Hey, I was looking back through Rezk's original paper on Theta_n-spaces, and I noticed something was stated without proof that I can't quite figure out.

arxiv.org/pdf/0901.3602.pdf

proposition 8.3

actually, nevermind. I think it's fine. It's not clear with the internal homs, but I think it's clear using the mapping space object

yeah, it's immediate

the actual content of the proof must be earlier, where he probably shows that that the intertwiner is a simplicial left-quillen adjoint