Outer Automorphisms of the Category of Free Non-Associative Algebras with Unit

The goal of this paper is to describe the group of outer automorphisms of the category of free finitely generated algebras with unit for the variety of non-associative algebras and for some of its subvarieties, in particular for the varieties of commutative, Jordan, alternative and power associative algebras. The motivation of this research is tightly connected with some problems in Universal Algebraic Geometry. More precisely, the group of outer automorphisms measures the difference between two types of geometric equivalences of algebras.