Timeline for Model categories as a tool to resolve size issues for localizing categories
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Feb 11 at 21:32 | vote | accept | user267839 | ||
| Feb 10 at 13:51 | history | edited | David White | CC BY-SA 4.0 |
Fixed various typos
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| Feb 10 at 8:36 | history | became hot network question | |||
| Feb 10 at 2:41 | answer | added | David White | timeline score: 12 | |
| Feb 10 at 1:20 | comment | added | user509184 | You form the homotopy category of a model category $\mathcal{M}$ by taking the full subcategory of $\mathcal{M}$ spanned by all the fibrant-cofibrant objects, then modding out by an equivalence relation (homotopy) on morphisms. Both of those operations--passing to the full subcat, and modding out the equiv. rel.--make the category SMALLER, not BIGGER. So the homotopy category doesn't have size issues like the Gabriel-Zisman localization: the hom-sets can't "blow up" into proper classes. But the homotopy category still succeeds in inverting the weak equivalences (between fib-cofib. objects). | |
| Feb 10 at 0:53 | history | edited | user267839 | CC BY-SA 4.0 |
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| Feb 10 at 0:41 | history | edited | user267839 | CC BY-SA 4.0 |
added 63 characters in body
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| Feb 10 at 0:36 | history | asked | user267839 | CC BY-SA 4.0 |