{"product_id":"initial-algebras-and-terminal-coalgebras-the-theory-of-fixed-points-of-functors-hardback-9781108835466","title":"Initial Algebras and Terminal Coalgebras; The Theory of Fixed Points of Functors (Hardback) 9781108835466","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eInitial Algebras and Terminal Coalgebras\u003c\/font\u003e\u003cbr\u003e\r\n\u003cfont size=\"5\"\u003eThe Theory of Fixed Points of Functors\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cem\u003eAn in-depth treatment of an active research area of theoretical computer science, presenting and extending its most important results.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eJiří Adámek (Author), Stefan Milius (Author), Lawrence S. Moss (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781108835466, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 6 February 2025\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e642 pages\u003cbr\u003e23.5 x 15.9 x 3.8 cm, 1.06 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003e'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\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eProviding 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.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e1. Introduction\u003cbr\u003e 2. Algebras and coalgebras\u003cbr\u003e 3. Finitary iteration\u003cbr\u003e 4. Finitary set functors\u003cbr\u003e 5. Finitary iteration in enriched settings\u003cbr\u003e 6. Transfinite iteration\u003cbr\u003e 7. Terminal coalgebras as algebras, initial algebras as coalgebras\u003cbr\u003e 8. Well-founded coalgebras\u003cbr\u003e 9. State minimality and well-pointed coalgebras\u003cbr\u003e 10. Fixed points determined by finite behaviour\u003cbr\u003e 11. Sufficient conditions for initial algebras and terminal coalgebras\u003cbr\u003e 12. Liftings and extensions from Set\u003cbr\u003e 13. Interaction between initial algebras and terminal coalgebras\u003cbr\u003e 14. Derived functors\u003cbr\u003e 15. Special topics\u003cbr\u003e A. Functors with initial algebras or terminal coalgebras\u003cbr\u003e B. A primer on fixed points in ordered and metric structures\u003cbr\u003e C. Set functors\u003cbr\u003e References\u003cbr\u003e Index of categories\u003cbr\u003e Subject index.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mathematical theory of computation [\u003ca title=\"See our other books on Mathematical theory of computation\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20theory%20of%20computation%20%5BUYA%5D%22\"\u003eUYA\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Brand New","offer_id":52502956540184,"sku":"9781108835466","price":124.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/files\/9781108835466i.jpg?v=1786321245","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/initial-algebras-and-terminal-coalgebras-the-theory-of-fixed-points-of-functors-hardback-9781108835466","provider":"Freshly Printed Books","version":"1.0","type":"link"}