nLab Hoàng Xuân Sính

Hoàng Xuân Sính is a Vietnamese mathematician who was a student of Grothendieck. Her thesis was on Gr-categories (now more often called (weak) 2-groups) and Picard category (also called symmetric 2-groups, i.e. symmetric monoidal categories with all objects invertible and all morphisms invertible).

For more on Hoàng Xuân Sính see:

• Wikipedia entry

• John Baez, Hoàng Xuân Sính $n$-Category Café (June 20, 2022)

Selected writings:

Early discussion of 2-groups:

• Hoàng Xuân Sính, Gr-catégories, PhD thesis, Hanoi (1973, 1975) [web, pdf, pdf]

The version linked to above is a handwritten draft copy, with some annotations by someone (perhaps Grothendieck). A typed version does exist which does not contain the preliminary material in the first file. The date of the official thesis defense was 22 May 1975, with Jean-Louis Verdier, Henri Cartan, Laurent Schwartz and Michel Zisman as well as Alexander Grothendieck as the ‘jury’. It was a ‘doctorat d’état’. The link to her thesis contains other material, including a collection of remarks by Grothendieck on her work as well as two papers by Sính related to the subject of her thesis:

• Hoàng Xuân Sính, Gr-catégories strictes, Acta Mathematica Vietnamica 3 2 (1978) 47-59 [pdf]

• Hoàng Xuân Sính, Catégories de Picard restreintes, Acta Mathematica Vietnamica 7 1 (1983) 117-122 [pdf]

The first appears to prove that every 2-group is equivalent to a strict 2-group arising from a crossed module. The second calls a symmetric 2-group a Picard category, and calls a Picard category restrained if the braiding $B_{x,x} \colon x \otimes x \to x \otimes x$ is the identity for all objects $x$. It then proves that every Picard category is equivalent to one arising from a 2-term chain complex of abelian groups.

Related entries

• 2-group, symmetric 2-group

• crossed module

• Picard groupoid

category: people