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Dendriform Algebras Relative to a Semigroup
Symmetry, integrability and geometry: methods and applications, Tome 16 (2020) Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: dendriform algebra, monoidal category, dimonoidal category. 
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     author = {Marcelo Aguiar},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2020_16_a65/}
}
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Marcelo Aguiar. Dendriform Algebras Relative to a Semigroup. Symmetry, integrability and geometry: methods and applications, Tome 16 (2020). http://geodesic.mathdoc.fr/item/SIGMA_2020_16_a65/

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