I'm very interested in the work of Louis Crane, Dan Freed and others on how extending TQFTs to higher dimensions or higher codimensions can be nicely phrased in the language of n-categories. Luckily James Dolan is here at UCR now and is educating me in such matters. He and I are beginning to struggle towards a nice concept of "weak n-categories," or even better "weak omega-categories," or perhaps even better, "weak Z-categories" (in some sense a homotopical analog of chain complexes). I am interested in these things for doing physics, but I dimly realize that lots of people have struggled with these concepts, and I want to get a better grasp of what the key achievements and problems in this subject are. I have read Kapranov and Voevodsky's massive preprint on Braided Monoidal 2-categories, 2-vector spaces and Zamolodchikov tetrahedra equations, and soon I should receive a copy of the new paper on coherence in 3-categories by Gordon, Powell, and Street. What are the other main things I should find out about? How come all you categorists haven't yet invented a notion of "weak Z-categories," in which there are n-morphisms for all integers n, and all relations between n-morphisms are expressed in terms of (n+1)-morphisms? Regards, John Baez ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++