TABLE OF CONTENTS For the sake of convenience of the reader, several mathematical topics are compiled in this Chapter.
We refer the reader to [45; 289; 314] for the basics of category theory.
A category 
consists of a class Ob 
of objects and a class Mor 
of morphisms which obey the following conditions.
A class Hom ( K, K') of morphisms is assigned to each ordered pair of objects ( K, K').
Any morphism 
belongs to only one class Hom (.,.).
Given pairs of objects ( K, K') and ( K', K"), there is the composition ? ? ? ? Hom ( K, K") of morphisms ? ? Hom ( K, K') and ? ? Hom ( K', K"). This composition is associative.
Any class Hom ( K, K) contains an identity morphism Id K such that, whenever 
, we have
It should be emphasized that this definition of a category is formulated in the framework of a system of axiomatic set theory (e.g., the G del-Bernays one) where the notion of a class differs from that of a set. Namely, classes unlike sets can not be elements of classes and sets. One often requires that all classes Hom(.,.) of a category are sets, called homsets. A category is called small if its morphisms constitute a set. Small categories and their functors...
