Bir kategorik cebir ve Lawvere teorileri incelemesi

In this thesis we review category theoretical foundations of universal algebra. Universal algebra studies algebraic structures as theories based on sets, operations and equational axioms. Meanwhile, category theory is the abstract study of mathematical notions all together, so that it is often regarded as "bird's eye view of mathematics". Lawvere theories provide a universal category theoretical understanding of algebraic structures. In this thesis, our main purpose is to study some basic properties of Lawvere theories. For this purpose we first go through basics of category theory. Then we give definition and properties of Lawvere theories. Finally we list some examples of Lawvere theories associated to known algebraic structures.