2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73906Given a variety of universal algebras. A method is suggested for describing automorphisms of a category of free algebras of this variety. Applying this general method all automorphisms of such categories are found in two cases: 1) for the variety of all free associative K-algebras over an infinite field K and 2) for the variety of all representations of groups in unital R-modules over a commutative associative ring R with unit. It turns out that they are almost inner in a sense.32 pages. Continuation of math.CT/0411408, 2004Rings and AlgebrasCategory Theory08B20, 03C05,16B50,20C07text