URegina Topology & Geometry Seminar: Martin Frankland

Given a category C with a class of "weak equivalences" W, Dwyer and Kan constructed a simplicial localization of C that turns the morphisms in W into equivalences. We will go over this construction, its properties, and some tools to compute the mapping spaces. We will then discuss the Bergner model structure on simplicial categories, which allows us to view simplicial categories as a model for infinity-categories.