On algebras over multicategories

S. N. Tronin

Chair of Algebra and Mathematical Logic, Kazan (Volga Region) Federal University, 18 Kremlyovskaya str., Kazan, 420008 Russia

Abstract: We introduce a notion of a monoidal category over verbal category. In such categories we define algebras over multicategories over the same verbal categories. We also explicitly compute categories of algebras for two classes of multicategories.

Keywords: verbal category, multicategory, multifunctor, natural multitransformation, algebra over multicategory, commutative operad.

UDC: 512.565

Received: 08.07.2014

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2016, 60:2, 52–61

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