m.d. - The associated sheaf construction and exactness properties - 30/10

Post date: 29-oct-2015 23:53:38

In this talk we construct the associated sheaf functor for a site by the classical "LL construction", where L is given by locally compatible sections modulo refinements. This shields a left adjoint to the inclusion of sheaves in presheaves, which by construction is exact, hence sheaves sit as a reflexive subcategory of presheaves. From this we will deduce that all the classic exactness properties of sets transfer to every topos, i.e. a category equivalent to a category of sheaves over a site. We will also state a proposition to recognize covering families inside the topos.