  When formulating universal properties for objects in a dagger category, one
usually expects a universal property to characterize the universal object up to
unique unitary isomorphism. We observe that this is automatically the case in
the important special case of C$^*$-categories, provided that one uses
enrichment in Banach spaces. We then formulate such a universal property for
infinite direct sums in C$^*$-categories, and prove the equivalence with the
existing definition due to Ghez, Lima and Roberts in the case of
W$^*$-categories. These infinite direct sums specialize to the usual ones in
the category of Hilbert spaces, and more generally in any W$^*$-category of
normal representations of a W$^*$-algebra.
  Finding a universal property for the more general case of direct integrals
remains an open problem.
