  B. Magajna and J. Schweizer showed in 1997 and 1999, respectively, that
C*-algebras of compact operators can be characterized by the property that
every norm-closed (and coinciding with its biorthogonal complement, resp.)
submodule of every Hilbert C*-module over them is automatically an orthogonal
summand. We find out further generic properties of the category of Hilbert
C*-modules over C*-algebras which characterize precisely the C*-algebras of
compact operators.
