Timeline for Where does the ''hyper'' go?
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Jun 28, 2013 at 19:25 | comment | added | Fernando Muro | Ronald, you're right: ncatlab.org/nlab/show/simplicial+skeleton I really meant that I only knew that for groupoids. My idea is that coskeletal simplicial sets are Postnikov pieces, and this is true for Kan complexes, but not for arbitrary simplicial sets. | |
| Jun 28, 2013 at 19:20 | comment | added | Ronald Bernard | Dear @FernandoMuro, are you saying this is false for categories that aren't groupoids? Why? I don't believe that. | |
| Jun 28, 2013 at 19:07 | comment | added | Fernando Muro | The nerve of any groupoid. | |
| Jun 28, 2013 at 18:55 | comment | added | Ronald Bernard | The nerve of any category is $2$-coskeletal, ok. Thank you! | |
| Jun 28, 2013 at 18:43 | comment | added | Fernando Muro | Yes, nerves of groupoids don't have higher homotopy groups. They are coskeletal rather than skeletal. | |
| Jun 28, 2013 at 18:26 | comment | added | Ronald Bernard | Dear @FernandoMuro, thanks for the comment. The nerve of a groupoid has all $\pi_n$ with $n\geq 2$ trivial, correct? I forgot this, sorry, then the Corollary answers the second question. Do you know if the nerve of a groupoid is $2$-skeletal, i.e. the same as its $2$-skeleton? | |
| Jun 28, 2013 at 17:31 | comment | added | Fernando Muro | Concerning your first question, the problem is showing that $A$ preserves cofibrations, isn't it? I don't see it either, the explanation offered in 'A homotopy theory for stacks' is nor clear enough to me. About your second question, isn't this Corollary A.9 in 'Hypercovers and simplicial presheaves'? In this case, the argument in the proof does look convincing. | |
| Jun 28, 2013 at 16:48 | history | asked | Ronald Bernard | CC BY-SA 3.0 |