Initial Algebras and Terminal Coalgebras
The Theory of Fixed Points of Functors
Lawrence S Moss author Jiří Adámek author Stefan Milius author
Format:Hardback
Publisher:Cambridge University Press
Publishing:28th Feb '25
£155.00
This title is due to be published on 28th February, and will be despatched as soon as possible.
An in-depth treatment of an active research area of theoretical computer science, presenting and extending its most important results.
This definitive treatment of results in category theory and theoretical computer science covers classical material from new viewpoints and develops a wealth of new topics. The centrepiece is a collection of existence theorems for initial algebras and terminal coalgebras. It will be the standard reference for years to come.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 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 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
ISBN: 9781108835466
Dimensions: unknown
Weight: unknown
640 pages