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I have added to full and faithful functor the fact that they are closed under pushouts in Cat, with references (thanks to MO twice).
I was about to polish-up the following reference items that were listed in the entry. But on second thought it is unclear why these references should be listed here at all. Probably they all mention fully faithful functors in some way. But it does not make sense to list here random articles mentioning this basic concept.
Therefore I am removing the following items from the entry. If anyone knows that and why they should be listed after all, let’s add them back with a comment on what we mean the reader to find there regarding ff functors:
R. Fritsch, D. M. Latch, Homotopy inverses for nerve, Math. Z. 177 (1981), no. 2, 147–179, doi:10.1007/BF01214196.
Alexandru E. Stanculescu, Constructing model categories with prescribed fibrant objects, Theory and Applications of Categories, Vol. 29, (2014) No. 23, pp 635-653, journal page, arXiv:1208.6005.
Remark that $I L \dashv R$ implies $L \dashv I R$ when $I$ is fully faithful, and link to dominant functor.
Corrected $I R$ to $R I$.
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