Introduction to coalgebra: towards mathematics of states and observation
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge ; New York ; Port Melbourne ; Daryaganj, Delhi ; Singapore
Cambridge University Press
2017
|
| Schriftenreihe: | Cambridge tracts in theoretical computer science
59 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xvi, 477 Seiten Illustrationen 24 cm |
| ISBN: | 9781107177895 1107177898 |
Internformat
MARC
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| 100 | 1 | |a Jacobs, Bart |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Introduction to coalgebra |b towards mathematics of states and observation |c Bart Jacobs (Radboud University Nijmegen) |
| 264 | 1 | |a Cambridge ; New York ; Port Melbourne ; Daryaganj, Delhi ; Singapore |b Cambridge University Press |c 2017 | |
| 300 | |a xvi, 477 Seiten |b Illustrationen |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
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| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Cambridge tracts in theoretical computer science |v 59 | |
| 650 | 4 | |a Associative algebras | |
| 650 | 4 | |a Universal enveloping algebras | |
| 650 | 4 | |a Algebra, Universal | |
| 650 | 0 | 7 | |a Theoretische Informatik |0 (DE-588)4196735-5 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804177329969168384 |
|---|---|
| adam_text | Titel: Introduction to coalgebra
Autor: Jacobs, Bart
Jahr: 2017
Contents
Preface page vii
1 Motivation 1
1.1 Naturalness of Coalgebraic Representations 2
1.2 The Power of the Coinduction 6
1.3 Generality of Temporal Logic of Coalgehras 18
1.4 Abstractness of the Coalgebraic Notions 24
2 Coalgebras of Polynomial Functors 33
2.1 Constructions on Sets 33
2.2 Polynomial Functors and Their Coalgebras 48
2.3 Final Coalgebras 67
2.4 Algebras 78
2.5 Adjunctions, Coffee Coalgebras, Behaviour-Realisation 94
3 Bisimulations 114
3.1 Relation Lifting, Bisimulations and Congruences 115
3.2 Properties of Bisimulations 122
3.3 Bisimulations as Spans and Cospans 131
3.4 Bisimulations and the Coinduction Proof Principle 142
3.5 Process Semantics 149
4 Logic, Lifting and Finality 159
4.1 Multiset and Distribution Functors 160
4.2 Weak Pullbacks 169
4.3 Predicates and Relations 183
4.4 Relation Lifting, Categorically 202
4.5 Logical Bisimulations 212
4.6 Existence of Final Coalgebras 222
4.7 Polynomial and Analytical Functors 232
v
vi
Contents
5 Monads, Comonads and Distributive Laws 246
5.1 Monads and Comonads: Definition and Examples 247
5.2 Kleisli Categories and Distributive Laws 263
5.3 Trace Semantics via Finality in Kleisli Categories 280
5.4 Eilenberg-Moore Categories and Distributive Laws 296
5.5 Bialgebras and Operational Semantics 316
6 Invariants and Assertions 334
6.1 Predicate Lifting 335
6.2 Invariants 347
6.3 Greatest Invariants and Limits of Coalgebras 354
6.4 Temporal Logic for Coalgebras 363
6.5 Modal Logic for Coalgebras 377
6.6 Algebras and Terms 391
6.7 Algebras and Assertions 401
6.8 Coalgebras and Assertions 419
6.9 Coalgebraic Class Specifications 434
References 440
Definition and Symbol Index 466
Subject Index 469
|
| any_adam_object | 1 |
| author | Jacobs, Bart |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
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| dewey-sort | 3512.46 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-10T07:46:21Z |
| institution | BVB |
| isbn | 9781107177895 1107177898 |
| language | English |
| lccn | 2016023664 |
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| physical | xvi, 477 Seiten Illustrationen 24 cm |
| publishDate | 2017 |
| publishDateSearch | 2017 |
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| publisher | Cambridge University Press |
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| series | Cambridge tracts in theoretical computer science |
| series2 | Cambridge tracts in theoretical computer science |
| spelling | Jacobs, Bart Verfasser aut Introduction to coalgebra towards mathematics of states and observation Bart Jacobs (Radboud University Nijmegen) Cambridge ; New York ; Port Melbourne ; Daryaganj, Delhi ; Singapore Cambridge University Press 2017 xvi, 477 Seiten Illustrationen 24 cm txt rdacontent n rdamedia nc rdacarrier Cambridge tracts in theoretical computer science 59 Associative algebras Universal enveloping algebras Algebra, Universal Theoretische Informatik (DE-588)4196735-5 gnd rswk-swf Assoziative Algebra (DE-588)4293934-3 gnd rswk-swf Assoziative Algebra (DE-588)4293934-3 s Theoretische Informatik (DE-588)4196735-5 s DE-604 Cambridge tracts in theoretical computer science 59 (DE-604)BV000754528 59 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029601454&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Jacobs, Bart Introduction to coalgebra towards mathematics of states and observation Cambridge tracts in theoretical computer science Associative algebras Universal enveloping algebras Algebra, Universal Theoretische Informatik (DE-588)4196735-5 gnd Assoziative Algebra (DE-588)4293934-3 gnd |
| subject_GND | (DE-588)4196735-5 (DE-588)4293934-3 |
| title | Introduction to coalgebra towards mathematics of states and observation |
| title_auth | Introduction to coalgebra towards mathematics of states and observation |
| title_exact_search | Introduction to coalgebra towards mathematics of states and observation |
| title_full | Introduction to coalgebra towards mathematics of states and observation Bart Jacobs (Radboud University Nijmegen) |
| title_fullStr | Introduction to coalgebra towards mathematics of states and observation Bart Jacobs (Radboud University Nijmegen) |
| title_full_unstemmed | Introduction to coalgebra towards mathematics of states and observation Bart Jacobs (Radboud University Nijmegen) |
| title_short | Introduction to coalgebra |
| title_sort | introduction to coalgebra towards mathematics of states and observation |
| title_sub | towards mathematics of states and observation |
| topic | Associative algebras Universal enveloping algebras Algebra, Universal Theoretische Informatik (DE-588)4196735-5 gnd Assoziative Algebra (DE-588)4293934-3 gnd |
| topic_facet | Associative algebras Universal enveloping algebras Algebra, Universal Theoretische Informatik Assoziative Algebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029601454&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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