Initial algebras and terminal coalgebras : the theory of fixed points of functors / Jiří Adámek, Stefan Milius, Lawrence S. Moss.

Format:

Book

Author/Creator:

Adámek, Jiří, 1947- author.

Milius, Stefan, author.

Moss, Lawrence Stuart, 1959- author.

Series:

Cambridge tracts in theoretical computer science ; 62.

Cambridge tracts in theoretical computer science ; 62

Language:

English

Subjects (All):

Categories (Mathematics).

Recursion theory.

Induction (Mathematics).

Fixed point theory.

Duality theory (Mathematics).

Physical Description:

1 online resource (xiii, 626 pages) : digital, PDF file(s).

Edition:

First edition.

Place of Publication:

Cambridge, United Kingdom ; New York, NY : Cambridge University Press, 2025.

Summary:

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.

Notes:

Title from publisher's bibliographic system (viewed on 27 Jan 2025).

Includes bibliographical references and index.

ISBN:

9781108880671

1108880673

9781108884112

1108884113