IJPAM: Volume 78, No. 2 (2012)

CARTESIAN CLOSED ALGEBRAIC CATEGORIES

Vijaya L. Gompa
Professor and Chair
Department of Mathematics
Troy University-Dothan Campus
P.O. Box 8368, Dothan, Alabama, 36304, USA


Abstract. It is well known that the category $Alg(1)$ of all universal algebras with one unary operation is cartesian closed. We extend this result for the category $Alg(\Sigma)$ of universal algebras of a fixed type $\Sigma $ all of whose operations are unary. That is, we show that the category $Alg(\Sigma)$ is cartesian closed. In fact, we characterize some cartesian closed full isomorphism closed subcategories of $Alg(\Sigma)$ using a concept called $T$-friendly.

Received: March 13, 2012

AMS Subject Classification: 08A25, 08A60, 08A30, 08C05, 17A30, 18A40, 18B99, 18D15, 54A05

Key Words and Phrases: topological category, topological functors, universal algebra, topological algebra, cartesian closed, canonical function spaces

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 78
Issue: 2