Timeline for Localizations or quotients of categories?
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Nov 28, 2014 at 4:14 | comment | added | David Roberts♦ | You might want to look at Quillen's monograph Homotopical Algebra link.springer.com/book/10.1007%2FBFb0097438, if you have access. | |
| Nov 28, 2014 at 4:11 | comment | added | David Roberts♦ | One can take quotients of categories to calculate localisations in certain cases. For instance (the following may be roughly right) when one takes the fibrant and cofibrant objects in a model category with a cylinder object, then taking the quotient of the full subcategory by the relation of homotopy gives the localisation at the weak equivalences. This is a serious theorem of Quillen, and showed that localisations of model categories are locally small. Chain complexes have a model structure with weak equivalences the quasi-isomorphisms (and this was one of the motivating examples for Quillen) | |
| Nov 27, 2014 at 23:39 | comment | added | Filippo Alberto Edoardo | I tried to follow the link, but it seems to me thatit only describes localizations and I find no reference to quotients. | |
| Nov 27, 2014 at 23:07 | history | answered | David Roberts♦ | CC BY-SA 3.0 |