  Conformal nets are a classical topic in quantum field theory: they assign
operator algebras to one-dimensional manifolds, and have close connections with
one-dimensional topological field theories.
  It seems to be well-known that the usual axioms for these constructions imply
close relations between the action of the projective group on the line, and
Connes' intrinsic flow on $C^*$-algebras. This note attempts to pin down this
specific fact, in terms of a category of (noncommutative) algebras and
equivalence classes, under inner automorphisms, of homomorphisms between them.
That category may be of independent interest.
