{"product_id":"9789814425933","title":"Homological Algebra: In Strongly Non-abelian Settings: In Strongly Non-Abelian Settings","description":"\u003cp\u003eWe propose here a study of ‘semiexact’ and ‘homological' categories as a basis for a generalised homological algebra. Our aim is to extend the homological notions to deeply non-abelian situations, where satellites and spectral sequences can still be studied.\u003c\/p\u003e\u003cp\u003eThis is a sequel of a book on ‘Homological Algebra, The interplay of homology with distributive lattices and orthodox semigroups’, published by the same Editor, but can be read independently of the latter.\u003c\/p\u003e\u003cp\u003eThe previous book develops homological algebra in p-exact categories, i.e. exact categories in the sense of Puppe and Mitchell — a moderate generalisation of abelian categories that is nevertheless crucial for a theory of ‘coherence’ and ‘universal models’ of (even abelian) homological algebra. The main motivation of the present, much wider extension is that the exact sequences or spectral sequences produced by unstable homotopy theory cannot be dealt with in the previous framework.\u003c\/p\u003e\u003cp\u003eAccording to the present definitions, a \u003ci\u003esemiexact\u003c\/i\u003e category is a category equipped with an ideal of ‘null’ morphisms and provided with kernels and cokernels \u003ci\u003ewith respect to this ideal\u003c\/i\u003e. A \u003ci\u003ehomological\u003c\/i\u003e category satisfies some further conditions that allow the construction of subquotients and induced morphisms, in particular the homology of a chain complex or the spectral sequence of an exact couple.\u003c\/p\u003e\u003cp\u003eExtending abelian categories, and also the p-exact ones, these notions include the usual \u003ci\u003edomains\u003c\/i\u003e of homology and homotopy theories, e.g. the category of ‘pairs’ of topological spaces or groups; they also include their \u003ci\u003ecodomains\u003c\/i\u003e, since the sequences of homotopy ‘objects’ for a pair of pointed spaces or a fibration can be viewed as exact sequences in a homological category, whose objects are actions of groups on pointed sets.\u003c\/p\u003e\u003cp\u003eHomological Algebra: The Interplay of Homology with Distributive Lattices and Orthodox Semigroups\u003c\/p\u003e\u003cb\u003eContents:\u003c\/b\u003e\u003cul\u003e\n\u003cli\u003eIntroduction\u003c\/li\u003e\n\u003cli\u003eSemiexact categories\u003c\/li\u003e\n\u003cli\u003eHomological Categories\u003c\/li\u003e\n\u003cli\u003eSubquotients, Homology and Exact Couples\u003c\/li\u003e\n\u003cli\u003eSatellites\u003c\/li\u003e\n\u003cli\u003eUniversal Constructions\u003c\/li\u003e\n\u003cli\u003eApplications to Algebraic Topology\u003c\/li\u003e\n\u003cli\u003eHomological Theories and Biuniversal Models\u003c\/li\u003e\n\u003cli\u003eAppendix A. Some Points of Category Theory\u003c\/li\u003e\n\u003c\/ul\u003e\u003cbr\u003e\u003cb\u003eReadership:\u003c\/b\u003e Graduate students, professors and researchers in pure mathematics, in particular category theory and algebraic topology.\u003cbr\u003e","brand":"World Scientific Publishing Company, Incorporated","offers":[{"title":"Default Title","offer_id":47140004495600,"sku":"9789814425933","price":51.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0737\/7593\/9824\/files\/9789814425933_p0.jpg?v=1763690838","url":"https:\/\/shop-qa.barnesandnoble.com\/products\/9789814425933","provider":"Barnes \u0026 Noble (DEV)","version":"1.0","type":"link"}