Abstract. The paper investigates the degree of categorical non-universality of the class of monounary algebras. It characterizes algebras whose endomorphisms are invertible, describes all abelian automorphism groups of monounary algebras and then represents each such group as the automorphism group by a proper class of pairwise non-isomorphic monounary algebras, and lists the isomorphism types of their commutative endomorphism monoids.

AMS Subject Classification (1991): 08A60, 08A35, 08C05

Keyword(s): monounary algebra, endomorphism monoid, automorphism group

Received June 16, 1997 and in revised form September 4, 1997. (Registered under 2642/2009.)