# Does the lax Gray tensor product preserve fully faithful 2-functors?

The question is in the title.

By fully faithful 2-functor, I mean 2-functors such that the maps on the hom categories are isomorphism, and by preserve, I mean in each variable.

I have an argument that seems to answer yes, but I am not sure about it.

Also, is there a good modern reference for Gray tensor products?