18 May
2003
18 May
'03
6:19 p.m.
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).