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
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