Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Political structures and the topology of simplicial complexes   We use the topology of simplicial complexes to model political structures
following [1]. Simplicial complexes are a natural tool to encode interactions
in the structures since a simplex can be used to represent a subset of
compatible agents. We translate the wedge, cone, and suspension operations into
the language of political structures and show how these constructions
correspond to merging structures and introducing mediators. We introduce the
notions of the viability of an agent and the stability of a political system
and examine their interplay with the simplicial complex topology, casting their
interactions in category-theoretic language whenever possible. We introduce a
refinement of the model by assigning weights to simplices corresponding to the
number of issues the agents agree on. In addition, homology of simplicial
complexes is used to detect non-viabilities, certain cycles of incompatible
agents, and the (non)presence of mediators. Finally, we extend some results
from [1], bringing viability and stability into the language of friendly
delegations and using homology to examine the existence of R-compromises and
D-compromises.

7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess