Geodesic
Method of verbal operations and automorphisms of the category of free algebras
Algebra i logika, Tome 61 (2022) no. 2, pp. 127-149.

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Let an arbitrary variety of algebras and the category of all free finitely generated algebras in that variety be given. This paper is the second in a series of papers started in [Algebra and Logic, 61, No. 1, 1—15 (2022)] where we deal with automorphisms of the category of free finitely generated algebras. Here we describe in detail a method of verbal operations. The method provides a characterization of automorphisms of the category of all free finitely generated algebras in a given variety. The characterization plays a crucial role in universal algebraic geometry. We supply the reader with illuminating examples which clarify the method.
Keywords: variety of algebras, category of free finitely generated algebras, universal algebraic geometry over arbitrary variety of algebras, group of automorphisms, method of verbal operations. 
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E. V. Aladova. Method of verbal operations and automorphisms of the category of free algebras. Algebra i logika, Tome 61 (2022) no. 2, pp. 127-149. http://geodesic.mathdoc.fr/item/AL_2022_61_2_a0/

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