Providing an in-depth treatment of an exciting research area, this text's central topics are initial algebras and terminal coalgebras, primary objects of study in all areas of theoretical computer science connected to semantics. It contains a thorough presentation of iterative constructions, giving both classical and new results on terminal coalgebras obtained by limits of canonical chains, and initial algebras obtained by colimits. These constructions are also developed in enriched settings, especially those enriched over complete partial orders and complete metric spaces, connecting the book to topics like domain theory. Also included are an extensive treatment of set functors, and the first book-length presentation of the rational fixed point of a functor, and of lifting results which connect fixed points of set functors with fixed points of endofunctors on other categories. Representing more than fifteen years of work, this will be the leading text on the subject for years to come.

‘The ultimate book explaining the state-of-the-art in the field of initial algebras and terminal coalgebras. Highly recommended to readers seeking both an introduction as well as an in-depth treatment of a general theory of iteration, with applications in algebraic specification, state-based modelling and behavioural equivalence.’

Barbara König - Universität Duisburg-Essen

‘Fixed points are central to computer science. The book is therefore a must for every categorically minded computer scientist.’

Ichiro Hasuo - National Institute of Informatics