Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ordered Exchange Graphs   The exchange graph of a cluster algebra encodes the combinatorics of
mutations of clusters. Through the recent "categorifications" of cluster
algebras using representation theory one obtains a whole variety of exchange
graphs associated with objects such as a finite-dimensional algebra or a
differential graded algebra concentrated in non-positive degrees. These
constructions often come from variations of the concept of tilting, the
vertices of the exchange graph being torsion pairs, t-structures, silting
objects, support $\tau$-tilting modules and so on. All these exchange graphs
stemming from representation theory have the additional feature that they are
the Hasse quiver of a partial order which is naturally defined for the objects.
In this sense, the exchange graphs studied in this article can be considered as
a generalization or as a completion of the poset of tilting modules which has
been studied by Happel and Unger. The goal of this article is to axiomatize the
thus obtained structure of an ordered exchange graph, to present the various
constructions of ordered exchange graphs and to relate them among each other.

23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th