导语

  

内容提要

  

    M.吉尔普、U.诺尔著的《幺半群作用和范畴(英文版)》的第一部分为学习幺半群、作用、变形、一致和非交换类别的学生提供了一个相对独立和宽泛的角度。同时这本书也给出了半群理论，自动机，标准语言和其他半群的应用的背景。幺半群圈积，作用和范畴在第二部分有详细的介绍。该书的第二部分主要集中在幺半群的同调分类结果，其中包括Morita类型理论在等值性和二象性和幺半群的同调特性。

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