Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Colimits, Stanley-Reisner algebras, and loop spaces   We study diagrams associated with a finite simplicial complex K, in various
algebraic and topological categories. We relate their colimits to familiar
structures in algebra, combinatorics, geometry and topology. These include:
right-angled Artin and Coxeter groups (and their complex analogues, which we
call circulation groups); Stanley-Reisner algebras and coalgebras; Davis and
Januszkiewicz's spaces DJ(K) associated with toric manifolds and their
generalisations; and coordinate subspace arrangements. When K is a flag
complex, we extend well-known results on Artin and Coxeter groups by confirming
that the relevant circulation group is homotopy equivalent to the space of
loops $\Omega DJ(K)$. We define homotopy colimits for diagrams of topological
monoids and topological groups, and show they commute with the formation of
classifying spaces in a suitably generalised sense. We deduce that the homotopy
colimit of the appropriate diagram of topological groups is a model for $\Omega
DJ(K)$ for an arbitrary complex K, and that the natural projection onto the
original colimit is a homotopy equivalence when K is flag. In this case, the
two models are compatible.

25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex