Hoàng Xuân Sính's Thesis: Categorifying Group Theory

Abstract

During what Vietnamese call the American War, Alexander Grothendieck spent three weeks teaching mathematics in and near Hanoi. Hoàng Xuân Sính 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 Hoàng Xuân Sính wrote her thesis, we explain some of its main results, and its context in the history of mathematics.