In this paper, we characterize the (covariant) isotropy groups of free, finitely generated racks and quandles. As a consequence, we show that the usual inner automorphisms of such racks and quandles are precisely those automorphisms that are “coherently extendible”. We then use this result to compute the global isotropy groups of the categories of racks and quandles, i.e. the automorphism groups of the identity functors of these categories.

中文翻译：

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自由架和 quandles 的各向同性群

在本文中，我们描述了自由的、有限生成的机架和四边形的（协变）各向同性群。因此，我们展示了这些 racks 和 quandles 的通常内部自同构正是那些“连贯可扩展”的自同构。然后我们使用这个结果来计算齿条和四边形类别的全局各向同性群，即这些类别的恒等函子的自同构群。