In Nikolaus and Schweigert's paper "Equivariance in higher geometry", they define \tau-prestack in Definition 2.12, page 10, via "fully faithful functor of bicategories". They explained in the definition without giving any reference that a functor of bicategories is called fully faithful, if all functors on Hom categories are equivalences of categories.

I think this definition of fully faithful bifunctor is reasonable. I saw the definition of fully faithful 2-functor here on nlab: https://ncatlab.org/nlab/show/full+sub-2-category, which is defined in the same way as that in Nikolaus and Schweigert's paper. However, on this page, there is no reference as well.

So my question is above at the beginning. ]]>