From objects to diagrams for ranges of functors:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2011
|
| Series: | Lecture notes in mathematics
2029 |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | X, 158 S. graph. Darst. |
| ISBN: | 9783642217739 3642217737 9783642217746 |
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MARC
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| 100 | 1 | |a Gillibert, Pierre |e Verfasser |0 (DE-588)1018523790 |4 aut | |
| 245 | 1 | 0 | |a From objects to diagrams for ranges of functors |c Pierre Gillibert ; Friedrich Wehrung |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2011 | |
| 300 | |a X, 158 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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Record in the Search Index
| _version_ | 1805144975002828800 |
|---|---|
| adam_text |
IMAGE 1
CONTENTS
BACKGROUND 1
1.1 INTRODUCTION 1
1.1.1 THE SEARCH FOR FUNCTORIAL SOLUTIONS TO CERTAIN REPRESENTATION
PROBLEMS 2
1.1.2 PARTIALLY FUNCTORIAL SOLUTIONS TO REPRESENTATION PROBLEMS 5
1.1.3 CONTENTS OF THE BOOK 8
1.1.4 HOW NOT TO READ THE BOOK 12
1.2 BASIC CONCEPTS 14
1.2.1 SET THEORY 14
1.2.2 STONE DUALITY FOR BOOLEAN ALGEBRAS 15
1.2.3 PARTIALLY ORDERED SETS (POSETS) AND LATTICES 15
1.2.4 CATEGORY THEORY 17
1.2.5 DIRECTED COLIMITS OF FIRST-ORDER STRUCTURES 20 1.3 KAPPA-PRESENTED
AND WEAKLY KAPPA-PRESENTED OBJECTS 24 1.4 EXTENSION OF A FUNCTOR BY
DIRECTED COLIMITS 26
1.5 PROJECTABILITY WITNESSES 33
BOOLEAN ALGEBRAS THAT ARE SCALED WITH RESPECT TO A POSET 35
2.1 PSEUDO JOIN-SEMILATTICES, SUPPORTED POSETS, AND ALMOST
JOIN-SEMILATTICES 35
2.2 P-NORMED SPACES, P-SCALED BOOLEAN ALGEBRAS 38
2.3 DIRECTED COLIMITS AND FINITE PRODUCTS OF P-SCALED BOOLEAN ALGEBRAS
41
2.4 FINITELY PRESENTED P-SCALED BOOLEAN ALGEBRAS 43
2.5 NORMAL MORPHISMS IN BOOLP AND IN BTOPP 45
2.6 NORM-COVERINGS OF A POSET; THE STRUCTURES 2\P] AND F(X) . 47
THE CONDENSATE LIFTING LEMMA (CLL) 51
3.1 THE FUNCTOR A - A S; CONDENSATES 51
3.2 LIFTERS AND THE ARMATURE LEMMA 53
IX
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1011731657
DIGITALISIERT DURCH
IMAGE 2
X CONTENTS
3.3 THE LOEWENHEIM-SKOLEM CONDITION AND THE BUTTRESS LEMMA 57
3.4 LARDERS AND THE CONDENSATE LIFTING LEMMA 60
3.5 INFINITE COMBINATORICS AND LAMBDA-LIFTERS 63
3.6 LIFTERS, RETRACTS, AND PSEUDO-RETRACTS 70
3.7 LIFTING DIAGRAMS WITHOUT ASSUMING LIFTERS 74
3.8 LEFT AND RIGHT LARDERS 77
4 GETTING LARDERS FROM CONGRUENCE LATTICES OF FIRST-ORDER STRUCTURES 81
4.1 THE CATEGORY OF ALL MONOTONE-INDEXED STRUCTURES 82
4.2 DIRECTED COLIMITS OF MONOTONE-INDEXED STRUCTURES 86 4.3 THE RELATIVE
CONGRUENCE LATTICE FUNCTOR WITH RESPECT TO A GENERALIZED QUASIVARIETY 89
4.4 PRESERVATION OF SMALL DIRECTED COLIMITS BY THE RELATIVE COMPACT
CONGRUENCE FUNCTOR 94
4.5 IDEAL-INDUCED MORPHISMS AND PROJECTABILITY WITNESSES IN GENERALIZED
QUASIVARIETIES 95
4.6 AN EXTENSION OF THE LOEWENHEIM-SKOLEM THEOREM 98
4.7 A DIAGRAM VERSION OF THE GRAETZER-SCHMIDT THEOREM 101 4.8 RIGHT
NO-LARDERS FROM CONGRUENCE-PROPER QUASIVARIETIES 104 4.9 RELATIVE
CRITICAL POINTS BETWEEN QUASIVARIETIES 108
4.10 STRONG CONGRUENCE-PROPERNESS OF CERTAIN FINITELY GENERATED
VARIETIES OF ALGEBRAS 113
4.11 A POTENTIAL USE OF LARDERS ON NON-REGULAR CARDINALS 114
5 CONGRUENCE-PERMUTABLE, CONGRUENCE-PRESERVING EXTENSIONS OF LATTICES
117
5. 1 THE CATEGORY OF SEMILATTICE-METRIC SPACES 118
5.2 THE CATEGORY OF ALL SEMILATTICE-METRIC COVERS 119
5.3 A FAMILY OF UNLIFTABLE SQUARES OF SEMILATTICE- METRIC SPACES 120
5.4 A LEFT LARDER INVOLVING ALGEBRAS AND SEMILATTICE-METRIC SPACES 124
5.5 CPCP-RETRACTS AND CPCP-EXTENSIONS 126
6 LARDERS FROM VON NEUMANN REGULAR RINGS 131
6.1 IDEALS OF REGULAR RINGS AND OF LATTICES 131
6.2 RIGHT LARDERS FROM REGULAR RINGS 136
7 DISCUSSION 139
REFERENCES 143
LIST OF FIGURES 146
SYMBOL INDEX 149
SUBJECT INDEX 153
AUTHOR INDEX 157 |
| any_adam_object | 1 |
| author | Gillibert, Pierre Wehrung, Friedrich 1961- |
| author_GND | (DE-588)1018523790 (DE-588)1018524207 |
| author_facet | Gillibert, Pierre Wehrung, Friedrich 1961- |
| author_role | aut aut |
| author_sort | Gillibert, Pierre |
| author_variant | p g pg f w fw |
| building | Verbundindex |
| bvnumber | BV039520462 |
| classification_rvk | SI 850 |
| classification_tum | MAT 182f |
| ctrlnum | (OCoLC)748652407 (DE-599)DNB1011731657 |
| dewey-full | 512.62 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.62 |
| dewey-search | 512.62 |
| dewey-sort | 3512.62 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV039520462 |
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| indexdate | 2024-07-21T00:06:39Z |
| institution | BVB |
| isbn | 9783642217739 3642217737 9783642217746 |
| language | English |
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| physical | X, 158 S. graph. Darst. |
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| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Gillibert, Pierre Verfasser (DE-588)1018523790 aut From objects to diagrams for ranges of functors Pierre Gillibert ; Friedrich Wehrung Berlin [u.a.] Springer 2011 X, 158 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 2029 Kategorientheorie (DE-588)4120552-2 gnd rswk-swf Ringtheorie (DE-588)4126571-3 gnd rswk-swf Funktor (DE-588)4130706-9 gnd rswk-swf Universelle Algebra (DE-588)4061777-4 gnd rswk-swf Funktor (DE-588)4130706-9 s Universelle Algebra (DE-588)4061777-4 s Ringtheorie (DE-588)4126571-3 s DE-604 Kategorientheorie (DE-588)4120552-2 s 1\p DE-604 Wehrung, Friedrich 1961- Verfasser (DE-588)1018524207 aut Erscheint auch als Online-Ausgabe 10.1007/978-3-642-21774-6 Lecture notes in mathematics 2029 (DE-604)BV000676446 2029 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3791510&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024372960&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Gillibert, Pierre Wehrung, Friedrich 1961- From objects to diagrams for ranges of functors Lecture notes in mathematics Kategorientheorie (DE-588)4120552-2 gnd Ringtheorie (DE-588)4126571-3 gnd Funktor (DE-588)4130706-9 gnd Universelle Algebra (DE-588)4061777-4 gnd |
| subject_GND | (DE-588)4120552-2 (DE-588)4126571-3 (DE-588)4130706-9 (DE-588)4061777-4 |
| title | From objects to diagrams for ranges of functors |
| title_auth | From objects to diagrams for ranges of functors |
| title_exact_search | From objects to diagrams for ranges of functors |
| title_full | From objects to diagrams for ranges of functors Pierre Gillibert ; Friedrich Wehrung |
| title_fullStr | From objects to diagrams for ranges of functors Pierre Gillibert ; Friedrich Wehrung |
| title_full_unstemmed | From objects to diagrams for ranges of functors Pierre Gillibert ; Friedrich Wehrung |
| title_short | From objects to diagrams for ranges of functors |
| title_sort | from objects to diagrams for ranges of functors |
| topic | Kategorientheorie (DE-588)4120552-2 gnd Ringtheorie (DE-588)4126571-3 gnd Funktor (DE-588)4130706-9 gnd Universelle Algebra (DE-588)4061777-4 gnd |
| topic_facet | Kategorientheorie Ringtheorie Funktor Universelle Algebra |
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| volume_link | (DE-604)BV000676446 |
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