Workshop on n-Categories: Foundations and Applications

摘要奖：DMS-0354538主要研究者：J. Peter May和John C. 2004年夏季计划的研究所数学及其应用是“n类：基础和应用”，在明尼阿波利斯，明尼苏达州的研究所的设施，在明尼苏达大学双城。 该奖项提供参与者支持，以增加夏季计划的成员，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。该研究所的暑期项目和后续工作会议特别旨在使美国学生和初级研究人员了解国际上正在追求的n-范畴的各种想法。 讲习班后的工作组试图将讲习班产生的更高的能量集中在讲习班期间确定的最有希望的问题上，这是一项创新，其进展将受到关注。“范畴”的数学概念是一个通用的概念，定义于20世纪世纪中期，用来概括各种数学对象的共同特征。 虽然抽象，范畴论的思想是广泛有用的，因为它们促进知识从一个领域转移到另一个领域，例如，从代数到理论计算机科学。 在世纪末，几个复杂的“n-范畴”的概念开始发挥作用，以满足代数、几何和物理理论的几个领域的需要，但我们还没有一个“n-范畴”的定义，它像最初的想法一样广泛适用。 这个暑期项目的领导者们的临时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.