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Monoids, acts and categories : with applications to wreath products and graphs : a handbook for students and researchers

Author: M Kilʹp; U Knauer; A V Mikhalev
Publisher: Berlin ; New York : Walter de Gruyter, 2000.
Series: De Gruyter expositions in mathematics, 29.
Edition/Format:   eBook : Document : EnglishView all editions and formats
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A discussion of monoids, acts and categories with applications to wreath products and graphs. It is divided into sections which address: elementary properties of monoids, acts and categories;  Read more...

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Genre/Form: Electronic books
Handbooks and manuals
Handbooks, manuals, etc
Additional Physical Format: Print version:
Kilʹp, M.
Monoids, acts and categories.
Berlin ; New York : Walter de Gruyter, 2000
(DLC) 99045793
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: M Kilʹp; U Knauer; A V Mikhalev
ISBN: 9783110812909 3110812908
OCLC Number: 811372326
Description: 1 online resource (xvii, 529 pages) : illustrations.
Contents: ""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 flat acts""; ""16 Pullback flat 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""
Series Title: De Gruyter expositions in mathematics, 29.
Responsibility: by Mati Kilp, Ulrich Knauer, Alexander V. Mikhalev.

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"The authors of this book are well-known specialists in the area of homological classification of monoids. The presentation is extremely clear and incisive. Without a doubt, the book could serve as a Read more...

 
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