Higher Segal Spaces

• Main Authors: Dyckerhoff, Tobias (Author, http://id.loc.gov/vocabulary/relators/aut), Kapranov, Mikhail (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2019.
• Edition: 1st ed. 2019.
• Series: Lecture Notes in Mathematics, 2244
• Subjects: Category theory (Mathematics).; Homological algebra.; K-theory.; Algebraic topology.; Category Theory, Homological Algebra.; K-Theory.; Algebraic Topology.

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 polyto...

Table of Contents:

• 1. 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.