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