Florian Schwarz

I call my area “categorical geometry”, generalizing geometric constructions to more abstract setups
using (higher) category theory. For this purpose I work with tangent categories, restriction categories,
bicategories and quasicategories. In particular, in my thesis I study bundles including tangent and
differential bundles in tangent categories and principal bundles in join restriction categories. Interest-
ingly, some examples for categorical geometry can be found in the Goodwillie functor calculus and the
Johnson McCarthy functor calculus.
In addition I am currently interested in monoidal closed categories their application to quantum infor-
mation.
For the future I am interested in applying my categorical techniques to other problems within mathe-
matics, in particular to network-based dynamical systems related to sustainability like energy grids.

Awards

Eyes High International Doctoral Scholarship, University of Calgary. 2025
Alberta Innovates Graduate student Sholarship, Province of Alberta. 2023
Alberta Graduate Excellence Sholarship, Province of Alberta. 2023
Henrietta Weyland Graduate Scholarship in Mathematics, Endowed by Henrietta Weyland. 2023
Studienstiftung des Deutschen Volkes, German Academic Scholarship Foundation. 2017

Publications

Lie groups in tangent join restriction categories . R. Cockett and F. Schwarz. (2025)
Differential bundles as functors from free modules . F. Schwarz. (2025)