From the text: "A Picard category is a Gr-category equipped with a commutativity constraint compatible with its associativity constraint. A Picard category P is said to be restricted if its commutativity constraint c satisfies c_{x,x}= identity for all objects x. We represent every Picard category by a complex of chains and we deduce
Copyright 2003 Vietnam News Briefs Vietnam News Briefs March 28, 2003 LENGTH: 95 words HEADLINE: SOCIAL & CULTURAL ISSUES: FEMALE VIETNAMESE SCIENTISTS RECEIVE FRENCH ORDER BODY: The French Government has awarded the French Order of Academic Palms to two Vietnamese scientists, Le Hong Sam and Hoang Xuan Sinh, for their contributions to boosting cooperation in culture and science between the two nations. Ms Sam is a researcher on French literature and currently works for the National University of Social Sciences & Humanities in Hanoi. Ms Sinh, a mathematician, is the principal of the Thang Long Open University in Hanoi. The presentation ceremony was held at the French Embassy in Hanoi on March 25. ********************************************************************** Her papers, as adapted from MathSciNet: Hoang Xuan Sinh Gr-categories strictes. (French) Acta Math. Vietnam. 3 (1978), no. 2, 47--59. 18D10 (20J05 20L10) A Gr-category is a groupoid P which is a monoidal category with product and unit such that each object X of P has an inverse (X', t, p), where t:X'*X -> 1 and p:X*X' -> 1. It is called a strict Gr-category if it is a strict monoidal category and t and p are identities for every X. The main theorem of this paper states that every Gr-category is Gr-equivalent to a strict Gr-category...The proof of this theorem uses a result of the author's thesis at the University of Paris VII, 1975 which is that every Gr-category P is determined up to a Gr-equivalence by two groups...As an application of the results of this paper, the author proves Lemma 9.1 of S. Eilenberg and S. Mac Lane [Ann. of Math. (2) 48 (1947), 326--341; MR 9, 7] on the realization of a 3-cocycle as the obstruction of a problem of extension. Reviewed by J. L. Williams Hoang Xuan Sinh Categories de Picard restreintes. (French) [Restricted Picard categories] Acta Math. Vietnam. 7 (1982), no. 1, 117--122 (1983). 18E99 that the classification of restricted prefastened (`preepinglees') Picard categories of type (M,N) is trivial."