  We propose a means to relate properties of an interconnected system to its
separate component systems in the presence of cascade-like phenomena. Building
on a theory of interconnection reminiscent of the behavioral approach to
systems theory, we introduce the notion of generativity, and its byproduct,
generative effects. Cascade effects, enclosing contagion phenomena and
cascading failures, are seen as instances of generative effects. The latter are
precisely the instances where properties of interest are not preserved or
behave very badly when systems interact. The goal is to overcome that
obstruction. We will show how to extract mathematical objects from the systems,
that encode their generativity: their potential to generate new phenomena upon
interaction. Those objects may then be used to link the properties of the
interconnected system to its separate systems. Such a link will be executed
through the use of exact sequences from commutative algebra.
