For functors $E,F,E',F':X\to Y$ I would like to say that transformations $\tau:E\to F$ and $\tau':E'\to F'$ are isomorphic if they are isomorpic in the arrow category of functors $X\to Y$, that is, there exist invertible transformations $i_E:E\to E'$ and $i_F:F\to F'$ such that $i_F\circ \tau=\tau'\circ i_E$.
Would you advise me to introduce some term for isomorphisms of this type ("arrow isomorphic"? "lax isomorphic"?)? Did anybody consider isomorphisms of this type and call them somehow?
