Timeline for (infinity,1)-categories directly from model categories
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
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| Dec 13, 2009 at 3:34 | comment | added | Mike Shulman | Well, yes, but all the models for $(\infty,1)$-categories are Quillen equivalent, so they are all "essentially the same thing." (-: Simplicially enriched and topologically enriched categories are certainly more closely related than either one is to quasicategories, but they are not identical either. For instance, every topologically enriched category is fibrant, which is not the case for simplicially enriched ones. | |
| Dec 12, 2009 at 21:49 | comment | added | Alicia Garcia-Raboso | Doesn't the fact that topological spaces and simplicial sets are Quillen equivalent imply that the variants you mention are essentially the same thing? | |
| Dec 12, 2009 at 20:46 | comment | added | Mike Shulman | There are more than four. In addition to variants of simplicially enriched categories, Segal categories, and complete Segal spaces which use, say, topological spaces instead of simplicial sets, there are also $A_\infty$-categories. | |
| Dec 12, 2009 at 15:32 | history | answered | Alicia Garcia-Raboso | CC BY-SA 2.5 |