Speaker: Rick Jardine

Title: Cocycle categories

Abstract: The set of maps between objects in a homotopy category can be identified with path components of a category of cocycles, in great generality. The applications, to date, have predominantly consisted of homotopy classification results in non-abelian cohomology theory. Cocycle category methods lead to an expanded (and interesting) version of the Verdier hypercovering theorem. Conjecturally, cocycle categories can also be used to give a new description of etale homotopy theory, which would involve neither hypercovers nor pro-objects.