Dendriform algebras relative to a semigroup. (English) Zbl 1472.18012
Recently, numerous generalizations of Rota-Baxter algebras and dendriform algebras appear, where one or two parameters belonging to a semigroup are used: these are family algebras. This paper first shows that similar objects exist for associative, associative commutative, Lie, and many other types of algebras. It then gives a categorical interpretation of these objects: it is shown that they are in fact classical objects in a monoidal category of graded objects over the chosen monoid, satisfying a uniformity condition.
Reviewer: Loïc Foissy (Calais)
MSC:
| 18M05 | Monoidal categories, symmetric monoidal categories |
| 17A30 | Nonassociative algebras satisfying other identities |
| 18C40 | Structured objects in a category (group objects, etc.) |
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