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 0 0   Download

Unemployment and Its Natural Rate presents categories of unemployment, how is unemployment measured, unions and collective bargaining, the theory of efficiency wages and summary.

49p talata_1 22-09-2014 60 5   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 48 6   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 47 5   Download

610 Chapter 14. Statistical Description of Data In the other category, model-dependent statistics, we lump the whole subject of fitting data to a theory, parameter estimation, least-squares fits, and so on. Those subjects are introduced in Chapter 15. Section 14.1 deals with so-called measures of central tendency, the moments of a distribution, the median and mode. In §14.2 we learn to test whether different data sets are drawn from distributions with different values of these measures of central tendency. This leads naturally, in §14.

6p babyuni 17-08-2010 68 4   Download