MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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?


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

share|cite|improve this question

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.