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A left shelf $(S, \rhd)$ is a magma with the left self-distributive law: $$ \forall x, y, z \in S: x \rhd (y \rhd z) = (x \rhd y) \rhd (x \rhd z). $$ Shelves are generalization of racks and quandles ...

(This is a follow-up question; the original question was about shelves.) A rack $(R, \rhd, \lhd)$ is a set $R$ with two binary operations $\rhd$ and $\lhd$ such that for all $x, y, z \in R$: $x \rhd ...

Given a finite quandle $Q$, for any knot $K$ one can associate an invariant, i.e. the number of proper colorings $p(K)$. Let us consider the inverse $K^{-1}$ and mirror image $K'$ of $K$. My queston ...

Let $X$ and $Y$ be two quandles and $f: X \rightarrow Y$ be a quandle homomorphism. Then we can define a map $\bar f: Inn(X) \rightarrow Inn(Y)$ as $\bar f(S_a)=S_{f(a)}$, where $a \in X$. Then $\bar ...