Representing endomorphisms and principal congruences

For every algebraU there is an algebraU ^* with (up to isomorphism) the same endomorphism, subalgebra and congruence structure as that ofU, for which every finitely generated subalgebra and every finitely generated congruence ofU ^* is singly generated. The theorem is proved in a somewhat more general category theoretic context.Presented by R. W. Quackenbush.This author's research was supported by an OTKA grant from Hungary.This author's research was supported by NSERC, The Natural Sciences and Engineering Research Council of Canada.