  Inspired by decomposition problems in rule-based formalisms in Computational
Systems Biology and recent work on compositionality in graph transformation,
this paper proposes to use arbitrary colimits to "deconstruct" models of
reactions in which states are represented as objects of adhesive categories.
The fundamental problem is the decomposition of complex reactions of large
states into simpler reactions of smaller states.
  The paper defines the local decomposition problem for transformations. To
solve this problem means to "reconstruct" a given transformation as the colimit
of "smaller" ones where the shape of the colimit and the decomposition of the
source object of the transformation are fixed in advance. The first result is
the soundness of colimit decomposition for arbitrary double pushout
transformations in any category, which roughly means that several "local"
transformations can be combined into a single "global" one. Moreover, a
solution for a certain class of local decomposition problems is given, which
generalizes and clarifies recent work on compositionality in graph
transformation.
