The Baum-Connes Conjecture via Localization of Categories

We redefine the Baum-Connes assembly map using simplicial approximation in the equivariant Kasparov category. This interpretation is ideal for studying functorial properties and gives analogues of the Baum-Connes assembly map for all equivariant homology theories.     

Making use of social prototypes: From fuzzy concepts to firm decisions

Evidence suggestive of the ‘fuzzy’ structure of many natural language (as opposed to scientific) categories is reviewed. Examples are drawn from categorization schemes for objects, such as cars, fruit or tables, as well as for people, such as extroverts, hippies and ‘fraternity types’. It is argued that despite the fuzziness of natural categories, there is orderliness and utility to these concepts, as well. Specifically, natural categories are organized around prototypes, representative category members, which serve as reference points for the category. The identification of category members involves a prototype-matching process. Prototypes about ‘kinds of people’ can be very useful in decisions about people with whom to affiliate and places in which to live. This process was illustrated by reference to a case analysis of students' preferences for university housing. It was concluded that natural categories may well be fuzzy, but they are far from being dispensible.     

评徐新吾主编的《江南土布史》

做为一部以资料为基础结合分析说明的史料书，《江南土布史》的特点在于：史料来源丰富，涉及面广，个别史料具有独到的学术价值；在体例编排上，采用了按语与史料相结合的方式，错落有致，脉络清晰，具有很强的历史感。     

Quiver varieties and Lusztig's algebra

We study preprojective algebras of graphs and their relationship to module categories over representations of quantum SL(2). As an application, ADE quiver varieties of Nakajima are shown to be subvarieties of the variety of representations of a certain associative algebra introduced by Lusztig.     

英、汉语空语类指称对比研究

空语类理论是乔姆斯基的管约论中重要的子理论。英、汉语空语类在指称特征上存在着共性,但也呈现出不同的个性特征。英语空语类和部分汉语空语类具有指称句内可识别性,但汉语空语类的指称存在着语用倾向性。     

A remark on a theorem by Deligne

We give a proof avoiding spectral sequences of Deligne's decomposition theorem for objects in a triangulated category admitting a Lefschetz homomorphism.

     

REDUCIBILITY IN SOME CATEGORIES OF PARTIAL RECURSIVE OPERATORS

We consider two categories with one object, namely the set of all partial functions of one variable from the set of natural numbers into itself; the morphisms are the partial recursive operators in one case, and certain continuous partial mappings in the other case. We show that these categories are recursion categories and we characterize the domains and the complete domains. Some observations are made on a notion of reducibility obtained by using the total morphisms of these categories, and, subsequently, the general recursive operators.