Automorphisms of categories of free algebras of varieties

Let Theta be an arbitrary variety of algebras and let Theta(0) be the category of all free finitely generated algebras from Theta. We study automorphisms of such categories for special Theta. The cases of the varieties of all groups, all semigroups, all modules over a noetherian ring, all associative and commutative algebras over a field are completely investigated. The cases of associative and Lie algebras are also considered. This topic relates to algebraic geometry in arbitrary variety of algebras Theta.