Matthew Burke

Title: Localisation of Simplicial Presheaf Categories
Abstract: In this talk we describe a special case of left Bousfield localisation that is of interest in the calculus of functors. In particular we work in the category of simplicially enriched presheaves of a small  category. First we sketch how the classical small object argument constructs factorisations from a set of presheaf morphisms. Then we describe how to generate a model category from these maps (and an appropriate specification of weak equivalences) by augmenting the small object argument with some results due to J. Smith. Finally if time permits we will work out the special case of interest in the calculus of functors.