I'd like to know a reference where the following property, that I believe to be true, is checked: given a diagram of categories and functors $B\leftarrow A\rightarrow C$ (I'm actually interested in the enriched case, over a closed symmetric monoidal category), if $A\rightarrow C$ is fully faithful then so is the functor to the (strict) push-out $B\rightarrow B\cup\_A C$.


I should say that I have been able to check this in some specific cases that I needed, but a reference would help me to reduce a paper in four pages ;-)



Push-outs of fully faithful (enriched) functors
A proof of this fact is given in Proposition 3.1 of


Alexandru Stanculescu, Constructing model categories with prescribed fibrant objects, [arXiv:1208.6005](https://arxiv.org/abs/1208.6005).


He attributes this result to an earlier paper from the 80's by Fritsch and Latch.


