Timeline for Examples of non-proper model structure
Current License: CC BY-SA 4.0
16 events
| when toggle format | what | by | license | comment | |
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| S Sep 7, 2019 at 17:00 | history | bounty ended | CommunityBot | ||
| S Sep 7, 2019 at 17:00 | history | notice removed | CommunityBot | ||
| Sep 3, 2019 at 21:22 | history | edited | Simon Henry | CC BY-SA 4.0 |
deleted 6 characters in body
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| S Aug 30, 2019 at 15:55 | history | bounty started | Mike Shulman | ||
| S Aug 30, 2019 at 15:55 | history | notice added | Mike Shulman | Draw attention | |
| Aug 27, 2019 at 1:56 | comment | added | Simon Henry | @MikeShulman : in its non-functorial version (or if one works in the combinatorial settings) the hypothesis of Quillen path's object argument are equivalent to the existence of the transfered model structure. So in theory they indeed do not implies properness. | |
| Aug 26, 2019 at 17:05 | comment | added | Tim Campion | I think Inna Zakharevich has some unusual ways to construct model structures. If I recall correctly, one way has something to do with starting with one model structure and then passing to an elementarily equivalent category to get a model structure on it. I think she also has studied model structures on posets in some detail, and may have interesting ways of constructing model structures on them. But I'm not sure such methods can break properness. | |
| Aug 26, 2019 at 16:18 | comment | added | Mike Shulman | Do the hypotheses of Quillen's path object argument for acyclicity for lifted model structures imply right properness of the lifted model structure? I wasn't aware of that, but it could be so. | |
| Aug 26, 2019 at 4:17 | comment | added | Mike Shulman | @SimonHenry I was just suggesting what seemed to me the most promising place to look for examples. But I see your point. | |
| Aug 25, 2019 at 16:52 | comment | added | Simon Henry | @MikeShulman : Indeed, Transfer right transfer preserves right properness, and left transfer preserves left properness, but they can potentially destroy the other properness assumption. But I what I mean in this case is that I do not know any examples where one can prove that the transfered model structure exists (and is really a Quillen model structure) without using some technique that also implies or use right or left properness. | |
| Aug 25, 2019 at 13:39 | comment | added | Mike Shulman | So to list some general techniques for constructing model structures: Bousfield localization assumes properness, while mixed and intermediate model structures have the same weak equivalences as some other model structure and so don't take us out of the world of properness. What about left and right lifting? E.g. if we right-lift a model structure that is not right proper, could we obtain one that is neither right nor left proper? | |
| S Aug 24, 2019 at 17:51 | history | suggested | Matt Feller | CC BY-SA 4.0 |
Removed parenthetical remark made obsolete by Simon's edit, plus a couple minor grammar edits
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| Aug 24, 2019 at 17:10 | review | Suggested edits | |||
| S Aug 24, 2019 at 17:51 | |||||
| Aug 24, 2019 at 16:58 | history | edited | Simon Henry | CC BY-SA 4.0 |
added 211 characters in body
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| Aug 24, 2019 at 15:55 | comment | added | Matt Feller | I like this question! Maybe it's worth mentioning that a non-proper model structure can't have the same weak equivalences as a proper one. (See the comments here by Rezk, Nikolaus, and Shulman.) So, for example, an answer to this question can't come from shrinking the class of cofibrations of a Cisinski model structure so that not everything is cofibrant; it seems like it really would require a fundamentally different approach, like you're saying. | |
| Aug 24, 2019 at 14:21 | history | asked | Simon Henry | CC BY-SA 4.0 |