10:45 PM
I would like to say that, given a Quillen equivalence of "nice" simplicial model categories, I get a pair of 1-simplices in $Cat_\infty$ and a couple of 2-simplices telling me that their compositions equivalent to the identity functors. Is this true? And if so, where is it written down?
I think that this is pretty close to being in a paper by @AaronMazel-Gee but I can only find it for adjunctions rather than equivalences.
More generally, I can't seem to find a good discussion of adjoint equivalences of quasicategories anywhere.
I feel like I just want to say that the unit transformation, which is required to exist to have an adjunction of quasicategories, is an equivalence.