ON AUTOMORPHISMS OF CATEGORIES OF UNIVERSAL ALGEBRAS

Let [Formula: see text] be a variety of universal algebras. We suggest an approach for describing automorphisms of a category [Formula: see text] of free [Formula: see text]-algebras. In particular, this approach allows us to answer the question: is an automorphism of such a category inner? Most of the results actually deal with arbitrary categories supplied with a represented forgetful functor.