[Here][1], I asked wether taking lax pullback preserves continuity, but got no precise answer. However, I have found [this][2] recent article by Riehl and Verity which proves something very similar, but I can't see wether it applies immediately in the context I want. Can someone familiar with the paper (or perhaps the authors) say if it implies the following: > Suppose $F:C\rightarrow D$ and $G:B\rightarrow D$ are functors of > 2-categories which send comma objects to comma objects, is it true > that the map $F\downarrow G\rightarrow B$ sends comma objects to comma > objects? [1]: http://mathoverflow.net/questions/162633/is-continuity-of-a-functor-stable-under-pullback [2]: http://arxiv.org/abs/1401.6247