  We provide a definition of POVM in terms of abstract tensor structure only.
It is justified in two distinct manners. i. At this abstract level we are still
able to prove Naimark's theorem, hence establishing a bijective correspondence
between abstract POVMs and abstract projective measurements on an extended
system, and this proof is moreover purely graphical. ii. Our definition
coincides with the usual one for the particular case of the Hilbert space
tensor product. We also point to a very useful normal form result for the
classical object structure introduced in quant-ph/0608035.
