Date: Tue, 09 May 2000 09:38:11 +0200
From: Rainer Vogt <rainer@mathematik.Uni-Osnabrueck.DE>
Subject: Re: report on model categories

Response to the following posting.  www.lehigh.edu/~dmd1/sc55
> Date: Fri, 05 May 2000 10:48:58 -0400
> From: "Steven R. Costenoble" <Steven.R.Costenoble@Hofstra.edu>
> Subject: Model category structures on Cat

Heggie's strong coideals are what Thomason calls Dwyer maps in his paper.
Any of Thomason's cofibrations is a Dwyer map, but the converse is not
true!
Thomason proved a number of results about Dwyer maps, which imply most of
the main results of Heggie's paper: the nerve functor maps pushouts along
Dwyer maps to homotopy pushouts. As a Corollary one obtains Prop. 5.1
of Heggie (it allready appears in Thomason's paper). Heggie's Propositions
6.1
and 6.11 are proven by Thomason (6.11 is not stated verbatim but is
implicit).
Thomason also shows (implicitly) that Dwyer maps and the usual weak
equivalences
form a cofibration category structure on Cat.

Regards,
Rainer Vogt