Braid semistatistics and doubly regular R-matrix
  We introduce "noninvertible" generalization of statistics - semistatistics replacing condition when double exchanging gives identity to "regularity" condition. Then in categorical language we correspondingly generalize braidings and the quantum Yang-Baxter equation. We define the doubly regular R-matrix and introduce obstructed regular bialgebras. 
S. Duplij (Kharkov National University) and W. Marcinek (University of   Wroclaw)