Ho\`ang Xu\^an S\'inh's Thesis: Categorifying Group Theory

Abstract

During what Vietnamese call the American War, Alexander Grothendieck spent three weeks teaching mathematics in and near Hanoi. Ho\`ang Xu\^an S\'inh took notes on his lectures and later did her thesis work with him by correspondence. In her thesis she developed the theory of "Gr-categories", which are monoidal categories in which all objects and morphisms have inverses. Now often called "2-groups", these structures allow the study of symmetries that themselves have symmetries. After a brief account of how Ho\`ang Xu\^an S\'inh wrote her thesis, we explain some of its main results, and its context in the history of mathematics.