Limit in category theory

In this thesis, the elementary concepts of category theory are investigated taking as reference Adámek, Herrlich and Strecker (1990), Anderson and Fuller (1992), Lane (1998). Then some well-known concepts of mathematics are considered from a categorical point of view and generalizations of these concepts are studied. In the second section, some preliminary information concerning category theory, which will be used in this thesis frequently, is given. In the third section, the definition of categories is given. Then, generalizations of some set-related concepts are studied. In the fourth chapter, the concept of functors are examined with their basic properties. Using functors, we also give some relationships between different categories. Lastly, isomorphism and equivalence of two categories are studied. In the fifth section, the concepts of diagram and natural transformations are introduced. Using natural transformations, relationships between two functors are discussed and limit, an important notion of mathematics, is studied from a categorical point of view. Then, the concepts introduced in the third section such as product and equalizer in addition to direct and inverse limit used in module theory are shown to be special cases of categorical limit and colimit.