Let $A$, $B$, and $C$ be three categories and $G\colon A\to C$ and $H\colon B\to C$ two functors. Assume that $F\colon A\to B$ and $E\colon B\to A$ form an equivalence between $A$ and $B$.
Suppose that
$$ H \circ F = G \qquad \text{and} \qquad G \circ E = H $$
(which should be equivalent to say that the triangle formed by $A$, $B$, and $C$ as objects and $F$, $E$, $G$, and $H$ as morphism commutes, since $F$ is an equivalence).
Is there a property, a definition, or a concept in general that describes such a relation between $H$ and $G$ under the equivalence $F$?