Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dendriform Algebras Relative to a Semigroup   Loday's dendriform algebras and its siblings pre-Lie and zinbiel have
received attention over the past two decades. In recent literature, there has
been interest in a generalization of these types of algebra in which each
individual operation is replaced by a family of operations indexed by a fixed
semigroup $S$. The purpose of this note is twofold. First, we add to the
existing work by showing that a similar extension is possible already for the
most familiar types of algebra: commutative, associative, and Lie. Second, we
show that these concepts arise naturally and in a unified manner from a
categorical perspective. For this, one simply has to consider the standard
types of algebra but in reference to the monoidal category of $S$-graded vector
spaces.

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The categories of this paper are: mtrl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: quant-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: cs
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The categories of this paper are: physics
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The categories of this paper are: astro-ph
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The categories of this paper are: econ
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The categories of this paper are: q-fin
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: supr-con
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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
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The categories of this paper are: math-ph