2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/108865In this paper, we prove that all automorphisms of categories of free S-acts are semi-inner, which solves a variation of a well known B. Plotkin's problem in the case of monoids. We also give a description of automorphisms of categories of finitely generated free algebras of varieties of unary algebras, and show that among varieties of unary algebras only the variety of mono-unary algebras is perfect.Rings and Algebras08A60, 20M30, 20M99 (Primary); 08A35, 08C05, 20M50 (Secondary)text