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Higher Segal Spaces (Paperback, 1st ed. 2019)
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Higher Segal Spaces (Paperback, 1st ed. 2019)
Series: Lecture Notes in Mathematics, 2244
Expected to ship within 10 - 15 working days
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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.
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