On automorphisms of categories of free algebras of some varieties
  Given 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. 
Boris Plotkin (Institute of Mathematics, Hebrew University, Jerusalem,   Israel) and Grigori Zhitomirski (Department of Math...