The notion of T-complex is discussed on the ncatlab which writes: "A T-complex is a higher-dimensional combinatorial structure with a class of designated thin elements. The concept can be made sense of for various shapes:" (and then gives cubical and simplicial). I have put a link on that page http://ncatlab.org/nlab/show/T-complex to David Jones 1983 thesis `A general theory of polyhedral sets and the corresponding T-complexes' which was kindly scanned recently by Stephen Gaito. The theory there is for higher groupoids, and it is not clear how to do higher categories in the same spirit. The aims of this thesis were first to incorporate shapes like pentagons, or other diagrams representing group relations, such as x^17=1, then to formulate multiple compositions, and finally to relate this theory to that of simplicial T-complexes; but there are surely lots of other issues worth pursuing further. I liked the way the concept of shellability is used in describing the basic `shapes', in order to give power to the filling process. While writing, I'll mention that pdf's of my seminar at Gottingen on May 5 on `Applications of a nonabelian tensor product of groups' are available on my preprint page: http://www.bangor.ac.uk/r.brown/brownpr.html Ronnie Brown [For admin and other information see: http://www.mta.ca/~cat-dist/ ]