  We argue that notions in quantum theory should have universal properties in
the sense of category theory. We consider the completely positive trace
preserving (CPTP) maps, the basic notion of quantum channel. Physically,
quantum channels are derived from pure quantum theory by allowing discarding.
We phrase this in category theoretic terms by showing that the category of CPTP
maps is the universal monoidal category with a terminal unit that has a functor
from the category of isometries. In other words, the CPTP maps are the affine
reflection of the isometries.
