关于范畴自等价的几点注记
Some remarks on autoequivalences of categories
摘要：
Boris I教授Plotkin [arXiv：math.GM/0210194，arXiv：math.GM/0204245]提请注意当两个范畴之间的等价作为函子同构于它们之间的同构时的问题。证明了它在泛代数几何中是十分重要的，并且主要涉及由$X$的有限子集自由生成的自由泛代数范畴$Θ\sp 0 (X) $的某些簇$Θ$.本文给出了Plotkin问题的一个完整回答：范畴$Θ\sp 0 (X) $不存在真自等价.并对相关问题进行了讨论。
英文摘要：
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.
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