Bobtcheva and Quinn have developed a systematic setting for computing in the categories themselves, Numerical presentations of tortile categories . Implementation of these algorithms, and data sets, are available under Categories . See the Category Guide for details. 2-dimensional complexes are technically the simplest, though perhaps the least well explored, of the three target areas. 4-manifolds, see Quinn, Lectures on axiomatic . . .
Current software implements single computations of field invariants using a known category.
See the 2-d Field Guide under Fields . Much of our current research is aimed at systematic understanding of an entire field theory, cf. Probable evaluation of 2-complex topological field theories and Parameterization of induced homomorphisms . . . . This material is not yet sufficiently complete for public posting, though inquiries are welcome.