Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quiver-theoretical approach to dynamical Yang-Baxter maps   A dynamical Yang-Baxter map, introduced by Shibukawa, is a solution of the
set-theoretical analogue of the dynamical Yang-Baxter equation. In this paper,
we initiate a quiver-theoretical approach for the study of dynamical
Yang-Baxter maps. Our key observation is that the category of dynamical sets
over a set $\Lambda$, introduced by Shibukawa to establish a categorical
framework to deal with dynamical Yang-Baxter maps, can be embedded into the
category of quivers with vertices $\Lambda$. By using this embedding, we shed
light on Shibukawa's classification result of a certain class of dynamical
Yang-Baxter maps and extend his construction to obtain a new class of dynamical
Yang-Baxter maps. We also discuss a relation between Shibukawa's bialgebroid
associated to a dynamical Yang-Baxter map and Hayashi's weak bialgebra
associated to a star-triangular face model.

1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org