艾米莉·里尔: 语境中的范畴论 Category Theory in Context

基本信息

Format:Paperback / softback 272 pages

Publisher:Dover Publications Inc.

Imprint:Dover Publications Inc.

ISBN:9780486809038

Published:30 Dec 2016

Weight:358g

Dimensions:156 x 333 x 18 (mm)

页面参数仅供参考，具体以实物为准

书籍简介

范畴论为数学提供了一种跨学科的语言，旨在描述一般现象，使思想能够从一个研究领域转移到另一个研究领域。

范畴理论为二十世纪纯数学的许多重大进展奠定了基础。这本简明扼要的原版教材是作者艾米莉-里尔（Emily Riehl）在哈佛大学和约翰-霍普金斯大学教授的课程的基础上编写的，适用于一学期的课程。

本书介绍了范畴论的基本概念：

 -范畴、函数、自然转换

-米田(Yoneda)两难、极限和余限

-结、单子和其他主题

适合数学专业的高年级本科生和研究生阅读，为理解和解决以下方面的难题提供了工具：

 -代数、数论

-代数几何和代数拓扑学

-前提条件：熟悉一些基本的集合论和逻辑学

作者从范畴的角度出发，通过大量数学实例，说明范畴论的概念和构造是如何从更基本的数学思想中产生并照亮更基本的数学思想的。

Category theory provides a cross-disciplinary language for mathematics designed to delineate general phenomena, which enables the transfer of ideas from one area of study to another.

Category theory has provided the foundations for many of the twentieth century's most significant advances in pure mathematics. This concise, original text for a one-semester course on the subject is derived from courses that author Emily Riehl taught at Harvard and Johns Hopkins Universities.

The treatment introduces the essential concepts of category theory:

Categories, functors, natural transformations

The Yoneda lemma, limits and colimits

Adjunctions, monads, and other topics

Suitable for advanced undergraduates and graduate students in mathematics, the text provides tools for understanding and attacking difficult problems in the following:

Algebra, number theory

Algebraic geometry, and algebraic topology

Prerequisites are limited to familiarity with some basic set theory and logic

Drawing upon a broad range of mathematical examples from the categorical perspective, the author illustrates how the concepts and constructions of category theory arise from and illuminate more basic mathematical ideas.

Dover is widely recognized for a magnificent mathematics list featuring such world-class theorists as Paul J. Cohen (Set Theory and the Continuum Hypothesis), Alfred Tarski (Undecidable Theories), Gary Chartrand (Introductory Graph Theory), Hermann Weyl (The Concept of a Riemann Surface), Shlomo Sternberg (Dynamical Systems), and multiple works by C. R. Wylie in geometry, plus Stanley J. Farlow's Partial Differential Equations for Scientists and Engineers.

作者简介

Emily Riehl 是约翰霍普金斯大学数学系助理教授。她于 2011 年获得芝加哥大学博士学位，并于 2011-15 年间在哈佛大学担任本杰明-皮尔斯（Benjamin Pierce）和国家科学基金会博士后研究员。她还是《分类同调理论》一书的作者。

Emily Riehl is Assistant Professor in the Department of Mathematics at Johns Hopkins University. She received her Ph.D. from the University of Chicago in 2011 and was a Benjamin Pierce and NSF Postdoctoral Fellow at Harvard University from 2011–15. She is also the author of Categorical Homotopy Theory.