Automorphisms of the category of free non-associative algebras with unit

Abstract

The goal of this paper is to describe the group of strongly stable automorphisms of the category of free finitely generated non-associative algebras with unit. The motivation of this research comes from universal algebraic geometry. From this perspective, our main result tells us what are the non-associative algebras with unit geometrically similar to a given one. The characterization of strongly stable automorphisms is provided by the method of verbal operations. We also specify some facts related to behavior of nullary operations on arbitrary algebraic structures.