Limits and colimits in Rel?

[Uwe.Wolter@ii.uib.no]

Dear all,

I remember that there was some time ago a discussion on this list
about limits and colimits in the category Rel of binary relations.
Unfortunately, I can not remember or trace the final answer. But, if I
remember right there are, besides initial and terminal objects, in
general no limits or colimits in Rel.

So my questions are:

1. Is there a characterization of monomorphisms and epimorphisms in Rel?
2. Is it true that there are, in general, no products and equalizer
(sums and coequalizer) in Rel?
3. Are there some general results about what limits/colimits exist or
don't exist?
4. Is the presumable non-existence related to the fact that the
formation of converse relations establishes an isomorphism between Rel
and its opposite Rel^op?

Any reply or reference is well-come.

Best regards

Uwe Wolter


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