The Fundamentals and Rudiments of Homological Algebra

A category C consists of a class of C - Objects and a class of C - Morphisms denoted respectfully by Ob(C) and Mor(C) for each ordered pair (A B) of C - Objects which satisfies the axioms of Composition of Morphisms Products of Morphisms an Identity of Morphisms as well as the Domain and the Co-domain (Range). In any case each object A in the given category C is uniquely determined by the Identity Morphism. On the other hand the Identity is uniquely determined by A. And so by replacing as C the Identity Morphisms a category can then be defined alternatively and entirely in terms of Morphisms.