Monoids, acts and categories: with applications to wreath products and graphs ; a handbook for students and researchers
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; New York
<<de>> Gruyter
2000
|
| Schriftenreihe: | De Gruyter expositions in mathematics
29 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVII, 529 S. graph. Darst. : 25 cm |
| ISBN: | 3110152487 |
Internformat
MARC
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| 264 | 1 | |a Berlin ; New York |b <<de>> Gruyter |c 2000 | |
| 300 | |a XVII, 529 S. |b graph. Darst. : 25 cm | ||
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Datensatz im Suchindex
| _version_ | 1804127735191175168 |
|---|---|
| adam_text | Contents
Foreword vii
Introduction xii
I Elementary properties of monoids, acts and categories 1
1 Sets and relations 1
2 Groupoids, semigroups and monoids 13
3 Some classes of semigroups 24
4 Acts over monoids (monoid automata) 42
5 Decompositions and components 62
6 Categories 78
7 Functors 89
II Constructions 103
1 Products and coproducts 103
2 Pullbacks and pushouts 114
3 Free objects and generators 138
4 Cofree objects and cogenerators 149
5 Tensor products 155
6 Wreath products of monoids and acts 165
7 The wreath product of a monoid with a small category .... 175
III Classes of acts 183
1 Injective acts 184
2 Divisible acts 195
3 Principally weakly injective acts 200
4 fg weakly injective acts 204
5 Weakly injective acts 205
6 Absolutely pure acts 207
7 Cogenerators and overview 214
8 Torsion free acts 218
9 Flatness of acts and related properties 223
10 Principally weakly flat acts 225
11 Weakly flat acts 233
vi Contents
12 Flat acts 238
13 Acts satisfying Condition (P) 249
14 Acts satisfying Condition (E) 257
15 Equalizer flat acts 262
16 Pullback flat acts and overview 267
17 Projective acts 274
18 Generators 291
19 Regular acts and overview 300
IV Homological classification of monoids 306
1 Principal weak injectivity 307
2 On fg weak injectivity 311
3 Weak injectivity 319
4 Absolute purity 322
5 Injectivity and overview 326
6 Torsion freeness and principal weak flatness 335
7 Weak flatness 339
8 Flatness 344
9 Condition (P) 360
10 Strong flatness 367
11 Projectivity 372
12 Projective generators 381
13 Freeness and overview 385
14 Regularity of acts 394
V Equivalence and Duality 397
1 Adjoint functors 398
2 Categories equivalent to Act — S 427
3 Morita equivalence of monoids 437
4 Endomorphism monoids of generators 455
5 On Morita duality 467
Bibliography 483
Index of symbols 517
Index 521
|
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| author | Kilp, Mati Knauer, Ulrich 1942- Michalev, Aleksandr V. |
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| callnumber-first | Q - Science |
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| classification_rvk | SK 320 |
| ctrlnum | (OCoLC)42397437 (DE-599)BVBBV013038255 |
| dewey-full | 512/.55 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.55 |
| dewey-search | 512/.55 |
| dewey-sort | 3512 255 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV013038255 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:38:04Z |
| institution | BVB |
| isbn | 3110152487 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008882892 |
| oclc_num | 42397437 |
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| physical | XVII, 529 S. graph. Darst. : 25 cm |
| publishDate | 2000 |
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| publisher | <<de>> Gruyter |
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| series | De Gruyter expositions in mathematics |
| series2 | De Gruyter expositions in mathematics |
| spelling | Kilp, Mati Verfasser aut Monoids, acts and categories with applications to wreath products and graphs ; a handbook for students and researchers by Mati Kilp ; Ulrich Knauer ; Alexander V. Mikhalev Berlin ; New York <<de>> Gruyter 2000 XVII, 529 S. graph. Darst. : 25 cm txt rdacontent n rdamedia nc rdacarrier De Gruyter expositions in mathematics 29 Algebra, Homological Categories (Mathematics) Monoids Homologische Algebra (DE-588)4160598-6 gnd rswk-swf Kategorie Mathematik (DE-588)4129930-9 gnd rswk-swf Monoid (DE-588)4170465-4 gnd rswk-swf Monoid (DE-588)4170465-4 s Homologische Algebra (DE-588)4160598-6 s Kategorie Mathematik (DE-588)4129930-9 s DE-604 Knauer, Ulrich 1942- Verfasser (DE-588)14404787X aut Michalev, Aleksandr V. Verfasser aut De Gruyter expositions in mathematics 29 (DE-604)BV004069300 29 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008882892&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kilp, Mati Knauer, Ulrich 1942- Michalev, Aleksandr V. Monoids, acts and categories with applications to wreath products and graphs ; a handbook for students and researchers De Gruyter expositions in mathematics Algebra, Homological Categories (Mathematics) Monoids Homologische Algebra (DE-588)4160598-6 gnd Kategorie Mathematik (DE-588)4129930-9 gnd Monoid (DE-588)4170465-4 gnd |
| subject_GND | (DE-588)4160598-6 (DE-588)4129930-9 (DE-588)4170465-4 |
| title | Monoids, acts and categories with applications to wreath products and graphs ; a handbook for students and researchers |
| title_auth | Monoids, acts and categories with applications to wreath products and graphs ; a handbook for students and researchers |
| title_exact_search | Monoids, acts and categories with applications to wreath products and graphs ; a handbook for students and researchers |
| title_full | Monoids, acts and categories with applications to wreath products and graphs ; a handbook for students and researchers by Mati Kilp ; Ulrich Knauer ; Alexander V. Mikhalev |
| title_fullStr | Monoids, acts and categories with applications to wreath products and graphs ; a handbook for students and researchers by Mati Kilp ; Ulrich Knauer ; Alexander V. Mikhalev |
| title_full_unstemmed | Monoids, acts and categories with applications to wreath products and graphs ; a handbook for students and researchers by Mati Kilp ; Ulrich Knauer ; Alexander V. Mikhalev |
| title_short | Monoids, acts and categories |
| title_sort | monoids acts and categories with applications to wreath products and graphs a handbook for students and researchers |
| title_sub | with applications to wreath products and graphs ; a handbook for students and researchers |
| topic | Algebra, Homological Categories (Mathematics) Monoids Homologische Algebra (DE-588)4160598-6 gnd Kategorie Mathematik (DE-588)4129930-9 gnd Monoid (DE-588)4170465-4 gnd |
| topic_facet | Algebra, Homological Categories (Mathematics) Monoids Homologische Algebra Kategorie Mathematik Monoid |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008882892&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004069300 |
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