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• W1520461343 abstract "This is the first paper in a series on new higher categorical structures called higher Segal spaces. For every d > 0, we 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. In the case d=1, we recover Rezk's theory of Segal spaces. The present paper focuses on 2-Segal spaces. The starting point of the theory is the observation that Hall algebras, as previously studied, are only the shadow of a much richer structure governed by a system of higher coherences captured in the datum of a 2-Segal space. This 2-Segal space is given by Waldhausen's S-construction, a simplicial space familiar in algebraic K-theory. Other examples of 2-Segal spaces arise naturally in classical topics such as Hecke algebras, cyclic bar constructions, configuration spaces of flags, solutions of the pentagon equation, and mapping class groups." @default.
• W1520461343 created "2016-06-24" @default.
• W1520461343 creator A5027075877 @default.
• W1520461343 creator A5048007436 @default.
• W1520461343 date "2019-01-01" @default.
• W1520461343 modified "2023-10-10" @default.
• W1520461343 title "Higher Segal Spaces" @default.
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• W1520461343 doi "https://doi.org/10.1007/978-3-030-27124-4" @default.
• W1520461343 hasPublicationYear "2019" @default.
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