Ext and tor functors

Category theory is a mathematical theory that deals in an abstract way with mathematical structures and relationships between them. It is also known as ?Abstract nonsense?. The study of categories is an attempt to axiomatically capture what is commonly found in various classes of related mathematical structures by relating them to the structure-preserving functions between them. A systematic study of category theory then allows us to prove general results about any of these types of mathematical structures from the axioms of a category.In category theory, a branch of mathematics, a functor is a special type of mapping between categories. Functors can be thought of as morphisms in the category of small categories. It is possible to relate various categories by using functors. Functors are generalization of functions that relate any object of a category to an object of another category, and any morphism in a category to a morphism of another category.The word "functor" was borrowed by mathematicians from the philosopher Carnap. Functors were first considered in algebraic topology, where algebraic objects (like the fundamental group) are associated to topological spaces, and algebraic homomorphisms are associated to continuous maps. Nowadays, functors are used throughout modern mathematics to relate various categories.In this study; the basic background about the category theory and functors are given in the second and third chapters. Ext and Tor functors, that have an important place in homological algebra, are mentioned in the last chapter.