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.
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Translated from Algebra i Logika, Vol. 61, No. 2, pp. 127-149, March-April, 2022. Russian DOI: https://doi.org/10.33048/alglog.2022.61.201.
To the 95th birthday of my teacher B. I. Plotkin
E. V. Aladova is supported by the ISF grants 1623/16, 1994/20, and by Gelbart Institute for Mathematical Sciences, Department of Mathematics, Bar-Ilan University, Israel
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Aladova, E.V. Method of Verbal Operations and Automorphisms of the Category of Free Algebras. Algebra Logic 61, 87–103 (2022). https://doi.org/10.1007/s10469-022-09679-7
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DOI: https://doi.org/10.1007/s10469-022-09679-7