么半群、作用和範疇

《么半群、作用和範疇》是2016年世界圖書出版公司出版的著作，作者是[愛沙尼亞] M.吉爾普，[德] U.諾爾 。

基本介紹

• 中文名：么半群、作用和範疇
• 作者：[愛沙尼亞] M.吉爾普、[德] U.諾爾
• 出版社： 世界圖書出版公司 
• 出版時間：2016年12月01日
• 定價：119 元
• 開本：16 開
• 裝幀：平裝
• ISBN：9787519214722

內容簡介

這本書的第一部分為學習么半群、作用、變形、一致和非交換類別的學生提供了一個相對獨立和寬泛的角度。同時這本書也給出了半群理論，自動機，標準語言和其他半群的套用的背景。么半群圈積，作用和範疇在第二部分有詳細的介紹。該書的第二部分主要集中在么半群的同調分類結果，其中包括Morita類型理論在等值性和二象性和么半群的同調特性。

目錄

Foreword

Introduction

Ⅰ Elementary properties of monoids, acts and categories

1 Sets and relations

2 Groupoids, semigroups and monoids

3 Some classes of semigroups

4 Acts over monoids (monoid automata)

5 Decompositions and components

6 Categories

7 Functors

Ⅱ Constructions

1 Products and coproducts

2 Pullbacks and pushouts

3 Free objects and generators

4 Cofree objects and cogenerators

5 Tensor products

6 Wreath products of monoids and acts

7 The wreath product of a monoid with a small category

Ⅲ Classes of acts

1 Injective acts

2 Divisible acts

3 Principally weakly injective acts

4 fg-weakly injective acts

5 Weakly injective acts

6 Absolutely pure acts

7 Cogenerators and overview

8 Torsion free acts

9 Flatness of acts and related properties

10 Principally weakly flat acts

11 Weakly flat acts

12 Flat acts

13 Acts satisfying Condition (P)

14 Acts satisfying Condition (E)

15 Equalizer fiat acts

16 Pullback fiat acts and overview

17 Projective acts

18 Generators

19 Regular acts and overview

Ⅳ Homological classification of monoids

1 Principal weak injectivity

2 On fg-weak injectivity

3 Weak injectivity

4 Absolute purity

5 Injectivity and overview

6 Torsion freeness and principal weak flatness

7 Weak flatness

8 Flatness

9 Condition (P)

10 Strong flatness

11 Projectivity

12 Projective generators

13 Freeness and overview

14 Regularity of acts

Ⅴ Equivalence and Duality

1 Adjoint functors

2 Categories equivalent to Act -- S

3 Morita equivalence of monoids

4 Endomorphism monoids of generators

5 On Morita duality

Bibliography

Index of symbols

Index