We prove that every small strongly connected category *k* has a full
embedding preserving all limits existing in *k* into a category
of unary universal algebras. The number of unary operations
can be restricted to |mor *k*| in case when *k* has a terminal
object and only preservation of limits over finitely many
objects is desired. And all limits existing in such a category *k*
are preserved by a full embedding of *k* into the category of
all algebraic systems with |mor *k*| unary operation and one unary
relation.

Keywords: universal algebra, unary algebra, limit, full embedding, limit preserving functor

2000 MSC: Primary: 08B25, Secondary: 18B15

*Theory and Applications of Categories,*
Vol. 21, 2008,
No. 2, pp 21-36.

http://www.tac.mta.ca/tac/volumes/21/2/21-02.dvi

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http://www.tac.mta.ca/tac/volumes/21/2/21-02.pdf

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/21/2/21-02.dvi

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