The category of groupoids as a categorification of the ring of rational numbers.  See [this MO question][1] and this [n-category cafe post][2]. 


  [1]: http://mathoverflow.net/questions/22860/do-rational-numbers-admit-a-categorification-which-respects-the-following-dualit
  [2]: http://golem.ph.utexas.edu/category/2008/12/groupoidification_made_easy.html