HOMOMORPHISMS OF UNARY ALGEBRAS WITH A GIVEN QUOTIENT

For a unary algebra A with κ≥2 fundamental operations, let H(A) denote the class of all unary algebras that have a homomorphisrn into A, and let the class Q(A) consist of all algebras having A as one of their quotients. If A is freely indecomposable then H(A) and Q(A) are shown to be categorically universal if and only if either class contains a rigid algebra; this, in turn, is equivalent to the absence of homomorphisms from A into a free algebra. © 1990 Birkhäuser Verlag.