Accessible categories: the foundations of categorical model theory
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, R.I.
American Mathematical Society
1989
|
| Series: | Contemporary mathematics
104 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 176 S. |
| ISBN: | 082185111X |
Staff View
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Record in the Search Index
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| adam_text | Contents
Introduction 1
Chapter 1 Preliminaries
§1.1. K filtered colimits 11
§1.2. K flat functors 14
Chapter 2 Accessible categories and functors
§2.1. /c accessible categories 17
§2.2. Small categories and accessibility 20
§2.3. Raising the index of accessibility 22
§2.4. Accessible functors 31
§2.5. An equivalent definition of accessibility 34
Chapter 3 Sketches and logic
§3.1. Sketches 39
§3.2. Logic 42
§3.3. The downward Lowenheim Skolem theorem 53
§3.4. Examples 57
Chapter 4 Sketching accessible categories
§4.1. Preliminaries on 2 categories 67
§4.2. The canonical sketch associated with a rc accessible category . . 81
§4.3. Small sketches for an accessible category 86
§4.4. Diagrams of accessible categories and diagrams of sketches ... 91
§4.5. Axiomatizing an accessible subcategory 95
Chapter 5 Limits and Colimits of accessible categories
§5.1. Colimits of sketches and Limits of accessible categories .... 97
§5.2. Some results concerning Grothendieck toposes 107
§5.3. Accessible fibrations 113
§5.4. Lax Colimits of accessible categories 122
§5.5. The powerful image of an accessible functor 138
Chapter 6 Limits and colimits in accessible categories
§6.1. Completeness and cocompleteness in accessible categories . . . 141
§6.2. Models of a sketch in an accessible category 146
§6.3. Detectability of colimits 153
§6.4. Completing an accessible category 160
vii
viii CONTENTS
References 165
Index 167
Glossary of notation 173
|
| any_adam_object | 1 |
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| bvnumber | BV003087764 |
| classification_rvk | SI 805 |
| ctrlnum | (OCoLC)260184807 (DE-599)BVBBV003087764 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV003087764 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:53:25Z |
| institution | BVB |
| isbn | 082185111X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001936089 |
| oclc_num | 260184807 |
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| physical | VIII, 176 S. |
| publishDate | 1989 |
| publishDateSearch | 1989 |
| publishDateSort | 1989 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Contemporary mathematics |
| series2 | Contemporary mathematics |
| spelling | Makkai, Michael Verfasser aut Accessible categories the foundations of categorical model theory Michael Makkai ; Robert Paré Providence, R.I. American Mathematical Society 1989 VIII, 176 S. txt rdacontent n rdamedia nc rdacarrier Contemporary mathematics 104 Kategorie Mathematik (DE-588)4129930-9 gnd rswk-swf Modelltheorie (DE-588)4114617-7 gnd rswk-swf Kategorientheorie (DE-588)4120552-2 gnd rswk-swf Kategorie Mathematik (DE-588)4129930-9 s Modelltheorie (DE-588)4114617-7 s DE-604 Kategorientheorie (DE-588)4120552-2 s Paré, Robert Verfasser aut Contemporary mathematics 104 (DE-604)BV000003365 104 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001936089&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Makkai, Michael Paré, Robert Accessible categories the foundations of categorical model theory Contemporary mathematics Kategorie Mathematik (DE-588)4129930-9 gnd Modelltheorie (DE-588)4114617-7 gnd Kategorientheorie (DE-588)4120552-2 gnd |
| subject_GND | (DE-588)4129930-9 (DE-588)4114617-7 (DE-588)4120552-2 |
| title | Accessible categories the foundations of categorical model theory |
| title_auth | Accessible categories the foundations of categorical model theory |
| title_exact_search | Accessible categories the foundations of categorical model theory |
| title_full | Accessible categories the foundations of categorical model theory Michael Makkai ; Robert Paré |
| title_fullStr | Accessible categories the foundations of categorical model theory Michael Makkai ; Robert Paré |
| title_full_unstemmed | Accessible categories the foundations of categorical model theory Michael Makkai ; Robert Paré |
| title_short | Accessible categories |
| title_sort | accessible categories the foundations of categorical model theory |
| title_sub | the foundations of categorical model theory |
| topic | Kategorie Mathematik (DE-588)4129930-9 gnd Modelltheorie (DE-588)4114617-7 gnd Kategorientheorie (DE-588)4120552-2 gnd |
| topic_facet | Kategorie Mathematik Modelltheorie Kategorientheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001936089&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000003365 |
| work_keys_str_mv | AT makkaimichael accessiblecategoriesthefoundationsofcategoricalmodeltheory AT parerobert accessiblecategoriesthefoundationsofcategoricalmodeltheory |