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2014•Unpublished venueRequires access

Extending Chang's construction to the category of m-zeroids and some category containing the category of Abelian '-groups with strong unit

Joshua B. Palmatier

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Abstract

In this note we prove that it is impossible to extend the natural equivalence between the category of MV-algebras and the cat- egory of Abelian '-groups with strong unit described by C. C. Chang, 1958, and Cignoli & Mundici, 1997, to a natural equivalence between the category of m-zeroids and some category containing the category of Abelian '-groups with strong unit.

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What this paper is about

In this note we prove that it is impossible to extend the natural equivalence between the category of MV-algebras and the cat- egory of Abelian '-groups with strong unit described by C. C. Chang, 1958, and Cignoli & Mundici, 1997, to a natural equivalence between the category of m-zeroids and some category containing the category of Abelian '-groups with strong unit.

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Available abstract

In this note we prove that it is impossible to extend the natural equivalence between the category of MV-algebras and the cat- egory of Abelian '-groups with strong unit described by C. C. Chang, 1958, and Cignoli & Mundici, 1997, to a natural equivalence between the category of m-zeroids and some category containing the category of Abelian '-groups with strong unit.

Key concepts: Category of groups, Closed category, Abelian group, Mathematics, Abelian category, Unit (ring theory), Equivalence (formal languages), Category of sets

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