I have just started reading MacLane's chapter Abelian Categories in Categories for the Working Mathematician. I am stuck in the second page, where he discusses the equivalence relation on a set of arrows with a fixed codomain in a category with a zero object. He defines a preorder <= with f<=g if and only if f factors through g. This is probably very silly of me but, can we not always use the zero arrow between the domains of the two arrows (in any direction) to provide such a factorization?
Thanks very much for any help, Mark
(Also, would MacLane be your suggestion for beginning to study Abelian Categories from a category theorist's prespective?)