The sphere spectrum as categorification of the integers, as remarked in a comment of Thomas Kragh below his answer <a href="http://mathoverflow.net/questions/22860/do-rational-numbers-admit-a-categorification-which-respects-the-following-dualit">here</a>, and which I believe is due to Joyal. 

Hm, that's a lot of answers from me. Should I stop now, or keep going?