Subject: Re: two questions From: Tom Goodwillie Date: Mon, 21 May 2007 20:41:43 -0400 > > 1) The 2-out-of-6 property implies the 2-out-of-3 property. Could you give me > an example of class of morphisms satisfying the 2-out-of-3 property and not > the 2-out-of-6 property ? How's this? Let R be the ring Z_(2), the integers localized at 2. (Alternatively, the same example will work with R = Z/8.) In the category of R-modules, consider the class of morphisms consisting of the map 2: R --> R/4 together with every map isomorphic to that one and all the isomorphisms. The 2-out-of-3 property follows basically from the fact that there are no maps R/4 --> R except zero. The 2-out-of-6 fails, as shown by the diagram 2 1 2 R ---> R ---> R/4 ---> R/4 TG