Lower higher categories: what they are and why you should care

In this talk, I will give a gentle introduction to 2-categories and why a person might hypothetically care about them.  I will begin with a discussion of cohomology classes on a topological space and how they correspond to geometric objects.  I will then discuss 0-categories, 1-categories, and 2-categories, and how they fit into this question of geometric objects corresponding to cohomology classes.  I will also give some examples to convince you that you already care about some 2-categories, even though you probably didn't know it.  Although my motivation for this question comes from algebraic geometry, I will not assume any background beyond a basic knowledge of singular cohomology.