Dear All, re categories with relational composition: David Espinosa <espinosa@cs.columbia.edu> asked: "Has there been any work on "categories" with composition as a relation instead of a function? We would allow several "composites" of two arrows but would likely require unique composition with the identity: f o id = {f} Such objects naturally occur in some studies of homotopy coherence in abstract homotopy theory. There is a set of possible composites so a choice of composite is made to make life easy, but in this context, any two choices are related by higher dimensional data. Of course associativity does not work but does up to higher diemnsional data. This is linked to some ideas in bicategories. Perhaps the fact that the resulting THING is constructed rather like a Kleisli category but with a choice of "multiplication" on the "monad" is significant. If anyone is interested I can expand further on this. Tim Tim Porter, Bangor, e-mail: mas013@clss1.bangor.ac.uk