Timeline for Model category structures on categories of complexes in abelian categories
Current License: CC BY-SA 2.5
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| Aug 8, 2012 at 21:41 | comment | added | David White | This answer also fits into the framework of Gillespie's work. Asking for a small projective generator is related to asking for the cotorsion pair $(A,B)$ of Mike's answer to be cogenerated by a one-element set (cogenerated by a set means there is a set $S\subset A$ such that $b\in B$ iff $Ext^1(S,b)=0$). In a Grothendieck category with enough projectives, being cogenerated by a set forces $(A,B)$ to be a complete cotorsion pair. You'll also get the dual complete cotorsion pair, and thence the Hovey model structure described by Mike. | |
| Oct 6, 2009 at 22:58 | history | answered | Eric Wofsey | CC BY-SA 2.5 |