Timeline for Does the Monoid Axiom hold for k-spaces?
Current License: CC BY-SA 3.0
7 events
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
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| Feb 18, 2013 at 18:11 | vote | accept | David White | ||
| Feb 12, 2013 at 20:28 | answer | added | Karol Szumiło | timeline score: 2 | |
| Sep 17, 2012 at 22:56 | comment | added | David White | I suppose I should have been more explicit in my question about which model structure to place on $k$-spaces. If you use the Quillen model structure (weak homotopy equivalences and Serre fibrations) then you're cofibrantly generated but not all objects are cofibrant. If you use the Strom model structure (homotopy equivalences and Hurewicz fibrations) then you are not cofibrantly generated. I'm interested in either case, but more so in the former. There's also the mixed model structure and I'd be interested to know about the monoid axiom there too. | |
| Sep 17, 2012 at 20:50 | comment | added | David White | Clark Barwick's answer to a different question (mathoverflow.net/questions/11059) shows that you do have a model structure on topological monoids, but it's for a different category of topological spaces (namely, I think the result he cites needs Top to be Compactly Generated Hausdorff spaces). So you could view my question as trying to make this work for a larger class of topological spaces. If you go with the whole category of topological spaces the question doesn't make sense because you don't have a closed symmetric monoidal category. That's why CG comes in: for function spaces. | |
| Sep 17, 2012 at 20:44 | comment | added | David White | Re-reading the Vogt paper which I cited below the first question, I realized that his claim is not as strong as I said. He only claims there is no known Quillen model structure on topological monoids where weak equivalences are (based) maps in $Top^*$ which are not-necessarily-based homotopy equivalences | |
| Sep 14, 2012 at 15:07 | history | asked | David White | CC BY-SA 3.0 |