Timeline for Model category structure on Set without axiom of choice
Current License: CC BY-SA 2.5
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| Aug 16, 2010 at 3:36 | comment | added | David Roberts♦ | This is very late, but I hope it gives some insight. One could cook up anafunctors without pseudoinverses, if instead of all surjections one uses a Grothedieck pretopology J on Set which has as covers surjections from some restricted class. I'm thinking of the example of surjections with finite fibres. If p:X->Y is a surjection with infinite fibres with no projective cover P->Y in J for which p admits a section, the anafunctor Y<-C(X) = C(X) has no pseudoinverse. Here C(X) is the groupoid with object set X and arrow set X\times_Y X, with the obvious structure. | |
| Dec 31, 2009 at 18:02 | history | answered | Reid Barton | CC BY-SA 2.5 |