LEADER 03909nam 22006255 450 001 9910349327603321 005 20251116220404.0 010 $a3-030-27124-2 024 7 $a10.1007/978-3-030-27124-4 035 $a(CKB)4100000009606180 035 $a(MiAaPQ)EBC5963092 035 $a(DE-He213)978-3-030-27124-4 035 $a(PPN)241115256 035 $a(EXLCZ)994100000009606180 100 $a20191017d2019 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aHigher Segal Spaces /$fby Tobias Dyckerhoff, Mikhail Kapranov 205 $a1st ed. 2019. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2019. 215 $a1 online resource (xv, 218 pages) $cillustrations 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v2244 311 08$a3-030-27122-6 320 $aIncludes bibliographical references. 327 $a1. 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. 330 $aThis monograph initiates a theory of new categorical structures that generalize the simplicial Segal property to higher dimensions. The authors introduce the notion of a d-Segal space, which is a simplicial space satisfying locality conditions related to triangulations of d-dimensional cyclic polytopes. Focus here is on the 2-dimensional case. Many important constructions are shown to exhibit the 2-Segal property, including Waldhausen?s S-construction, Hecke-Waldhausen constructions, and configuration spaces of flags. The relevance of 2-Segal spaces in the study of Hall and Hecke algebras is discussed. Higher Segal Spaces marks the beginning of a program to systematically study d-Segal spaces in all dimensions d. The elementary formulation of 2-Segal spaces in the opening chapters is accessible to readers with a basic background in homotopy theory. A chapter on Bousfield localizations provides a transition to the general theory, formulated in terms of combinatorial model categories, that features in the main part of the book. Numerous examples throughout assist readers entering this exciting field to move toward active research; established researchers in the area will appreciate this work as a reference. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v2244 606 $aCategories (Mathematics) 606 $aAlgebra, Homological 606 $aK-theory 606 $aAlgebraic topology 606 $aCategory Theory, Homological Algebra$3https://scigraph.springernature.com/ontologies/product-market-codes/M11035 606 $aK-Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M11086 606 $aAlgebraic Topology$3https://scigraph.springernature.com/ontologies/product-market-codes/M28019 615 0$aCategories (Mathematics) 615 0$aAlgebra, Homological. 615 0$aK-theory. 615 0$aAlgebraic topology. 615 14$aCategory Theory, Homological Algebra. 615 24$aK-Theory. 615 24$aAlgebraic Topology. 676 $a514.23 676 $a512.6 700 $aDyckerhoff$b Tobias$4aut$4http://id.loc.gov/vocabulary/relators/aut$0769122 702 $aKapranov$b M. M$g(Mikhail M.),$f1962-$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910349327603321 996 $aHigher Segal Spaces$92525168 997 $aUNINA