofacial resolutions (the ones with left contractions). In section 3 simplicial coaugmented functors are defined, giving several examples and results. The main result of the paper is proved in section 4: homotopy limits of \(J\)-modules are themselves \(J_n\)-modules for suitable functors \(J_n\). Section 5 is dedicated to the definition of generalized Eilenberg MacLane spaces (GEMs) and thin-polyGEMs, and to the investigation of some consequences of the main theorem regarding the unstable Adams spectral sequence of these spaces. The paper concludes with an appendix, where a proof for a special case of theorem \(3.2\) in part II of the present paper [Topology 42, 569-602 (2003; Zbl 1025.55008)] is sketched.