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

TL;DR

This paper discusses the development of 'Gr-categories' or 2-groups, a categorification of group theory, which enable the study of symmetries with their own symmetries, based on Hoàng Xuân Sính's thesis influenced by Grothendieck.

Contribution

It introduces the concept of Gr-categories (2-groups), a novel categorification of groups, expanding the framework for symmetry analysis in mathematics.

Findings

Development of the theory of Gr-categories (2-groups)

Connection to symmetries with symmetries

Historical context of the thesis work

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.