Lecture notes on topoi and quasitopoi:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore
World Scientific
1991
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 290 S. |
| ISBN: | 9810201532 |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804118703406579712 |
|---|---|
| adam_text | CONTENTS
Preface v
0. Categorical Toolchest 1
1. Categories 1
2. Functors 3
3. Natural Transformations 5
4. Universal Morphisms and Adjunctions 8
5. Special Adjunctions 12
6. Limits and Colimits 16
7. Properties of Limits and Colimits 18
8. Monads and Comonads 22
9. Cartesian Closed Categories 26
10. Diagonal Polarity 30
11. Concrete and Topological Categories 32
1. Basic Properties 37
12. Subobjects 38
13. Relations and Powerset Objects 40
14. Subobject Classifiers 44
15. Topoi are Cartesian Closed 46
16. Partial Morphisms 49
17. Slice Categories 52
18. Locally Cartesian Closed Categories 56
19. Two Definitions of Quasitopoi 58
20. Universal Quantifiers 61
21. Coarse Objects of a Quasitopos 63
22. The Dual Category of a Topos is Algebraic 66
23. Exactness Properties of Quasitopoi 68
2. Examples of Topoi and Quasitopoi 73
24. Heyting Algebras 73
25. Spectral Theory 78
26. Set valued Presheaves 80
27. Examples and Complements 84
ix
x Contents
28. Sheaves for a Complete Heyting Algebra 87
29. Separated Presheaves 90
30. Sheaves on Topological Spaces 93
31. Examples of Topological Quasitopoi 96
3. Logic in a Quasitopos 101
32. Propositional Connectives 102
33. Quantifiers 107
34. The Language of a Quasitopos Ill
35. Interpretations of Formulas 115
36. Internal Validity 118
37. Rules of Internal Logic 121
38. Some Constructions in a Quasitopos 125
39. Internal Unions and Intersections 128
40. Composition of Relations 130
4. Topologies and Sheaves 135
41. Closed and Dense Monomorphisms 136
42. Separated Objects and Sheaves 139
43. Associated Separated Objects and Sheaves 143
44. Reflectors for Sheaves and Separated Objects 146
45. Strong Topologies and Coarse Sheaves 149
46. Solid Quasitopoi 152
47. Grothendieck Topologies 157
48. Canonical Topologies 160
5. Geometric Morphisms 163
49. Coalgebras for Left Exact Comonads 163
50. Coalgebras Define a Quasitopos 167
51. Geometric Morphisms 170
52. Topologies from Sheaves 173
53. Factorization of Geometric Morphisms 176
6. Internal Categories and Diagrams 179
54. Internal Categories 179
55. Internal Diagrams 183
56. Internal Functors 186
57. Internal Limits and Colimits 189
58. Internal Diagrams over a Quasitopos 193
Contents xi
7. Topological Quasitopoi 197
59. Categories of p Sieves 198
60. p Sieves Define a Quasitopos 200
61. Dense p Sieves 203
62. Corefiections for Dense Sieves 206
63. Quotient Sinks 209
64. Quasitopological Categories 212
65. Left Exact Concrete Categories 217
66. p Topologies 220
67. Properties of Dense Sieves 224
68. Dense Completions 227
69. Quasitopos Completions and Quasitopos Hulls 230
70. Examples 232
8. Quasitopoi of Fuzzy Sets 237
71. The Category of I fuzzy Sets 239
72. i? valued Sets and Relations 242
73. Categories Set H and Mod# of H valued sets 245
74. tf valued Subsets 249
75. Constructions for .ff valued Sets 252
76. Sheaves and Presheaves in Set H 257
77. Set H is a Topos and Mod if a Quasitopos 261
78. The Topos Structure of ff Sets 264
79. Fuz H and Related Categories 269
80. First Order Fuzzy Logic 272
Bibliography 277
Index 285
|
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| dewey-ones | 512 - Algebra |
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| dewey-sort | 3512 255 |
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| discipline | Mathematik |
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| id | DE-604.BV004574579 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:14:31Z |
| institution | BVB |
| isbn | 9810201532 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002814153 |
| oclc_num | 22813002 |
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| physical | XI, 290 S. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Wyler, Oswald 1922-2006 Verfasser (DE-588)125964900 aut Lecture notes on topoi and quasitopoi Oswald Wyler Singapore World Scientific 1991 XI, 290 S. txt rdacontent n rdamedia nc rdacarrier Topos (Mathématiques) ram Toposes Topos Mathematik (DE-588)4185717-3 gnd rswk-swf Topos Mathematik (DE-588)4185717-3 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002814153&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wyler, Oswald 1922-2006 Lecture notes on topoi and quasitopoi Topos (Mathématiques) ram Toposes Topos Mathematik (DE-588)4185717-3 gnd |
| subject_GND | (DE-588)4185717-3 |
| title | Lecture notes on topoi and quasitopoi |
| title_auth | Lecture notes on topoi and quasitopoi |
| title_exact_search | Lecture notes on topoi and quasitopoi |
| title_full | Lecture notes on topoi and quasitopoi Oswald Wyler |
| title_fullStr | Lecture notes on topoi and quasitopoi Oswald Wyler |
| title_full_unstemmed | Lecture notes on topoi and quasitopoi Oswald Wyler |
| title_short | Lecture notes on topoi and quasitopoi |
| title_sort | lecture notes on topoi and quasitopoi |
| topic | Topos (Mathématiques) ram Toposes Topos Mathematik (DE-588)4185717-3 gnd |
| topic_facet | Topos (Mathématiques) Toposes Topos Mathematik |
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