A functor-valued extension of knot quandles

Abstract

For an oriented knot K, we construct a functor from the category of pointed quandles to the category of quandles in three different ways. This functor-valued invariant of a knot is an extension of the knot quandle. We also extend the quandle cocycle invariants of knots by using these quandle-valued invariants, and study their properties.