Gustav Sædén Ståhl: Representable functors, universal properties and the Yoneda embedding

In category theory, a representable functor is a functor from some category C to the category of sets which can be described by morphisms to (or from) a certain object in C. Thus, knowing that a functor is representable will tell us a lot about the structure of the functor. I will start by giving a short introduction to category theory and then define, and give examples, of these representable functors. I will go on by explaining their connection to the concept of universal properties and finally I will describe the Yoneda embedding and its uses in algebraic geometry.