Matthew Burke

Title: Free co-completion, presheaves and sheaves
Abstract: In response to a special request this talk describes some fundamental aspects of sheaf theory. First we introduce the algebra of ends and co-ends for the purpose of making our subsequent calculations more concrete. Then we describe how the construction of a presheaf category of a small category corresponds to the free co-completion of that category. Finally we describe how the sheaf construction allows us to construct a non-free co-completion and choose which co-cones in the original category become colimit co-cones in the co-completion category. If we have time we sketch how to interpret various logical formulae in the internal logic of a sheaf category.