Sebastian Öberg: Large categories and the problems of categorical homotopy theory

We will talk of the inherent problems of set-theory, like Russels paradox, and how they translate into problems when talking about the homotopy theory of categories. We will discuss ways of avoiding these problems by constructing what is called the core of a category, which allows us to make homotopical statements about categories which are not small. Here a small category is a category where the objects and morphisms can be viewed as a sets.