Higher segal spaces [Documento eletrónico] / Tobias Dyckerhoff, Mikhail Kapranov
Language: eng.Country: Switzerland, Swiss Confederation, Cham.Publication: Cham : Springer International Publishing, 2019Description: XV, 218 p. : il.ISBN: 978-3-030-27124-4.Series: Lecture Notes in Mathematics, vol. 2244Subject - Topical Name: Algebra, Homological | K -- theory | Algebraic topology Online Resources:Click here to access onlineItem type | Current library | Collection | Call number | Copy number | Status | Date due | Barcode | |
---|---|---|---|---|---|---|---|---|
E-Books | Biblioteca NOVA FCT Online | Não Ficção | QA169.SPR FCT (Browse shelf(Opens below)) | 1 | Available | 96224 |
Browsing Biblioteca NOVA FCT shelves, Shelving location: Online, Collection: Não Ficção Close shelf browser (Hides shelf browser)
QA169.SPR FCT Temporal type theory, a topos-theoretic approach to systems and behavior | QA169.SPR FCT Effective kan fibrations in simplicial sets | QA169.SPR FCT Simplicial methods for higher categories, segal-type models of weak n-categories | QA169.SPR FCT Higher segal spaces | QA169.SPR FCT Involutive category theory | QA169.SPR FCT Introduction to infinity-categories | QA169.SPR FCT Lie methods in deformation theory |
This 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.
There are no comments on this title.