Modelling homotopy n-types in algebraic topology and category theory

Homotopy n-types are topological spaces with trivial homotopy groups in dimension greater than n. They arise naturally in algebraic topology and category theory. Both these areas of mathematics have seen the development of models of n-types. In this talk I will describe some of these models and I will address the question on how to compare some of them. I will also talk about some recent results I have obtained about this comparison problem.