Categories for types:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
1993
|
| Edition: | 1. publ. |
| Series: | Cambridge mathematical textbooks
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XVII, 335 S. graph. Darst. |
| ISBN: | 0521450926 0521457017 |
Staff View
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Record in the Search Index
| _version_ | 1804124011864522752 |
|---|---|
| adam_text | Contents
Preface x
Advice for the Reader xiv
1 Order, Lattices and Domains 1
1.1 Introduction 1
1.2 Ordered Sets 2
1.3 Basic Lattice Theory 12
1.4 Boolean and Heyting Lattices 20
1.5 Elementary Domain Theory 24
1.6 Further Exercises 33
1.7 Pointers to the Literature 36
2 A Category Theory Primer 31
2.1 Introduction 37
2.2 Categories and Examples 40
2.3 Functors and Examples 45
2.4 Natural Transformations and Examples 49
2.5 Isomorphisms and Equivalences 52
2.6 Products and Coproducts 55
2.7 The Yoneda Lemma 61
2.8 Cartesian Closed Categories 67
2.9 Monies, Equalisers, Pullbacks and their Duals 73
2.10 Adjunctions 77
2.11 Limits and Colimits 91
2.12 Strict Indexed Categories 106
2.13 Further Exercises 113
2.14 Pointers to the Literature 118
vii
viii Contents
3 Algebraic Type Theory 120
3.1 Introduction 120
3.2 Definition of the Syntax 121
3.3 Algebraic Theories 127
3.4 Motivating a Categorical Semantics 129
3.5 Categorical Semantics 132
3.6 Categorical Models and the Soundness Theorem 134
3.7 Categories of Models 137
3.8 Classifying Category of an Algebraic Theory 139
3.9 The Categorical Type Theory Correspondence 147
3.10 Further Exercises 151
3.11 Pointers to the Literature 152
4 Functional Type Theory 154
4.1 Introduction 154
4.2 Definition of the Syntax 156
4.3 Ax Theories 161
4.4 Deriving a Categorical Semantics 163
4.5 Categorical Semantics 168
4.6 Categorical Models and the Soundness Theorem 171
4.7 Categories of Models 172
4.8 Classifying Category of a Ax Theory 175
4.9 The Categorical Type Theory Correspondence 180
4.10 Categorical Gluing 185
4.11 Further Exercises 192
4.12 Pointers to the Literature 199
5 Polymorphic Functional Type Theory 201
5.1 Introduction 201
5.2 The Syntax and Equations of 2Ax Theories 203
5.3 Deriving a Categorical Semantics 214
5.4 Categorical Semantics and Soundness Theorems 224
5.5 A PER Model 234
5.6 A Domain Model 241
Contents ix
5.7 Classifying Hyperdoctrine of a 2Ax Theory 262
5.8 Categorical Type Theory Correspondence 268
5.9 Pointers to the Literature 274
6 Higher Order Polymorphism 215
6.1 Introduction 275
6.2 The Syntax and Equations of u Ax Theories 275
6.3 Categorical Semantics and Soundness Theorems 285
6.4 A PER Model 291
6.5 A Domain Model 292
6.6 Classifying Hyperdoctrine of an wAx Theory 310
6.7 Categorical Type Theory Correspondence 313
6.8 Pointers to the Literature 314
Bibliography 315
Index 320
|
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| id | DE-604.BV009667150 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:38:53Z |
| institution | BVB |
| isbn | 0521450926 0521457017 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006392987 |
| oclc_num | 31243575 |
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| physical | XVII, 335 S. graph. Darst. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series2 | Cambridge mathematical textbooks |
| spelling | Crole, Roy L. Verfasser aut Categories for types Roy L. Crole 1. publ. Cambridge [u.a.] Cambridge Univ. Press 1993 XVII, 335 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Cambridge mathematical textbooks Hier auch später erschienene, unveränderte Nachdrucke Categorieën (wiskunde) gtt Typentheorie gtt Categories (Mathematics) Lambda calculus Kategorientheorie (DE-588)4120552-2 gnd rswk-swf Kategorientheorie (DE-588)4120552-2 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006392987&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Crole, Roy L. Categories for types Categorieën (wiskunde) gtt Typentheorie gtt Categories (Mathematics) Lambda calculus Kategorientheorie (DE-588)4120552-2 gnd |
| subject_GND | (DE-588)4120552-2 |
| title | Categories for types |
| title_auth | Categories for types |
| title_exact_search | Categories for types |
| title_full | Categories for types Roy L. Crole |
| title_fullStr | Categories for types Roy L. Crole |
| title_full_unstemmed | Categories for types Roy L. Crole |
| title_short | Categories for types |
| title_sort | categories for types |
| topic | Categorieën (wiskunde) gtt Typentheorie gtt Categories (Mathematics) Lambda calculus Kategorientheorie (DE-588)4120552-2 gnd |
| topic_facet | Categorieën (wiskunde) Typentheorie Categories (Mathematics) Lambda calculus Kategorientheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006392987&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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