Initial Algebras and Terminal Coalgebras: The Theory of Fixed Points of Functors (Cambridge Tracts in Theoretical Computer Science, Series Number 62) (PDF)

By Jiří Adámek, Stefan Milius, Lawrence S. Moss 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.
Product Details

Publisher ‏ : ‎ Cambridge University Press
Publication date ‏ : ‎ February 6, 2025
Edition ‏ : ‎ 1st
Language ‏ : ‎ English
ISBN-10 ‏ : ‎ 1108835465
ISBN-13 ‏ : ‎ 978-1108835466
Part of series ‏ : ‎ Cambridge Tracts in Theoretical Computer Science