n-Category: 2 (actually I think it's 1 and a half....it tends towards 0 depending on the time of day :-) )*
*Dan Freed claims his is still 1
So what the hell is an n-Category anyway?
Higher-Dimensional Categories: an illustrated guide bookand I happen the like this neat mix of sheaves and modal logic found here:
Eugenia Cheng and Aaron Lauda
University of Cambridge, 2004