Aarrgghh!

> there are only two universal properties

Yeah? So what are they???

Hm, Wikipedia (http://en.wikipedia.org/wiki/Universal_property) thinks there are a lot more than two:

"This article gives a general treatment of universal properties. To understand the concept, it is useful to study several examples first, of which there are many: all free objects, direct product and direct sum, free group, free lattice, Grothendieck group, product topology, Stone–Čech compactification, tensor product, inverse limit and direct limit, kernel and cokernel, pullback, pushout and equalizer."