Let $G$ be a group acting on the sets $X$ and $Y$. A function $f:X\to Y$ is $G$-equivariant if for all $x\in X$ and all $g\in G$, \(f(g\cdot x) = g\cdot f(x).\)
If the function $f$ is bijective, then this function is called a $G$-isomorphism.
Wikidata ID: Q256355