Timeline for A category with weak equivalences that is not a model category

7 events

when toggle format	what		by	license	comment
Apr 13, 2017 at 12:58	history	edited	CommunityBot		replaced http://mathoverflow.net/ with https://mathoverflow.net/
Jun 8, 2013 at 4:01	history	edited	Inna	CC BY-SA 3.0	corrected omission of isomorphisms from A
Jun 8, 2013 at 1:17	comment	added	Inna		Yes, I meant that the subcategory of weak equivalences is the subcategory of all isomorphisms and also all morphisms in A. Obviously, without all isomorphisms it can't be the subcategory of weak equivalences, but for more trivial reasons.
Jun 7, 2013 at 23:05	comment	added	Fernando Muro		Inna's example is a generalization of mine, which was the case $\kappa=0$. As Tom says, it's easy to see they are not the weak equivalences of a model structure since they do not contain all identities. Actually, as the question is phrased, there are tons of examples. Prof. May's answer above is too interesting and deserves a better question!
Jun 7, 2013 at 22:47	comment	added	Peter May		Inna means to include all isomorphisms in A (she said as much in my office an hour ago).
Jun 7, 2013 at 22:11	comment	added	Tom Goodwillie		Do you really want to call it a "category with weak equivalences" if not every identity map is a weak equivalence?
Jun 7, 2013 at 21:53	history	answered	Inna	CC BY-SA 3.0