Lecture 10: Sheaves form a topos (Part 1)

In his two earlier talks, Patrick defined the category of presheaves on a small category, and within this category the subcategory of sheaves for a given Grothendieck topology. Both of these categories, presheaves and sheaves, are examples of topoi, but this fact was only stated and not proved in his earlier lectures. In this lecture and its sequel, Patrick will prove that these categories form topoi.