UCalgary Peripatetic Seminar: Florian Schwarz

Principal bundles arise in different areas of matematics with different definitions. However, they all have in common some kind of local triviality. Here I will present some work in progress on generalizing these in terms of join restriction categories, a notion that means to capture properties of partial maps.

Most of the time we will spend on join-restriction categories and their properties. Then, abstracting concepts from differential geometry, we will consider fiber bundles and principal bundles and see that the existence of a global right action is a consequence and does not need to be demanded.