  The problem for interface solutions in the quantum theory of heterostructures
comprising narrow-gap semiconductors is reformulated in the language of
commutative diagrams. By this way the theory of interface states in such
heterostructures is naturally factorized in the two subproblems:
  (i) Criterion for the existence of interface states,
  (ii) Their localization in the common energy gap; the solution of both of
them being presented by the requirement for commutativity of the relevant
diagrams. It is shown that these two problems are dual in the sense of
categorical duality, the passing from the one commutative diagram to the other
being realized by a (contravariant) functor Op.
