Workshop on n-Categories: Foundations and Applications

n 类别研讨会：基础与应用

• 批准号: 0354538
• 负责人: J May
• 金额: $ 2.5万
• 依托单位: University of Chicago
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-06-01 至 2005-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0354538&HistoricalAwards=false
• 关键词: Workshop; Categories; Foundations; Applications

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.

[摘要]获奖：dms -0354538首席研究员：J. Peter May和John C. baez2004年美国数学及其应用研究所暑期项目“n类：基础与应用”，将在明尼苏达州明尼阿波利斯市明尼苏达大学双城分校的研究所设施中举行。该奖项为参与者提供支持，以增加夏季项目的成员数量，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-分类理论描述为一个受到国际关注的领域，但在美国相对较少。该研究所的夏季项目和随后的工作会议特别旨在使美国学生和初级研究人员接触到国际上正在追求的n-分类的各种想法。讲习班后工作组是一种尝试，旨在将讲习班产生的更高能量集中在讲习班期间确定的最有希望的问题上，这是一种创新，其进展将受到饶有兴趣的关注。“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。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。20世纪末，为了满足代数、几何和物理理论等多个领域的需要，出现了一些关于“n类”的复杂概念，但我们至今还没有一个像最初构想那样广泛适用的“n类”定义。这个暑期项目的领导者们的论述和研究工作旨在实现这一缺失的综合。