{"product_id":"abelian-model-category-theory-hardback-9781009449465","title":"Abelian Model Category Theory (Hardback) 9781009449465","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eAbelian Model Category Theory\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eBridges the gap between traditional methods of homological algebra and Quillen's abstract notion of model category structures.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eJames Gillespie (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781009449465, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 2 January 2025\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e438 pages\u003cbr\u003e23.5 x 16 x 3 cm, 0.742 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eOffering a unique resource for advanced graduate students and researchers, this book treats the fundamentals of Quillen model structures on abelian and exact categories. Building the subject from the ground up using cotorsion pairs, it develops the special properties enjoyed by the homotopy category of such abelian model structures. A central result is that the homotopy category of any abelian model structure is triangulated and characterized by a suitable universal property – it is the triangulated localization with respect to the class of trivial objects. The book also treats derived functors and monoidal model categories from this perspective, showing how to construct tensor triangulated categories from cotorsion pairs. For researchers and graduate students in algebra, topology, representation theory, and category theory, this book offers clear explanations of difficult model category methods that are increasingly being used in contemporary research.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eIntroduction and main examples: 1. Additive and exact categories\u003cbr\u003e 2. Cotorsion pairs\u003cbr\u003e 3. Stable categories from cotorsion pairs\u003cbr\u003e 4. Hovey triples and abelian model structures\u003cbr\u003e 5. The homotopy category of an abelian model structure\u003cbr\u003e 6. The triangulated homotopy category\u003cbr\u003e 7. Derived functors and abelian monoidal model structures\u003cbr\u003e 8. Hereditary model structures\u003cbr\u003e 9. Constructing complete cotorsion pairs\u003cbr\u003e 10. Abelian model structures on chain complexes\u003cbr\u003e 11. Mixed model structures and examples\u003cbr\u003e 12. Cofibrant generation and well-generated homotopy categories\u003cbr\u003e A. Hovey's correspondence for general exact categories\u003cbr\u003e B. Right and left homotopy relations\u003cbr\u003e C. Bibliographical notes\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":52475051901208,"sku":"9781009449465","price":53.89,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/files\/9781009449465i.jpg?v=1785803726","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/abelian-model-category-theory-hardback-9781009449465","provider":"Freshly Printed Books","version":"1.0","type":"link"}