The n-Category Café

Here is the book in honor of Hoàng Xuân Sính’s birthday:

Her thesis was hand-written in French, and you can see its title reproduced here. ‘Gr-catégories’ are categories like groups. I later called them ‘2-groups’, and that seems to have caught on.

Here is the table of contents:

The introduction includes the following remarks:

In later years, Professor Hoàng Xuân Sính no longer had time to devote to mathematical research, as she devoted all her energy and enthusiasm to building Thang Long University. Her life is the consistent journey of a patriotic intellectual and talented scientist: from the decision to leave a comfortable life in France to return to contribute to Vietnamese education during the war years, determined to reach the pinnacle of science in extremely difficult conditions, to extraordinary efforts and determination to overcome countless challenges, building the first non-public university in Vietnam’s education system.

In the first part of this book, the reader can see part of the handwritten manuscript of the thesis, which Professor Hoàng Xuân Sính sent to Paris. At that time, it was almost impossible to type the Thesis! This manuscript is a valuable document that Thang Long University has thanks to the enthusiastic and generous help of Professor Nguyen Tien Dung (Toulouse University) and Dr. Jean Malgoire, Grothendieck’s last graduate student.

You can also see her thesis typeset in LaTeX here (in French), and the original hand-written version and much more here. My essay in this book can be gotten here:

• 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.