Dear all, The trace of a category C is a well-known construction: it is the set given by taking the 'trace' of the identity functor on C in the bicategory of profunctors. Concretely, it is the set given by endomorphisms in C, modulo the equivalence relation generated by f.g~g.f for all pairs of functions f and g with opposite types. Abstractly, it is the coend of the identity functor on C. In general, I'm sure the trace of an n-category would be an (n-1)-category. I'm interested in what happens when you iterate this all the way down, and hence obtain a set from any n-category. Can someone give me a concrete description of the set one obtains in this way from a strict n-category? I want something that I can get my hands on, and try out on my favourite strict n-categories, rather than an abstract statement about taking higher coends. What if I had a strict omega-category? Its trace would presumably be another omega-category. Should I expect to be able to somehow trace it down to a set? With best wishes, Jamie. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]