Dear Colleagues, A preprint version of my CTCS-paper "A monadic approach to polycategories" is available from http://www.iti.cs.tu-bs.de/TI-INFO/koslowj/RESEARCH/ Here's the abstract: Polycategories form a rather natural generalization of multicategories. Besides the domains also the codomains of morphisms are allowed to be strings of objects. While small multicategories can be characterized elegantly as monads in a suitable bicategory of special spans with free monoids as domains, no similar description of polycategories was known. To find one, we first investigate distributive laws in the sense of Beck between cartesian monads S and T on a category X with pullbacks as tools for constructing new bicategories of S-T-spans. We identify a class of ``strongly cartesian'' distributive laws that indeed produce such bicategories in a straightforward manner. If we decompose the free monoid monad (_)^* into the free semigroup monad and the exception monad, a relation on (_)^** can be defined by means of three strongly cartesian distributive laws such that the resulting bicategory of (_)^*-(_)^*-spans has precisely the small planar polycategories as monads. General polycategories require a different construction and a span instead of a relation. However, only the notion of planar polycategory can be generalized to 2-dimensional structures, where objects are replaced by typed 1-cells. Their characterization as monads in a bicategory of modified spans between graphs rather than sets essentially mimics that of planar polycategories. One of the distributive laws mentioned above, a complementation on the free semigroup monad, seems to be new. We identify its algebras as associative double semi-groups. Finally, we address the question, which spans between TS and ST correctly generalize (strongly cartesian) distributive laws and provide an associative composition with canonical units for S-T-spans in X. We obtain four simple sufficient conditions, best formulated in the double-category of spans and morphisms in [X,X], that not only clarify the notion of strongly cartesian distributive law, but also justifies the added generality. Comments are welcome. -- Juergen P.S. 35 years ago today, Jimi Hendrix played his first show in the US with the Experience at the Monterey Pop Festival after achieving major success in England. Then they embarked on a tour with The Monkeys :-) --=20 Juergen Koslowski If I don't see you no more on this world ITI, TU Braunschweig I'll meet you on the next one koslowj@iti.cs.tu-bs.de and don't be late! http://www.iti.cs.tu-bs.de/~koslowj Jimi Hendrix (Voodoo Child, SR) 19-Jun-2002 16:30:15 -0300,1022;000000000000-00000000