On Profinite Quandles

Abstract: We undertake the study of profinite quandles. We provide several constructions of profinite quandles from profinite groups, and from other profinite quandle. We characterize which subquandles of profinite quandles are again profinite. Finally, we provide a characterization of algebraically connected profinite quandles in terms of the profinite completion of their inner automorphism groups $\widehat{\Inn(Q)}$. It is anticipated that the results herein will find applications to the \'{e}tale homotopy theory of number fields. v.2 has been updated to include an example due to Ariel Davis settling in the negative the question of whether all Stone topological quandles are profinite.