  The prototype of mutually independent systems are systems which are localized
in spacelike separated regions. In the framework of locally covariant quantum
field theory we show that the commutativity of observables in spacelike
separated regions can be encoded in the tensorial structure of the functor
which associates unital $C^*$-algebras (the local observable algebras) to
globally hyperbolic spacetimes. This holds under the assumption that the local
algebras satisfy the split property and involves the minimal tensor product of
$C^*$-algebras.
