Categorical Non-commutative Geometry
  The purpose of this short note was to outline the current status, then in 2011, of some research programs aiming at a categorification of parts of A.Connes' non-commutative geometry and to provide an outlook on some possible subsequent developments in categorical non-commutative geometry. 
Paolo Bertozzini, Roberto Conti, Wicharn Lewkeeratiyutkul
math.OA math-ph math.CT math.MP