In Gurskis definition (page 32 of his thesis) of a strict functor $F$ of tricategories he requires that

$F$ maps the adjoint equivalences $a,l,r$ in the source tricategory to the same adjoint equivalences in the target tricategory.

This means for example $F (a_{fgh}) = a_{FfFgFh}$. (Note that these morphisms are indeed parallel, because of the strictness of $F$.)

However it is not required, that the modifications in the definition of a tricateory $(\pi,\lambda,\mu,\rho)$ are preserved as well. For example $ F (\pi _{fghk}) $ is not required to be equal to $ \pi_{FfFgFhFk} $. So my question is:

Why isn't it required that $(\pi,\lambda,\mu,\rho)$ are preserved? Is this because this is already implied by the other requirements? Or are there strict functors which doesn't preserve the modifications $(\pi,\lambda,\mu,\rho)?$

**EDIT**

Let me draw some parallel to the definition of strict functors between bicategories: ($*$ denotes composition along objects)

There it is only required that the constraint-2-cells $$ F(f)*F(g) \to F(f*g) $$ and $$ 1_{Fa} \to F(1_a) $$ are identities. That $a,l,r$ are preserved is not demanded by definition, but it follows easily from the functor axioms.

Therefore one might hope that in the case of a strict functor of tricategories it follows somewhat analoge that the "highest" constraint data $\pi,\lambda,\mu,\rho$ are preserved, although it is not demanded by definition.