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Isotropy Groups of Free Racks and Quandles (2010.09837v2)
Published 19 Oct 2020 in math.CT and math.GR
Abstract: In this article, 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.