{"product_id":"grothendieck-construction-of-bipermutative-indexed-categories","title":"Grothendieck Construction of Bipermutative-Indexed Categories","description":"\u003cp\u003eThe Grothendieck construction provides an explicit link between indexed categories and opfibrations. It is a fundamental concept in category theory and related fields with far-reaching applications. Bipermutative categories are categorifications of rings. They play a central role in algebraic \u003ci\u003eK\u003c\/i\u003e-theory and infinite loop space theory.\u003c\/p\u003e\u003cp\u003eThis monograph is a detailed study of the Grothendieck construction over a bipermutative category in the context of categorically enriched multicategories, with new and important applications to inverse \u003ci\u003eK\u003c\/i\u003e-theory and pseudo symmetric \u003ci\u003eE\u003c\/i\u003e∞-algebras. After carefully recalling preliminaries in enriched categories, bipermutative categories, and enriched multicategories, we show that the Grothendieck construction over a small tight bipermutative category is a pseudo symmetric Cat-multifunctor and generally not a Cat-multifunctor in the symmetric sense.\u003c\/p\u003e\u003cp\u003ePseudo symmetry of Cat-multifunctors is a new concept we introduce in this work.\u003c\/p\u003e\u003cp\u003eThe following features make it accessible as a graduate text or reference for experts:\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eComplete definitions and proofs\u003c\/li\u003e\n\u003cli\u003eSelf-contained background. Parts of Chapters 1–3, 7, 9, and 10 contain background material from the research literature\u003c\/li\u003e\n\u003cli\u003eExtensive cross-references\u003c\/li\u003e\n\u003cli\u003eConnections between chapters. Each chapter has its own introduction discussing not only the topics of that chapter but also its connection with other chapters\u003c\/li\u003e\n\u003cli\u003eOpen questions. Appendix A contains open questions that arise from the material in the text and are suitable for graduate students\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eThis book is suitable for graduate students and researchers with an interest in category theory, algebraic \u003ci\u003eK\u003c\/i\u003e-theory, homotopy theory, and related fields. The presentation is thorough and self-contained, with complete details and background material for non-expert readers.\u003c\/p\u003e","brand":"Taylor \u0026 Francis Ltd","offers":[{"title":"Default Title","offer_id":54236730687832,"sku":"9781032584041","price":167.4,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0278\/1295\/4195\/files\/9781032584041_50cb1a1a-5e7f-4256-b08d-ee6c2ab6bc45.jpg?v=1780992945","url":"https:\/\/agendabookshop.com\/products\/grothendieck-construction-of-bipermutative-indexed-categories","provider":"Agenda Bookshop","version":"1.0","type":"link"}