Categorical Language and Hierarchical Models for Cell Systems

The aim is to explain and explore some of the current ideas from category theory that enable various mathematical descriptions of hierarchical structures. We review some aspects of the history and motivations behind the development of category theory and how it has impacted on developments in theoretical biology and theoretical computer science. This leads on to a discussion of hierarchical systems and a discussion of some simple examples. The important idea of colimit is then introduced. Towards the end of the chapter a number of open questions and problems are discussed.