TL;DR
This paper characterizes all endofunctors of the category of quandles that commute with the forgetful functor, showing they are precisely the power operations, and provides a similar result for racks.
Contribution
It identifies the only endofunctors commuting with the forgetful functor in the categories of quandles and racks, revealing their structure as power operations.
Findings
Endofunctors of quandles are exactly the power operations.
Similar characterization holds for racks.
Provides a complete description of these endofunctors.
Abstract
We show that the only endofunctors of the category of quandles commuting with the forgetful functor to sets are the power operations. We also give a similar statement for racks.
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