| 查看: 1268 | 回复: 13 | |||||
| 【奖励】 本帖被评价12次，作者maojun1998增加金币 9.6 个 | |||||
[资源]
【Graduate Texts in Mathematics 26】【Algebraic Theories】可复制文字
|
|||||
 Preface In the past decade, category theory has widened its scope and now interacts with many areas of mathematics. This book develops some of the interactions between universal algebra and category theory as well as some of the resulting applications. We begin with an exposition of equationally defineable classes from the point of view of "algebraic theories," but without the use of category theory. This serves to motivate the general treatment of algebraic theories in a category, which is the central concern of the book. (No category theory is presumed; rather, an independent treatment is provided by the second chapter.) Applications abound throughout the text and exercises and in the final chapter in which we pursue problems originating in topological dynamics and in automata theory. This book is a natural outgrowth of the ideas of a small group of mathematicians, many of whom were in residence at the Forschungsinstitut für Mathematik of the Eidgenössische Technische Hochschule in Zürich, Switzerland during the academic year 1966-67. It was in this stimulating atmosphere that the author wrote his doctoral dissertation. The "Zürich School," then, was Michael Barr, Jon Beck, John Gray, Bill Lawvere, Fred Linton, and Myles Tierney (who were there) and (at least) Harry Appelgate, Sammy Eilenberg, John Isbell, and Saunders Mac Lane (whose spiritual presence was tangible.) I am grateful to the National Science Foundation who provided support, under grants GJ 35759 and OCR 72-03733 A01, while I wrote this book. I wish to thank many of my colleagues, particularly Michael Arbib, Michael Barr, Jack Duskin, Hartrnut Ehrig, Walter Felscher, John Isbell, Fred Linton, Saunders Mac Lane, Robert Part\ Michael Pfender, Walter Tholen, Donovan Van Osdol, and Oswald Wyler, whose criticisms and suggestions made it possible to improve many portions of this book; and Saunders Mac Lane, who provided encouragement on many occasions. 目录 Table of Contents Introduction ............................................... . Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Chapter 1. Algebraic theories of Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1. Finitary Universal Algebra ............................ 7 2. The Clone of an Equational Presentation ................ 15 3. Algebraic Theories .................................... 24 4. The Algebras of a Theory .............................. 32 5. Infinitary Theories .................................... 50 Chapter 2. Trade Secrets of Category Theory .................... 82 1. The Base Category .................................... 82 2. Free Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 115 3. Objects with Structure ................................ 139 Chapter 3. Algebraic Theories in a Category . . . . . . . . . . . . . . . . . . . . .. 161 1. Recognition Theorems ................................ 161 2. Theories as Monoids .................................. 204 3. Abstract Birkhoff Subcategories ........................ 224 4. Regular Categories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 234 5. Fibre-Complete Algebra. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 246 6. Bialgebras............................................ 257 7. Colimits ............................................ 272 Chapter 4. Some Applications and Interactions . . . . . . . . . . . . . . . . . . .. 280 1. Minimal Algebras : Interactions with Topological Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 280 2. Free Algebraic Theories: the Minimal Realization of Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 292 3. Nondeterminism .......................... . . . . . . . . . . .. 309 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 341 Index. . . . . .. . . . . . . . . . . . . . . .. . . . . . . .. . . . . . . . . . . . . . . . . . . . . . .. 349 |
回复此楼» 本帖附件资源列表
-
欢迎监督和反馈：小木虫仅提供交流平台，不对该内容负责。
本内容由用户自主发布，如果其内容涉及到知识产权问题，其责任在于用户本人，如对版权有异议，请联系邮箱：xiaomuchong@tal.com - 附件 1 : Ernest_G._Manes__(auth.)_Algebraic_Theories.pdf
2016-01-01 11:00:57, 16.28 M
» 收录本帖的淘帖专辑推荐
 Allen的英文原版+百科 | 计算数学与经济统计 | Allen的数学 |
» 猜你喜欢
281求调剂（0805）
已经有8人回复
-
环境领域全国重点实验室招收博士1-2名
已经有3人回复
-
材料专硕306英一数二
已经有10人回复
-
301求调剂
已经有6人回复
-
一志愿天津大学化学工艺专业（081702）315分求调剂
已经有7人回复
-
302求调剂
已经有6人回复
-
26博士申请
已经有3人回复
-
268求调剂
已经有3人回复
-
311求调剂
已经有10人回复
-
被我言中：新模板不强调格式了，假专家开始管格式了
已经有4人回复
» 本主题相关价值贴推荐，对您同样有帮助:
- 【科技文章写作】《Academic Writing for Graduate Students》【已搜无重复】
已经有189人回复
- 【待做清单/待办事项】【BD-RMVB/956MB】【2013欧美喜剧】【中英双字】
已经有48人回复
- Graduate Texts in Contemporary Physics The Quantum Hall Effect【转载】
已经有8人回复
- 【转载】zz:Large Hadron Collider Phenomenology (Scottish Graduate Series)
已经有0人回复
- 【书籍】【Springer 2012】Green Solvents I 【不多解释】
已经有279人回复
- 【求助】关于structured graduate PhD programs
已经有4人回复
- 【其他】美国大学分专业排名Usnews_Best_Graduate_Shcool_2010
已经有227人回复
- 【Share】A day of my graduate life
已经有23人回复
- 【资源】How to be a graduate
已经有9人回复
- 【求助】询问一下申请美国的Graduate一些问题...
已经有5人回复
- 【Pure water】New graduate builds egg-like house in Beijing
已经有13人回复
- 【原创】身份是 Graduate intern/trainee， 什么意思
已经有1人回复
- 【Pure water】Graduate unemployment at highest level for 17 years
已经有2人回复
- 【求助】Graduate Studies Committee Chair 如何翻译
已经有1人回复
- 【Share】I have to wait quietly at home for my graduate school admission letter.
已经有12人回复
- 【素材】How to Be a Good Graduate Student
已经有10人回复
- 【资源】Crystal Field Handbook 【无重复】
已经有27人回复
简单回复
2016-01-01 14:27
回复
五星好评 顶一下，感谢分享！
2016-01-01 16:57
回复
五星好评 顶一下，感谢分享！
ha16684楼
2016-01-02 01:06
回复
五星好评 顶一下，感谢分享！
neuqyj5楼
2016-01-02 08:48
回复
五星好评 顶一下，感谢分享！
2016-01-02 09:14
回复
五星好评 顶一下，感谢分享！
2016-01-03 10:57
回复
五星好评 顶一下，感谢分享！
2016-01-03 16:14
回复
五星好评 顶一下，感谢分享！
tianwk9楼
2016-01-04 00:02
回复
五星好评 顶一下，感谢分享！
Quan.10楼
2016-01-04 05:15
回复
五星好评 顶一下，感谢分享！
lantianbihb11楼
2016-01-04 11:42
回复
五星好评 顶一下，感谢分享！
qiao1912楼
2016-01-26 14:30
回复
五星好评 顶一下，感谢分享！
tianwk13楼
2024-12-19 15:39
回复
顶一下，感谢分享！
Giant9514楼
2024-12-20 07:39
回复
五星好评 顶一下，感谢分享！
