  K-Theory for hermitian symmetric spaces of non-compact type, as developed
recently by the authors, allows to put Cartan's classification into a
homological perspective. We apply this method to the case of inductive limits
of finite dimensional hermitian symmetric spaces. This might be seen as an
indication of how much more powerful the homological theory is in comparison to
the more classical approach.
  When seen from high above, we follow the path laid out by a similar result in
the theory of C*-algebras. Important is a clear picture of the behavior of
morphisms between bounded symmetric domains of finite dimensions, which is more
complex than in the C*-case, as well as an accessible K-theory. We furthermore
have to slightly modify the invariant from our previous work. Roughly, we use
traces left by co-root lattices on K-groups, instead of co-roots themselves,
which had been used previously.
