Subject: simplicial spaces
From: John Baez
Date: Sun, 15 Apr 2007 12:53:35 -0700
Hi -
I have a question about simplicial spaces:
1) With the Reedy model category structure on simplicial spaces, is
the "geometric realization" functor from simplicial spaces to Top
a Quillen equivalence?
Some subsidiary questions:
1') The same question, but with Top replaced by the category of
simplicial spaces:
With the Reedy model category structure on bisimplicial sets, is
the "geometric realization" functor from bisimplicial sets to simplicial
sets a Quillen equivalence?
2) If two model categories are Quillen equivalent, are their
categories of simplicial objects also Quillen equivalent, with the
Reedy model category structure? (If not, someone should be fired.)
Finally, what I'd really like are some references that settle these
questions! Goerss and Jardine's book discusses the Reedy model structure
and a general concept of geometric realization, but I don't see these
questions being addressed.
Best,
jb