J. Austral. Math. Soc.  72 (2002), 161-172
Mono-unary algebras are strongly dualizable

Jennifer Hyndman
  Department of Mathematics and Computer Science
  University of Northern British Columbia
  Prince George BC V2N 4Z9

We show that mono-unary algebras have rank at most two and are thus strongly dualizable. We provide an example of a strong duality for a mono-unary algebra using an alter ego with (partial) operations of arity at most two. This mono-unary algebra has rank two and generates the same quasivariety as an injective, hence rank one, mono-unary algebra.
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