{"product_id":"higher-segal-spaces-paperback","title":"Higher Segal Spaces - Paperback","description":"\u003cp\u003eby \u003cb\u003eTobias Dyckerhoff\u003c\/b\u003e (Author), \u003cb\u003eMikhail Kapranov\u003c\/b\u003e (Author)\u003c\/p\u003e\u003cp\u003e1. Preliminaries.- 2. Topological 1-Segal and 2-Segal Spaces.- 3. Discrete 2-Segal Spaces.- 4. Model Categories and Bousfield localization.- 5. The 1-Segal and 2-Segal model structures.- 6. The path space criterion for 2-Segal Spaces.- 7. 2-Segal Spaces from higher categories.- 8. Hall Algebras associated to 2-Segal Spaces.- 9. Hall (∞,2)-Categories.- 10. An (∞,2)-categorical theory of Spans.- 11. 2-segal Spaces as monads in bispans App.- A: Bicategories.\u003c\/p\u003e\u003ch3\u003eBack Jacket\u003c\/h3\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThis monograph initiates a theory of new categorical structures that generalize the simplicial Segal property to higher dimensions. The authors introduce the notion of a \u003ci\u003ed\u003c\/i\u003e-Segal space, which is a simplicial space satisfying locality conditions related to triangulations of \u003ci\u003ed\u003c\/i\u003e-dimensional cyclic polytopes. Focus here is on the 2-dimensional case. Many important constructions are shown to exhibit the 2-Segal property, including Waldhausen's S-construction, Hecke-Waldhausen constructions, and configuration spaces of flags. The relevance of 2-Segal spaces in the study of Hall and Hecke algebras is discussed.\u003c\/p\u003e\u003cp\u003e\u003ci\u003eHigher Segal Spaces\u003c\/i\u003e marks the beginning of a program to systematically study \u003ci\u003ed\u003c\/i\u003e-Segal spaces in all dimensions \u003ci\u003ed\u003c\/i\u003e. The elementary formulation of 2-Segal spaces in the opening chapters is accessible to readers with a basic background in homotopy theory. A chapter on Bousfield localizations provides a transition to the general theory, formulated in terms of combinatorial model categories, that features in the main part of the book. Numerous examples throughout assist readers entering this exciting field to move toward active research; established researchers in the area will appreciate this work as a reference.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003ch3\u003eAuthor Biography\u003c\/h3\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003eTobias Dyckerhoff\u003c\/b\u003e is Lichtenberg Professor of Mathematics at the University of Hamburg, Germany. His research interests are centered on higher structures in algebra and geometry, and extend to mathematical physics.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eMikhail Kapranov\u003c\/b\u003e is Professor of Mathematics at the Kavli Institute for the Physics and Mathematics of the Universe in Japan. His research spans algebra, algebraic geometry and category theory, with a particular interest in using category theory to extend ideas at the interface of algebra and geometry. His previous books include \u003ci\u003eDiscriminants, Resultants, and Multidimensional Determinants\u003c\/i\u003e, with I. M. Gelfand and A. V. Zelevinsky, a Modern Birkhäuser Classic.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 218\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 0.5 x 9.21 x 6.14 IN\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003eIllustrated:\u003c\/strong\u003e Yes\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e October 18, 2019\u003c\/div\u003e","brand":"Books by splitShops","offers":[{"title":"Default Title","offer_id":42711399039039,"sku":"9783030271220","price":106.9,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0105\/8226\/1823\/files\/a038aaca277001b315c96cb06e31c31e.webp?v=1765058364","url":"https:\/\/dhlswag.com\/products\/higher-segal-spaces-paperback","provider":"BBB","version":"1.0","type":"link"}