On automorphisms of categories of universal algebras
  A new approach is suggested to characterize algebraically automorphisms of the category of free algebras of a given variety. It gives in many cases an answer to the problem set by the first of authors, if automorphisms of such a category are inner or not. This question is important for universal algebraic geometry [arXiv:math. GM\slash 0210187],[arXiv:math. GM\slash 0210194]. Most of results are actually valid for arbitrary categories with a represented forgetful functor. 
Boris Plotkin (Institute of Mathematics, Hebrew University, Jerusalem,   Israel) and Grigori Zhitomirski (Department of Math...