Based on Molecular Orbital Theory , how is it decided that the double bond in O2 molecule has one sigma bond and one pi bond? My Chemistry textbook says this in regard to a C2 molecule:


  It is important to note that double bond
  in C2 consists of both pi bonds because of the
  presence of four electrons in two pi molecular
  orbitals. 


Is it possible to account for the double bond in an Oxygen atom consisting of a sigma bond and a pi bond in the same way, based on MOT?
$\ce{O2}$ MO diagram
From the MO diagram, we can see that it has 2 electrons in a $\sigma$ orbital, 4 in $\pi$ orbitals, and 2 in $\pi$* orbitals. Taking this together gives a bond order 2, with 1 coming from the sigma electrons and another 1 being the net value for the $\pi$ and $\pi$* electrons.