Categories for the working mathematician:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York
Springer
1998
|
| Ausgabe: | second edition |
| Schriftenreihe: | Graduate texts in mathematics
5 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xii, 314 Seiten |
| ISBN: | 0387984038 9781441931238 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1804126927235055616 |
|---|---|
| adam_text | Contents
Preface to the Second Edition v
Preface to the First Edition vii
Introduction 1
I. Categories, Functors, and Natural Transformations 7
1. Axioms for Categories 7
2. Categories 10
3. Functors 13
4. Natural Transformations 16
5. Monies, Epis, and Zeros 19
6. Foundations 21
7. Large Categories 24
8. Horn-Sets 27
II. Constructions on Categories 31
1. Duality 31
2. Contravariance and Opposites 33
3. Products of Categories 36
4. Functor Categories 40
5. The Category of All Categories 42
6. Comma Categories 45
7. Graphs and Free Categories 48
8. Quotient Categories 51
III. Universals and Limits 55
1. Universal Arrows 55
2. The Yoneda Lemma 59
3. Coproducts and Colimits 62
4. Products and Limits 68
ix
x Contents
5. Categories with Finite Products 72
6. Groups in Categories 75
7. Colimits of Representable Functors 76
IV. Adjoints 79
1. Adjunctions 79
2. Examples of Adjoints 86
3. Reflective Subcategories 90
4. Equivalence of Categories 92
5. Adjoints for Preorders 95
6. Cartesian Closed Categories 97
7. Transformations of Adjoints 99
8. Composition of Adjoints 103
9. Subsets and Characteristic Functions 105
10. Categories Like Sets 106
V. Limits 109
1. Creation of Limits 109
2. Limits by Products and Equalizers 112
3. Limits with Parameters 115
4. Preservation of Limits 116
5. Adjoints on Limits 118
6. Freyd s Adjoint Functor Theorem 120
7. Subobjects and Generators 126
8. The Special Adjoint Functor Theorem 128
9. Adjoints in Topology 132
VI. Monads and Algebras 137
1. Monads in a Category 137
2. Algebras for a Monad 139
3. The Comparison with Algebras 142
4. Words and Free Semigroups 144
5. Free Algebras for a Monad 147
6. Split Coequalizers 149
7. Beck s Theorem 151
8. Algebras Are T-Algebras 156
9. Compact Hausdorff Spaces 157
VII. Monoids 161
1. Monoidal Categories 161
2. Coherence 165
Contents xi
3. Monoids 170
4. Actions 174
5. The Simplicial Category 175
6. Monads and Homology 180
7. Closed Categories 184
8. Compactly Generated Spaces 185
9. Loops and Suspensions 188
VIII. Abelian Categories 191
1. Kernels and Cokernels 191
2. Additive Categories 194
3. Abelian Categories 198
4. Diagram Lemmas 202
IX. Special Limits 211
1. Filtered Limits 211
2. Interchange of Limits 214
3. Final Functors 217
4. Diagonal Naturality 218
5. Ends 222
6. Coends 226
7. Ends with Parameters 228
8. Iterated Ends and Limits 230
X. Kan Extensions 233
1. Adjoints and Limits 233
2. Weak Universality 235
3. The Kan Extension 236
4. Kan Extensions as Coends 240
5. Pointwise Kan Extensions 243
6. Density 245
7. All Concepts Are Kan Extensions 248
XI. Symmetry and Braiding in Monoidal Categories 251
1. Symmetric Monoidal Categories 251
2. Monoidal Functors 255
3. Strict Monoidal Categories 257
4. The Braid Groups Bn and the Braid Category 260
5. Braided Coherence 263
6. Perspectives 266
xii Contents
XII. Structures in Categories 267
1. Internal Categories 267
2. The Nerve of a Category 270
3. 2-Categories 272
4. Operations in 2-Categories 276
5. Single-Set Categories 279
6. Bicategories 281
7. Examples of Bicategories 283
8. Crossed Modules and Categories in Grp 285
Appendix. Foundations 289
Table of Standard Categories: Objects and Arrows 293
Table of Terminology 295
Bibliography 297
Index 303
|
| any_adam_object | 1 |
| author | Mac Lane, Saunders 1909-2005 |
| author_GND | (DE-588)118575953 |
| author_facet | Mac Lane, Saunders 1909-2005 |
| author_role | aut |
| author_sort | Mac Lane, Saunders 1909-2005 |
| author_variant | l s m ls lsm |
| building | Verbundindex |
| bvnumber | BV012301405 |
| classification_rvk | SK 320 |
| classification_tum | MAT 180f |
| ctrlnum | (OCoLC)246649037 (DE-599)BVBBV012301405 |
| 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 | 3512.55 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | second edition |
| format | Book |
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| id | DE-604.BV012301405 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:25:13Z |
| institution | BVB |
| isbn | 0387984038 9781441931238 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008340566 |
| oclc_num | 246649037 |
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| physical | xii, 314 Seiten |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Springer |
| record_format | marc |
| series | Graduate texts in mathematics |
| series2 | Graduate texts in mathematics |
| spelling | Mac Lane, Saunders 1909-2005 (DE-588)118575953 aut Categories for the working mathematician Saunders Mac Lane second edition New York Springer 1998 xii, 314 Seiten txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 5 Categories (Mathematics) Mathematiker (DE-588)4037945-0 gnd rswk-swf Algebra (DE-588)4001156-2 gnd rswk-swf Kategorie Mathematik (DE-588)4129930-9 gnd rswk-swf Kategorie Mathematik (DE-588)4129930-9 s Mathematiker (DE-588)4037945-0 s 1\p DE-604 Algebra (DE-588)4001156-2 s 2\p DE-604 Graduate texts in mathematics 5 (DE-604)BV000000067 5 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008340566&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Mac Lane, Saunders 1909-2005 Categories for the working mathematician Graduate texts in mathematics Categories (Mathematics) Mathematiker (DE-588)4037945-0 gnd Algebra (DE-588)4001156-2 gnd Kategorie Mathematik (DE-588)4129930-9 gnd |
| subject_GND | (DE-588)4037945-0 (DE-588)4001156-2 (DE-588)4129930-9 |
| title | Categories for the working mathematician |
| title_auth | Categories for the working mathematician |
| title_exact_search | Categories for the working mathematician |
| title_full | Categories for the working mathematician Saunders Mac Lane |
| title_fullStr | Categories for the working mathematician Saunders Mac Lane |
| title_full_unstemmed | Categories for the working mathematician Saunders Mac Lane |
| title_short | Categories for the working mathematician |
| title_sort | categories for the working mathematician |
| topic | Categories (Mathematics) Mathematiker (DE-588)4037945-0 gnd Algebra (DE-588)4001156-2 gnd Kategorie Mathematik (DE-588)4129930-9 gnd |
| topic_facet | Categories (Mathematics) Mathematiker Algebra Kategorie Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008340566&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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