  Cheeger-Simons differential characters, Deligne cohomology in the smooth
category, the Hopkins-Singer construction of ordinary differential cohomology
and the recent Harvey-Lawson constructions are each in two distinct ways
Abelian group extensions of known functors. In one desciption these objects are
extensions of integral cohomology by the quotient space of all differential
forms by the subspace of closed forms with integral periods. In the other they
are extensions of closed differential forms with integral periods by the
cohomology with coefficients in the circle. These two series of short exact
sequences mesh with two interlocking long exact sequences (the Bockstein
sequence and a DeRham sequence) to form a commutative DNA-like array of
functors called the Character Diagram.
  Theorem 1.1 shows that on the category of smooth manifolds and smooth maps
any package consisting of a functor into graded abelian groups together with
four natural transformations that fit together so as to form a Character
Diagram as above is unique up to unique natural equivalence. Theorem 1.2 shows
the natural product structure on differential characters is uniquely
characterized by its compatibility with the product structures on the known
functors in the Character Diagram. The proof of Theorem 1.1 couples the
naturality with results about approximating smooth singular cycles and
homologies by embedded pseudomanifolds.
