  Expansion of the categorical point of view on many areas of the mathematics
and mathematical physics will cause to deeper understanding of genuine features
of these problems. New applications of categorical methods are connected with
new additional structures on categories. One of such structures, the double
category, is considered in this article. The double category structure is
defined as generalization of the bicategory structure. It is shown that double
categories exist in the topological and ordinary quantum field theories, and
for dynamical systems with inputs and outputs. Morphisms of all these double
categories are not maps of sets.
