Measurable Categories and 2-Groups [article]

L. Crane, D.N. Yetter
2003 arXiv   pre-print
Using the theory of measurable categories developped by Yetter in work in preparation, we provide a notion of representations of 2-groups more well-suited to physically and geometrically interesting examples than that proposed in unpublished work of Barrett and Mackaay using 2-VECT of Kapranov and Voevodsky. Using this theory we sketch a 2-categorical approach to the state-sum model for Lorentzian quantum gravity proposed in by the authors in previous work and suggest state-integral constructions for 4-manifold invariants.
arXiv:math/0305176v1 fatcat:nfm7a6jbcvhldgjduwu6objvvi