Subject: About accessibility of the weak equivalences of a
combinatorial model category
From: Gaucher Philippe
Date: Tue, 24 Jan 2006 15:09:01 +0100
Dear All
I asked the following question to the mailing-list "categories" without
success. I try here.
How can we prove that the class of weak equivalences of a combinatorial
model
category is accessible ? I know how to prove that the class of weak
equivalences of a combinatorial model category is accessibly embedded in
the
whole class of morphisms. And then it is accessible using Vopenka's
principle
by [Adamek-Rosicky's book Theorem 6.17] . Can we remove Vopenka's
principle
from the argument ? Or is this fact in the definition of a "combinatorial
model category" (for me, it's a cofibrantly generated model category such
that the underlying category is locally presentable) ?
Thanks in advance. pg.