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From: Peter Freyd <pjf@saul.cis.upenn.edu>
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Subject: Re: connected categories and epimorphisms.
Date: Sun, 18 May 2003 14:19:19 -0400 (EDT)
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The quickest natural example I know of a connected category in which
projections from products needn't be epi is the category of
commutative rings. Well, actually, the opposite category.  The
coproduct of  Z_2  and  Z_3  is the terminal ring. The two
co-projections fail to be monic (the coproduct of a pair of objects in
this category is their tensor product).