Automorphisms of categories of free algebras of some varieties

Let be a variety of universal algebras. We suggest a method for describing automorphisms of the category of free -algebras. All automorphisms of such categories are found in two cases: (1) is the variety of all associative K-algebras over an infinite field K; (2) is the variety of all representations of groups in unital R-modules over a commutative associative ring R with unit. We prove that all these automorphisms are close to inner automorphisms.