A functor-valued extension of knot quandles

Tetsuya Ito

Published 2010-06-10, updated 2010-07-05Version 2

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