@TECHREPORT{Lydakis98simplicialfunctors, author = {Manos Lydakis}, title = {Simplicial Functors and Stable Homotopy Theory}, institution = {}, year = {1998} }

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this paper) are well known: They are the FSPs, which were introduced in 1985 by Bokstedt [B]. There are interesting constructions with FSPs, e.g., topological cyclic homology, which can be considerably simplified and conceptualized using the smash product of simplicial functors [LS]. Note however that it is not clear that an E1-FSP has a commutative model, although the analogous statement is true for S-modules and symmetric spectra. This has, e.g., the disadvantage, that it is not clear how to give a model category structure to (or even how to define) MU-algebras using simplicial functors (although this can be done for modules over any any FSP, and algebras over any commutative FSP, by similar methods as in [Sch]). Returning to examining the special features of simplicial functors, in constrast to