2004/03/23 by Grigori Zhitomirski, Zhitomirski, Grigori
Mathematics · #08A35 #18A99 (Primery) 08B20 #Category Theory (math.CT) #FOS: Mathematics #General Mathematics (math.GM) #math.CT #math.GM #msc:08A35 #msc:08B20 #msc:18A99
paper · pdf · doi:10.48550/arxiv.math/0403394
9 pages
arxiv created 2004/03/23 · arxiv updated 2009/12/01
Prof. Boris I. Plotkin [arXiv:math.GM/0210194, arXiv:math.GM/0204245] drew attention to the question when an equivalence between two categories is isomorphic as a functor to an isomorphism between them. It turns out that it is quite important for universal algebraical geometry and concerns mainly the categories Θ\sp 0 (X) of free universal algebras of some variety Θ free generated by finite subsets of X. In the paper, a complete answer to the Plotkin's question is given: there are no proper autoequivalences of the category Θ\sp 0 (X) . Also some connected problems are discussed.