Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Higher Segal spaces I   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.

26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom