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Higher Segal Spaces: 2244 (Lecture Notes in Mathematics)
Tobias Dyckerhoff; Mikhail Kapranov (Author)
·
Springer
· Paperback
Higher Segal Spaces: 2244 (Lecture Notes in Mathematics) - Tobias Dyckerhoff; Mikhail Kapranov
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Synopsis "Higher Segal Spaces: 2244 (Lecture Notes in Mathematics)"
This monograph initiates a theory of new categorical structures that generalize the Segal property to higher dimensions. The authors introduce the notion of a d -Segal space, which is a... Leer másThis monograph initiates a theory of new categorical structures that generalize the 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 cyclic polytopes of dimension d. Focus here is on the case in dimension two. Many important constructions are shown to exhibit the 2-Segal property, including Waldhausen?s S-construction, Hecke algebras, configuration spaces of flags, and mapping class groups. By introducing a path space criterion, the authors verify that 2-Segal properties extend to ?-categories.Higher Segal Spaces marks the beginning of a program to study successively larger dimensions of Segal spaces. The elementary formulation of 2-Segal spaces in the opening chapters is accessible to readers with only a 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.
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The book is written in English.
The binding of this edition is Paperback.
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