Workshop on n-Categories: Foundations and Applications

摘要奖：DMS-0354538首席研究员：J·彼得·梅和约翰·C·贝兹2004年数学及其应用研究所的暑期计划将在明尼苏达州明尼阿波利斯市明尼苏达州双子城大学的研究所设施中举行，主题是“n-类别：基础和应用”。该奖项提供参与者支持，以扩大暑期项目的成员，并使一组研讨会参与者有可能加入领导组织者和他的学生在芝加哥大学举行的研讨会后工作会议。该提案将新兴的n-范畴理论描述为一个国际关注的领域，但在美国相对较少出现。该研究所的暑期计划和随后的工作会议特别旨在让美国学生和初级研究人员接触到国际上正在追求的关于n-范畴的各种想法。研讨会后工作组试图将研讨会产生的更多精力集中到研讨会期间确定的最有希望的问题上，这是一项创新，其进展将受到感兴趣的关注。“范畴”的数学概念是20世纪中期定义的一个通用概念，用于概括各种数学对象的共同特征。范畴理论的概念虽然抽象，但却非常有用，因为它们促进了知识从一个领域向另一个领域的转移，例如，从代数到理论计算机科学。在20世纪末，几个复杂的“n范畴”概念开始发挥作用，以满足代数、几何和物理理论的几个领域的需要，但我们还没有像最初的概念那样广泛适用的“n范畴”的定义。这个暑期计划的领导人的解释和研究工作旨在实现这一缺失的综合。

AbstractAward: DMS-0354538Principal Investigator: J. Peter May and John C. BaezThe 2004 Summer Program of the Institute for Mathematics and itsApplications is on "n-Categories: Foundations and Applications," to beheld in Minneapolis, Minnesota at the Institute's facilities at theUniversity of Minnesota - Twin Cities. This award providesparticipant support to augment the summer program's membership and tomake it possible for a group of workshop participants to join the leadorganizer and his students in a post-workshop working session at theUniversity of Chicago. The proposal describes the emerging theory ofn-categories as an area of international attention but of relativelylittle presence in the U.S. The Institute's summer program and thesubsequent working session particularly aim to expose U.S. studentsand junior researchers to the variety of ideas on n-categories beingpursued internationally. The post-workshop working group is anattempt to focus heightened energies resulting from the workshop ontoproblems of greatest promise, as identified during the workshop, andis an innovation whose progress will be watched with interest.The mathematical idea of a "category" is a versatile notion defined inthe mid-20th century to encapsulate the common features of a largevariety of mathematical objects. Although abstract, the ideas ofcategory theory are widely useful because they facilitate knowledgetransfer from one domain to another, for example, from algebra totheoretical computer science. At the end of the 20th century severalcomplicated notions of "n-category" had come into play to meet theneeds of several areas of algebra, geometry, and physical theory, butwe do not have a definition yet of "n-category" that is as broadlyapplicable as the original idea. The expository and research work ofthe leaders of this summer program aims to achieve that missingsynthesis.