Theory and applications of tangent categories
切范畴的理论与应用
基本信息
- 批准号:RGPIN-2019-04081
- 负责人:
- 金额:$ 1.24万
- 依托单位:
- 依托单位国家:加拿大
- 项目类别:Discovery Grants Program - Individual
- 财政年份:2020
- 资助国家:加拿大
- 起止时间:2020-01-01 至 2021-12-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
Calculus is the most useful and practical area of mathematics. It deals with how to calculate with changing quantities, and is thus a fundamental tool in sciences, economics, and engineering. However, while it is extremely important in applied contexts, its study is but one part of a much wider world of mathematics, which includes many other topics, such as combinatorics (counting), topology (the study of abstract shapes) and computer science.
On the other hand, in some of these other areas of mathematics, researchers have started to develop ideas that share many formal similarities with calculus. These have gone by various names: polynomial functors (in combinatorics), the functor calculus (in topology) and differential linear logic (in computer science). As these ideas have been developed, it has not been clear how they are related to each other, or if they truly share a direct similarity with ordinary calculus.
The research proposed for this grant offers a way to resolve this problem, by allowing one to view all these various notions as all aspects of one common idea, the notion of a tangent category. By providing a common framework for these different ideas, tangent categories provide an essential language to translate ideas between different areas of mathematics. Moreoever, one can develop much of differential geometry within the abstract setting of a tangent category, allowing the sophisticated ideas of differential geometry to be transferred into the study of polynomial functors, functor calculus, and differential linear logic. This work thus allows us an entirely new way to advance our understanding of these important ideas.
微积分是数学中最有用和最实用的领域。它涉及如何计算变化的量,因此是科学、经济和工程的基本工具。然而,虽然它在应用环境中非常重要,但它的研究只是更广阔的数学世界的一部分,其中包括许多其他主题,如组合学(计数),拓扑学(抽象形状的研究)和计算机科学。
项目成果
期刊论文数量(0)
专著数量(0)
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专利数量(0)
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Cruttwell, Geoffrey其他文献
Cruttwell, Geoffrey的其他文献
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{{ truncateString('Cruttwell, Geoffrey', 18)}}的其他基金
Theory and applications of tangent categories
切范畴的理论与应用
- 批准号:
RGPIN-2019-04081 - 财政年份:2022
- 资助金额:
$ 1.24万 - 项目类别:
Discovery Grants Program - Individual
Theory and applications of tangent categories
切范畴的理论与应用
- 批准号:
RGPIN-2019-04081 - 财政年份:2021
- 资助金额:
$ 1.24万 - 项目类别:
Discovery Grants Program - Individual
Theory and applications of tangent categories
切范畴的理论与应用
- 批准号:
RGPIN-2019-04081 - 财政年份:2019
- 资助金额:
$ 1.24万 - 项目类别:
Discovery Grants Program - Individual
Abstract tangent functors
抽象正切函子
- 批准号:
435766-2013 - 财政年份:2018
- 资助金额:
$ 1.24万 - 项目类别:
Discovery Grants Program - Individual
Abstract tangent functors
抽象正切函子
- 批准号:
435766-2013 - 财政年份:2017
- 资助金额:
$ 1.24万 - 项目类别:
Discovery Grants Program - Individual
Abstract tangent functors
抽象正切函子
- 批准号:
435766-2013 - 财政年份:2015
- 资助金额:
$ 1.24万 - 项目类别:
Discovery Grants Program - Individual
Abstract tangent functors
抽象正切函子
- 批准号:
435766-2013 - 财政年份:2014
- 资助金额:
$ 1.24万 - 项目类别:
Discovery Grants Program - Individual
Abstract tangent functors
抽象正切函子
- 批准号:
435766-2013 - 财政年份:2013
- 资助金额:
$ 1.24万 - 项目类别:
Discovery Grants Program - Individual
Doctor's Level Studies in Category Theory
范畴论博士级研究
- 批准号:
317865-2005 - 财政年份:2007
- 资助金额:
$ 1.24万 - 项目类别:
Postgraduate Scholarships - Doctoral
Doctor's Level Studies in Category Theory
范畴论博士级研究
- 批准号:
317865-2005 - 财政年份:2006
- 资助金额:
$ 1.24万 - 项目类别:
Postgraduate Scholarships - Doctoral
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