Lecture 6: Sheaves of sets (Part 1)

The most important examples of topoi are categories of sheaves of sets on a small category. Patrick Eilliott introduced this class of examples over two talks, of which is the first. In this talk he defines presheaves and sheaves on a topological space, and explains using the Yoneda lemma how to think about the sheaf condition in terms of sieves on objects in a category. This is preparation for his second lecture, where he defines sheaves with respect to a Grothendieck topology.