Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalized Rota-Baxter systems   Rota-Baxter systems of T. Brzezi\'{n}ski are a generalization of Rota-Baxter
operators that are related to dendriform structures, associative Yang-Baxter
pairs and covariant bialgebras. In this paper, we consider Rota-Baxter systems
in the presence of bimodule, which we call generalized Rota-Baxter systems. We
define a graded Lie algebra whose Maurer-Cartan elements are generalized
Rota-Baxter systems. This allows us to define a cohomology theory for a
generalized Rota-Baxter system. Formal one-parameter deformations of
generalized Rota-Baxter systems are discussed from cohomological points of
view. We further study Rota-Baxter systems, associative Yang-Baxter pairs,
covariant bialgebras and introduce generalized averaging systems that are
related to associative dialgebras. Next, we define generalized Rota-Baxter
systems in the homotopy context and find relations with homotopy dendriform
algebras. The paper ends by considering commuting Rota-Baxter systems and their
relation with quadri-algebras.

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The categories of this paper are: eess
34
The categories of this paper are: chem-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas
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The categories of this paper are: quant-ph
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The categories of this paper are: econ
5
The categories of this paper are: gr-qc
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The categories of this paper are: funct-an
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The categories of this paper are: nlin
3
The categories of this paper are: physics
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The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: adap-org
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The categories of this paper are: plasm-ph