Abstract

Mostly without knowing, you have all already met lots of objects with universal properties throughout your undergraduate courses. Working with the universal property of an object rather than its concrete implementation can have huge benefits: it gives an implementation-independent definition, which can therefore be used in many different mathematical areas at once. It also gives much greater conceptual clarity about the object in question and what role it plays within its area. In general, the concept of universal property is a very important one and crops up in nearly all areas of pure mathematics. My own field of category theory is the natural setting to investigate this concept. After a short introduction to the ideas of category theory I will spend most of the talk highlighting the universal properties of objects you are very familiar with, such as cartesian products and quotients, as well as giving you insight into a few you may not yet have met.