Why trivial quandle is trivial?

Question

A quandle is a set $X$ with a binary operation $*$ defined on $X$ and satisfying three axioms. The quandle where $x*y=x$ for any $x,y \in X$ is called a trivial quandle. I wonder why is it called trivial? I wonder if this has a relation with cocycle invariant defined for knots?

Answer 1

The most trivial quandle for a non-empty $X$ is the one-element set $X=\{s\}$, defined by $s\triangleright s=s$. In general, a trivial quandle decomposes as a disjoint union of these one-element quandles.

Every quandle $S$ has a quandle map to a trivial quandle $X$ defined by sending everything in $S$ to a single point in $X$. This is like how every group has a homomorphism to the trivial group.

For knots, a quandle map from the knot quandle to the trivial quandle corresponds to a trivial coloring of the knot. Looking for a non-trivial coloring of a knot by some quandle amounts to saying the image in the quandle is not a trivial quandle.