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.