Perfect categories

Perfect Derived Categories of Positively Graded DG Algebras

We investigate the perfect derived category dgPer(A) of a positively graded differential graded (dg) algebra A whose degree zero part is a dg subalgebra and semisimple as a ring. We introduce an equivalent subcategory of dgPer(A) whose objects are easy to describe, define a t-structure on dgPer(A) and study its heart. We show that dgPer(A) is a Krull-RemakSchmidt category and consider the case ...

In perfect harmony: synchronizing the self to activated social categories.

The self-concept is one of the main organizing constructs in the behavioral sciences because it influences how people interpret their environment, the choices they make, whether and how they initiate action, and the pursuit of specific goals. Because belonging to social groups and feeling interconnected is critical to human survival, the authors propose that people spontaneously change their wo...

Journal of Personality and Social Psychology In Perfect Harmony: Synchronizing the Self to Activated Social Categories

OPERADIC CATEGORIES, A∞-CATEGORIES AND n-CATEGORIES

When I offered to talk here, I asked myself if I had something suitable for a nice short 20 minute talk, and sent in an abstract about “cores of spaces and spectra”. However, since I have been given 50 minutes, I have decided to scrap that for something a little more substantial. It is brand new. I assume that I am among friends and that you won’t mind if some of what I say turns out to be nons...

CLUSTER ALGEBRAS AND CLUSTER CATEGORIES

These are notes from introductory survey lectures given at the Institute for Studies in Theoretical Physics and Mathematics (IPM), Teheran, in 2008 and 2010. We present the definition and the fundamental properties of Fomin-Zelevinsky’s cluster algebras. Then, we introduce quiver representations and show how they can be used to construct cluster variables, which are the canonical generator...