Timeline for Abstract Relation between Presehaves and Simplicial Sets
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
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| Nov 12, 2009 at 23:31 | comment | added | Urs Schreiber | If by "the local model structure" you mean the local injective one: yes. See the big diagram at ncatlab.org/nlab/show/model+structure+on+simplicial+presheaves which lists all the Quillen equivalences between the diferrent model structures. All Quillen equivalent structures yield the same homotopy category, in particular. But it's even better: they even yield equivalent (oo,1)-categories. | |
| Nov 12, 2009 at 23:23 | comment | added | Konrad Voelkel | Does the local projective model structure yield the same homotopy category as the local model structure? | |
| Nov 12, 2009 at 23:22 | comment | added | Konrad Voelkel | Thank you! I didn't understand before, that sheaves are precisely fibrant-cofibrant in the local model structure of presehaves on a site. Now the picture is much clearer. | |
| Nov 12, 2009 at 21:39 | history | edited | Urs Schreiber | CC BY-SA 2.5 |
added 28 characters in body; added 94 characters in body
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| Nov 12, 2009 at 21:29 | history | answered | Urs Schreiber | CC BY-SA 2.5 |