Quillen equivalence between sSet (Joyal's model structure) and sSetCat (Bergner's one)

Question

Let me consider two model categories:

• $ \mathsf{sSet} $: the category of simplicial sets with Joyal model structure,
• $ \mathsf{sSetCat} $: the category of simplicially enriched categories with Bergner model structure.

In Lurie's "Higher Topos Theory", he showed there is a Quillen equivalence between them. Lurie denote it as:

• $ \operatorname{N}: \mathsf{sSetCat} \to \mathsf{sSet} $: homotopy coherent nerve,
• $ \mathfrak{C}: \mathsf{sSet} \to \mathsf{sSetCat} $.

However, his proof is not easy to follow I think, because of so many hyperlinks.

Is there another proof on this fact, or a document which explains the outline of his proof?

Answer 1

Here's a second proof that followed Lurie's rather quickly. https://arxiv.org/abs/0911.0469