Florian Schwarz

At a previous presentation Geoff Cruttwell asked me, if the vertical bundle of a principal bundle in a join restriction category is trivial. This was not just an interesting question on its own, it also pointed towards more going on with group...

Abstract: In the first part of this talk we will discuss several ways, how principal bundles over a manifold can be described. The main two of them are maps from the base manifold into the group’s classifying space and assignments of group elements...

Tangent categories are a categorical generalization of the category of manifolds by having maps like the projection and the zero-section of the tangent bundle that fulfill certain relations. With a similar strategy, Cartesian differential categories...

A partial monoid is a set A with a multiplication and a unit, but the multiplication is only defined on a certain subset of pairs. This means the multiplication m:AxA -> A is a partial map, a map that is only defined on a certain subset of its domain...

Vector bundles and principal bundles are important objects in differential geometry. Vector bundles over a manifold M are manifolds that are locally isomorphic to the Cartesian product M times V for some vector space V, while principal bundles over M...

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...