Some remarks on autoequivalences of categories
Abstract
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 0 (X) of free universal algebras of some variety 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 0 (X) . Also some connected problems are discussed.
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