  We implement a novel representation of model search spaces as diagrams over a
category of models, where we have restricted attention to a broad class of
models whose structure is presented by \C-sets. (Co)limits in these diagram
categories allow the creation of composite model spaces from more primitive
spaces. We present a novel implementation of the computer algebra of finitely
presented categories and diagram categories (including their limits and
colimits), which formalizes a notion of model space exploration. This is
coupled with strategies to facilitate the selection of desired models from
these model spaces. We demonstrate our framework by generating a tool which
fits experimental data, searching an epidemiology-relevant subspace of
mass-action kinetic models.
