This article is cited in 5 papers

Multicategories and varieties of many-sorted algebras

S. N. Tronin

Kazan State University, Faculty of Mechanics and Mathematics

Abstract: We give a direct proof of the fact that every variety of many-sorted universal algebras is rationally equivalent to a variety of algebras over some FSet-multicategory (a many-sorted analog of FSet-operads). The construction of this multicategory is straightforward and uses the free algebras of the given variety.

Keywords: many-sorted algebra, multicategory, free algebra, variety, rational equivalence.

UDC: 512

Received: 20.02.2007

 English version: Siberian Mathematical Journal, 2008, 49:5, 944–958

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