8
$\begingroup$

During a reading course about Jacob Lurie's paper about Local TQFTs, I came across the notion of Segal spaces as models for $(\infty,1)$-categories. Looking at things like the "double nerve" for 2-categories, I also understand why $n$-fold Segal spaces provide a model for $(\infty, n)$-categories. What puzzles me is the completion of $n$-fold Segal spaces. There is a construction for $n=1$ in the case of bisimplicial sets by Rezk in his paper about the homotopy theory of homotopy theory. I can imagine that something similar can be done for Segal spaces which are simplicial spaces instead of bisimplicial sets. My questions are:

How does the completion generalize to $n$-fold Segal spaces?

and

Is the completion a fibrant replacement in the model category structure on simplicial spaces?

$\endgroup$

Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Browse other questions tagged or ask your own question.