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 CODOMAIN ( 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.