Categories, types, and structures: an introduction to category theory for the working computer scientist
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge, Mass. u.a.
MIT Press
1991
|
| Series: | Foundations of computing
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 289 - 299 |
| Physical Description: | XI, 306 S. graph. Darst. |
| ISBN: | 0262011255 |
Staff View
MARC
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| 100 | 1 | |a Asperti, Andrea |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Categories, types, and structures |b an introduction to category theory for the working computer scientist |c Andrea Asperti ; Giuseppe Longo |
| 264 | 1 | |a Cambridge, Mass. u.a. |b MIT Press |c 1991 | |
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| 337 | |b n |2 rdamedia | ||
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| 490 | 0 | |a Foundations of computing | |
| 500 | |a Literaturverz. S. 289 - 299 | ||
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Record in the Search Index
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| adam_text | Contents
Series Foreword viii
Introduction ix
I Categories and Structures
1 Categories 3
1.1 Category: Definition and Examples 3
1.2 Diagrams 5
1.3 Categories Out of Categories 6
1.4 Monic, Epic, and Principal Morphisms 7
1.5 Subobjects 10
2 Constructions 13
2.1 Initial and Terminal Objects 13
2.2 Products and Coproducts 15
2.3 Exponentials 18
2.4 Examples of CCCs 23
2.5 Equalizers and Pullbacks 30
2.6 Partial Morphisms and Complete Objects 34
2.7 Subobject Classifiers and Topoi 38
3 Functors and Natural Transformations 43
3.1 Functors 43
3.2 Natural Transformations 48
3.3 Cartesian and Cartesian Closed Categories Revisited 54
3.4 More Examples of CCCs 57
3.5 Yoneda s Lemma 61
3.6 Presheaves 62
4 Categories Derived from Functors and Natural Tranformations 67
4.1 Algebras Derived from Functors 67
4.2 From Monoids to Monads 71
4.3 Monoidal and Monoidal Closed Categories 76
4.4 Monoidal Categories and Linear Logic 83
5 Universal Arrows and Adjunctions 93
5.1 Universal Arrows 94
5.2 From Universal Arrows toward Adjunctions 97
5.3 Adjunctions 102
vi Contents
5.4 Adjunctions and Monads 108
5.5 More on Linear Logic 114
6 Cones and Limits 125
6.1 Limits and Colimits 125
6.2 Some Constructions Revisited 128
6.3 Existence of Limits 130
6.4 Preservation and Creation of Limits 132
6.5 co limits 134
7 Indexed and Internal Categories 137
7.1 Indexed Categories 137
7.2 Internal Category Theory 141
7.3 Internal Presheaves 148
7.4 Externalization 155
7.5 Internalization 160
Appendix 163
II Types as Objects
8 Formulae, Types, and Objects 171
8.1 X Notation 172
8.2 The Typed X Calculus with Explicit Pairs (Xpt]ji ) 173
8.3 The Intuitionistic Calculus of Sequents 176
8.4 The Cut Elimination Theorem 181
8.5 Categorical Semantics of Derivations 189
8.6 The Cut Elimination Theorem Revisited 191
8.7 Categorical Semantics of the Simply Typed Lambda Calculus 194
8.8 Fixpoint Operators and CCCs 201
9 Reflexive Objects and the Type Free Lambda Calculus 209
9.1 Combinatory Logic 211
9.2 From Categories to Functionally Complete Applicative Structures 213
9.3 Categorical Semantics of the X Calculus 219
9.4 The Categorical Abstract Machine 221
9.5 From Applicative Structures to Categories 225
9.6 Typed and Applicative Structures: Applications and Examples 230
Contents
10 Recursive Domain Equations 247
10.1 The Problem of Contravariant Functors 248
10.2 O Categories 251
11 Second Order Lambda Calculus 257
11.1 Syntax 258
11.2 The External Model 260
11.3 The External Interpretation 263
11.4 The Internal Model 264
11.5 The Internal Interpretation 267
11.6 Relating Models 269
12 Examples of Internal Models 277
12.1 Provable Retractions 277
12.2 PER Inside co Set 280
12.3 PL Categories Inside Their Groethendiek Completion 282
Bibliography 289
Index 301
|
| any_adam_object | 1 |
| author | Asperti, Andrea Longo, Giuseppe |
| author_facet | Asperti, Andrea Longo, Giuseppe |
| author_role | aut aut |
| author_sort | Asperti, Andrea |
| author_variant | a a aa g l gl |
| building | Verbundindex |
| bvnumber | BV005849907 |
| callnumber-first | Q - Science |
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| callnumber-search | QA76.7 |
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| callnumber-subject | QA - Mathematics |
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| dewey-ones | 005 - Computer programming, programs, data, security |
| dewey-raw | 005.13 |
| dewey-search | 005.13 |
| dewey-sort | 15.13 |
| dewey-tens | 000 - Computer science, information, general works |
| discipline | Informatik Mathematik |
| format | Book |
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| series2 | Foundations of computing |
| spelling | Asperti, Andrea Verfasser aut Categories, types, and structures an introduction to category theory for the working computer scientist Andrea Asperti ; Giuseppe Longo Cambridge, Mass. u.a. MIT Press 1991 XI, 306 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Foundations of computing Literaturverz. S. 289 - 299 Categorieën (wiskunde) gtt Categorías (Matemáticas) Catégories (Mathématiques) Catégories (mathématiques) ram Langages de programmation Langages de programmation ram catégorie inriac langage programmation inriac structure inriac sémantique langage programmation inriac théorie catégorie inriac type inriac Categories (Mathematics) Programming languages (Electronic computers) Datenstruktur (DE-588)4011146-5 gnd rswk-swf Kategorie Mathematik (DE-588)4129930-9 gnd rswk-swf Kategorientheorie (DE-588)4120552-2 gnd rswk-swf Kategorientheorie (DE-588)4120552-2 s Datenstruktur (DE-588)4011146-5 s DE-604 Kategorie Mathematik (DE-588)4129930-9 s Longo, Giuseppe Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003663439&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Asperti, Andrea Longo, Giuseppe Categories, types, and structures an introduction to category theory for the working computer scientist Categorieën (wiskunde) gtt Categorías (Matemáticas) Catégories (Mathématiques) Catégories (mathématiques) ram Langages de programmation Langages de programmation ram catégorie inriac langage programmation inriac structure inriac sémantique langage programmation inriac théorie catégorie inriac type inriac Categories (Mathematics) Programming languages (Electronic computers) Datenstruktur (DE-588)4011146-5 gnd Kategorie Mathematik (DE-588)4129930-9 gnd Kategorientheorie (DE-588)4120552-2 gnd |
| subject_GND | (DE-588)4011146-5 (DE-588)4129930-9 (DE-588)4120552-2 |
| title | Categories, types, and structures an introduction to category theory for the working computer scientist |
| title_auth | Categories, types, and structures an introduction to category theory for the working computer scientist |
| title_exact_search | Categories, types, and structures an introduction to category theory for the working computer scientist |
| title_full | Categories, types, and structures an introduction to category theory for the working computer scientist Andrea Asperti ; Giuseppe Longo |
| title_fullStr | Categories, types, and structures an introduction to category theory for the working computer scientist Andrea Asperti ; Giuseppe Longo |
| title_full_unstemmed | Categories, types, and structures an introduction to category theory for the working computer scientist Andrea Asperti ; Giuseppe Longo |
| title_short | Categories, types, and structures |
| title_sort | categories types and structures an introduction to category theory for the working computer scientist |
| title_sub | an introduction to category theory for the working computer scientist |
| topic | Categorieën (wiskunde) gtt Categorías (Matemáticas) Catégories (Mathématiques) Catégories (mathématiques) ram Langages de programmation Langages de programmation ram catégorie inriac langage programmation inriac structure inriac sémantique langage programmation inriac théorie catégorie inriac type inriac Categories (Mathematics) Programming languages (Electronic computers) Datenstruktur (DE-588)4011146-5 gnd Kategorie Mathematik (DE-588)4129930-9 gnd Kategorientheorie (DE-588)4120552-2 gnd |
| topic_facet | Categorieën (wiskunde) Categorías (Matemáticas) Catégories (Mathématiques) Catégories (mathématiques) Langages de programmation catégorie langage programmation structure sémantique langage programmation théorie catégorie type Categories (Mathematics) Programming languages (Electronic computers) Datenstruktur Kategorie Mathematik Kategorientheorie |
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