{"product_id":"introduction-to-homotopy-type-theory-hardback-9781108844161","title":"Introduction to Homotopy Type Theory (Hardback) 9781108844161","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eIntroduction to Homotopy Type Theory\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eAn essential and up-to-date introduction to homotopy type theory with minimal prerequisites and over 200 exercises.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eEgbert Rijke (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781108844161, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 6 November 2025\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e386 pages\u003cbr\u003e22.9 x 15.2 x 2.2 cm, 0.734 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'The book of Egbert Rijke is a friendly introduction to Homotopy Type Theory (HoTT), a formal system for a new foundation of mathematics based on type theory, instead of set theory. Martin-Löf Type Theory (MLTT) is presented in the first part of the book, and HoTT in the second part by adding Voevodsky's univalence axiom and general inductive types. The last chapter is devoted to the construction and study of the logical circle. The development of HoTT can be traced back to the discovery of the topological interpretation of MLTT by Awodey-Warren and Voevodsky. But the fact that this interpretation is seldom discussed in the book can be surprising to the reader. But I confess that my understanding of HoTT was greatly improved by reading the book as it stands. It contains a set of well-chosen exercises. The logical circle in the last chapter is a revolutionary application.' André Joyal, Université du Québec à Montréal\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eThis up-to-date introduction to type theory and homotopy type theory will be essential reading for advanced undergraduate and graduate students interested in the foundations and formalization of mathematics. The book begins with a thorough and self-contained introduction to dependent type theory. No prior knowledge of type theory is required. The second part gradually introduces the key concepts of homotopy type theory: equivalences, the fundamental theorem of identity types, truncation levels, and the univalence axiom. This prepares the reader to study a variety of subjects from a univalent point of view, including sets, groups, combinatorics, and well-founded trees. The final part introduces the idea of higher inductive type by discussing the circle and its universal cover. Each part is structured into bite-size chapters, each the length of a lecture, and over 200 exercises provide ample practice material.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePreface\u003cbr\u003e Introduction\u003cbr\u003e Part I. Martin-Löf's Dependent Type Theory: 1. Dependent type theory\u003cbr\u003e 2. Dependent function types\u003cbr\u003e 3. The natural numbers\u003cbr\u003e 4. More inductive types\u003cbr\u003e 5. Identity types\u003cbr\u003e 6. Universes\u003cbr\u003e 7. Modular arithmetic via the Curry-Howard interpretation\u003cbr\u003e 8. Decidability in elementary number theory\u003cbr\u003e Part II. The Univalent Foundations of Mathematics: 9. Equivalences\u003cbr\u003e 10. Contractible types and contractible maps\u003cbr\u003e 11. The fundamental theorem of identity types\u003cbr\u003e 12. Propositions, sets, and the higher truncation levels\u003cbr\u003e 13. Function extensionality\u003cbr\u003e 14. Propositional truncations\u003cbr\u003e 15. Image factorizations\u003cbr\u003e 16. Finite types\u003cbr\u003e 17. The univalence axiom\u003cbr\u003e 18. Set quotients\u003cbr\u003e 19. Groups in univalent mathematics\u003cbr\u003e 20. General inductive types\u003cbr\u003e Part III. The Circle: 21. The circle\u003cbr\u003e 22. The universal cover of the circle\u003cbr\u003e References\u003cbr\u003e Index.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mathematical foundations [\u003ca title=\"See our other books on Mathematical foundations\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20foundations%20%5BPBC%5D%22\"\u003ePBC\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":52460656918808,"sku":"9781108844161","price":42.19,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/files\/9781108844161i.jpg?v=1785456964","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/introduction-to-homotopy-type-theory-hardback-9781108844161","provider":"Freshly Printed Books","version":"1.0","type":"link"}