  We introduce a construction that turns a category of pure state spaces and
operators into a category of observable algebras and superoperators. For
example, it turns the category of finite-dimensional Hilbert spaces into the
category of finite-dimensional C*-algebras and completely positive maps. In
particular, the new category contains both quantum and classical channels,
providing elegant abstract notions of preparation and measurement. We also
consider nonstandard models, that can be used to investigate which notions from
algebraic quantum information theory are operationally justifiable.
