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. ]]>

Unless I missed it, that page doesn't mention this topic, nor provide a link to a web page where it is discussed.

I presume you DO cover this topic at [[pseudofunctor]] (yes? no?).

Would it not be a good idea to provide a link from the [[bicategory]] page to where their morphisms are named and discussed?

BTW, what motivated the issue was: at one of my own web pages I am using the accepted term [[bifunctor]] for a functor of two variables.

For this non-expert, that motivated the question.

Finally, I could add such a link myself, but really think someone more familiar with how you like to style things should do it (obviously it's an easy edit). ]]>