  Schr\"{o}dinger's famous Gedankenexperiment involving a cat is used as a
motivation to discuss the evolution of states of the composition of classical
and quantum systems in the groupoid formalism for physical theories introduced
recently. It is shown that the notion of classical system, in the sense of
Birkhoff and von Neumann, is equivalent, in the case of systems with a
countable number of outputs, to a totally disconnected groupoid with Abelian
von Neumann algebra. In accordance with Raggio's theorem, the impossibility of
evolving the product state of a composite system made up of a classical and a
quantum one into an entangled state by means of a unitary evolution which is
internal to the composite system itself is proved in the groupoid formalism.
