Category Theory

This article aims to introduce this important mathematical theory to the community of Vietnamese mathematicians in a hope to bring more attention of Vietnamese mathematicians and math students to this vibrant research area.

8p viling 11-10-2024 2 1   Download

The purpose of this paper aims to find out the language of “Affect”, “Judgement” and “Appreciation” in the category “Attitude” used in English restaurant reviews in terms of syntactic features and semantic features. The findings reveal that the semantic features, the positive evaluative Attitudes reflected in the samples outweigh the negative values.

6p vibenya 31-12-2024 15 2   Download

This paper introduces the notion of a stability condition on a triangulated category. The motivation comes from the study of Dirichlet branes in string theory, and especially from M.R. Douglas’s work on Π-stability. From a mathematical point of view, the most interesting feature of the definition is that the set of stability conditions Stab(D) on a fixed category D has a natural topology, thus defining a new invariant of triangulated categories.

30p noel_noel 17-01-2013 54 7   Download

Using a variety of methods developed in the literature (in particular, the theory of weak Hopf algebras), we prove a number of general results about fusion categories in characteristic zero. We show that the global dimension of a fusion category is always positive, and that the S-matrix of any (not necessarily hermitian) modular category is unitary. We also show that the category of module functors between two module categories over a fusion category is semisimple, and that fusion categories and tensor functors between them are undeformable (generalized Ocneanu rigidity).

63p noel_noel 17-01-2013 50 6   Download