  In the context of A. Connes' spectral triples, a suitable notion of morphism
is introduced. Discrete groups with length function provide a natural example
for our definitions. A. Connes' construction of spectral triples for group
algebras is a covariant functor from the category of discrete groups with
length functions to that of spectral triples. Several interesting lines for
future study of the categorical properties of spectral triples and their
variants are suggested.
