Initial Algebras and Terminal Coalgebras

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.