Timeline for What are surprising examples of Model Categories?
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| May 5, 2023 at 1:46 | comment | added | Zhen Lin | I thought this was well known. Basically the idea is to construct it as a left Bousfield localisation of the trivial (= discrete) model structure. The local equivalences are the morphisms inverted by the reflector. It is always the case that reflective subcategories are localisations, so the only thing to check is that we have the factorisations needed. This part I do not have a completely general argument for, but probably when the category is locally presentable and the reflector is accessible we can use Smith's theorem. If the reflector preserves (some) pullbacks we can do it by hand. | |
| May 4, 2023 at 14:49 | comment | added | Tim Campion | @ZhenLin Sure. Model structures are like elephants -- if one of them is sneaking up on you, you probably will notice it coming from some distance away, before it actually reaches out and tags you with its trunk. This one is like the elephant who paints its toenails rainbow colors and approaches through a river of M & M 's to get the jump on us. By the way, under what conditions exactly does a reflective subcategory give rise to a model structure? | |
| May 3, 2023 at 7:34 | comment | added | Zhen Lin | I'm not sure this is surprising if you know the general construction of model structures from (co)reflective subcategories... (The "classical" category of groups is a reflective subcategory of this category of group presentations.) | |
| May 3, 2023 at 2:50 | history | answered | Tim Campion | CC BY-SA 4.0 |