Post date: 15-oct-2015 23:57:18
In this talk we embark into topos theory, first with a historical motivation on the subject. Then we explore the classical theory of sheaves and étale spaces over a base space. We introduce an adjunction between spaces over a base space and presheaves, as a byproduct of Kan extension techniques. Then we observe that this adjunction restricts to the equivalence between étale spaces and sheaves, and moreover by a general fact obtain that sheaves sit in presheaves as a reflective subcategory, obtaining the associated sheaf functor. Finally, we study constant sheaves and obtain an equivalence between locally constant sheaves and covering spaces.