Operads, multicategories

An advertisement for an article, available by electric transmission from http://www.dpmms.cam.ac.uk/~leinster. ABSTRACT Notions of `operad' and `multicategory' abound. This work provides a single framework in which many of these various notions can be expressed. Explicitly: given a monad * on a category S, we define the term (S,*)-multicategory, subject to certain conditions on S and *. Different choices of S and * give some of the existing notions. We then describe the algebras for an (S,*)-multicategory, and finish with a selection of possible further developments. Our approach enable concise descriptions of Baez and Dolan's opetopes and Batanin's operads; both of these are included. Tom Leinster