Connections between adjoint functors and limits

Abstract

The concept of an adjoint functor is one of the most important concepts in category theory. Their close relation with universal arrows and limits makes them indispensable. In this thesis connections between adjoint functors and limits are explored. Firstly the general theory of adjoint functors is presented. In this respect characterization of adjunctions by universal arrows and also by units and counits are given. Secondly the notion of a limit and construction of limits by products and equalizers are presented. As the final step, general and special adjoint functor theorems are proven. These important theorems characterize the existence of a left adjoint to a functor in terms of limits and illuminate the adjoint functor-limit relation most. Also specific examples of adjunctions and applications of adjoint functor theorems in different fields of mathematics are presented.