Dear category list, Here is yet another operad paper that deals with issues of interest to people in categorical homotopy. The examples mentioned in the abstract actually make up the majority of the text, and come with illustrations. _________________________________________________ Combinatoric n-fold categories and n-fold operads Operads were originally defined as V-operads, that is, enriched in a symmetric or braided monoidal category V. The symmetry or braiding in V is required in order to describe the associativity axiom the operads must obey, as well as the associativity that must be a property of the action of an operad on any of its algebras. After a review of the role of operads in loop space theory and higher categories we go over definitions of iterated monoidal categories and introduce a large family of simple examples. Then we generalize the definition of operad by defining n-fold operads and their algebras in an iterated monoidal category. We discuss examples of these that live in the previously described categories. Finally we describe the (n-2)-fold monoidal category of n-fold V-operads. _________________________________________________ It is on the arxiv at: http://www.arxiv.org/abs/math.CT/0411561 or from my webpage: http://www.math.vt.edu/people/sforcey/class_home/research.htm Comments and suggestions are welcome indeed! Thanks, Stefan Forcey 30-Nov-2004 08:03:55 -0400,2670;000000000000-00000000