Endofunctors of quandles and racks

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.

KEYWORDS:

• Algebraic theories
• quandles
• racks

2000 MATHEMATICS SUBJECT CLASSIFICATION:

• 18C10
• 20N02
• 57M27

Acknowledgments

I thank M. Szymik and an anonymous referee for comments on a draft of this note.