Duality between existence condition and construction procedure for   interface states in a class of narrow-gap heterostructures
  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. 
B. D. Kandilarov, V. Detcheva