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.