On equivariant maps

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It is well know the notion of Equivariant map .

Now, consider the situation: $X$ and $Y$ being $G$- and $H$-sets, resp., and a homomorphism $\varphi: G\to H$.

How is called a map $f:X\to Y$ satisfying $f(gx)=\varphi(g)f(x)$ ?