Complements and the Krull-Schmidt theorem in arbitrary categories. 
Bodo Pareigis and Helmut R\"ohrl 
(17 pages) 

Abstract.
We study direct product decompositions of objects in a finitely complete and 
cocomplete category with zero object and certain axioms for a coimage 
factorization of morphisms. Direct products $C = A \times B$ can be 
characterized by "inner" properties of $C$ and its subobjects $A$ and $B$. 
We also show that the Fitting Lemma and the Krull-Schmidt Theorem hold.