Timeline for Model category structure on Set without axiom of choice

10 events

when toggle format	what		by	license	comment
Feb 16, 2012 at 1:14	history	edited	David White	CC BY-SA 3.0	Texified
Jan 1, 2010 at 13:22	answer	added	D.-C. Cisinski		timeline score: 2
Dec 31, 2009 at 23:06	vote	accept	Reid Barton
Dec 31, 2009 at 23:05	comment	added	Reid Barton		Yes, these are the two model category structures in which the cofibrations are the monomorphisms (at least under AC). I gave a rather ad-hoc description of the category I wanted to consider, but it falls into a family of more interesting ones: presheaves on the category of nonempty totally ordered sets of cardinality <= n+1 form a model category whose objects we can identify with the n-coskeletal simplicial sets, and whose homotopy category is that of (n-1)-types. (This works for -1 <= n <= infinity.)
Dec 31, 2009 at 19:02	comment	added	Mike Shulman		Is there a reason you want to treat empty sets specially? I think there's a simpler model structure in which the cofibrations are the injections, the fibrations are the surjections (or split surjections, if we don't assume choice), and everything is a weak equivalence. (I.e. it is just a single weak factorization system.)
Dec 31, 2009 at 18:51	answer	added	Mike Shulman		timeline score: 7
Dec 31, 2009 at 18:02	answer	added	Reid Barton		timeline score: 2
Dec 31, 2009 at 16:37	history	edited	Reid Barton	CC BY-SA 2.5	added 3022 characters in body
Dec 31, 2009 at 7:27	history	edited	Reid Barton	CC BY-SA 2.5	added 347 characters in body
Dec 31, 2009 at 7:07	history	asked	Reid Barton	CC BY-SA 2.5