11:51 PM
@PhilTosteson Sure, and basically that idea is straightforward to turn into an actual proof in the 1-categorical case. But in the $\infty$-categorical case it's not so clear to me...
Actually the reasoning I gave above doesn't work. So I'm back to not even knowing a proof at all.
I'm having trouble finding this in HTT, although 2.2.3.6 shows something similar for categories of left fibrations.
as opposed to functor categories