Abstract:
This paper is a first step in constructing the category of braided
sets and its closest relative, the category of Yang–Baxter
sets. Our main emphasis is on the construction of morphisms and
extensions of Yang–Baxter sets. This problem is important for the
possible constructions of new solutions of the Yang–Baxter equation
and the braid equation. Our main result is the description of a family of solutions of the Yang–Baxter equation on $B \otimes C$
and on $B \times C$, given two linear (set-theoretic) solutions $(B, R^B)$ and $(C, R^C)$ of the Yang–Baxter equation.
Keywords:Yang–Baxter equation, set-theoretic solution, quandle, Hopf
algebra, extension of Yang–Baxter sets, product of Yang–Baxter
sets, Drinfeld twist.