Introduction to coalgebra :: towards mathematics of states and observation /
The area of coalgebra has emerged within theoretical computer science with a unifying claim: to be the mathematics of computational dynamics. It combines ideas from the theory of dynamical systems and from the theory of state-based computation. Although still in its infancy, it is an active area of...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge, United Kingdom :
Cambridge University Press,
2017.
|
| Schriftenreihe: | Cambridge tracts in theoretical computer science ;
59. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | The area of coalgebra has emerged within theoretical computer science with a unifying claim: to be the mathematics of computational dynamics. It combines ideas from the theory of dynamical systems and from the theory of state-based computation. Although still in its infancy, it is an active area of research that generates wide interest. Written by one of the founders of the field, this book acts as the first mature and accessible introduction to coalgebra. It provides clear mathematical explanations, with many examples and exercises involving deterministic and non-deterministic automata, transition systems, streams, Markov chains and weighted automata. The theory is expressed in the language of category theory, which provides the right abstraction to make the similarity and duality between algebra and coalgebra explicit, and which the reader is introduced to in a hands-on manner. The book will be useful to mathematicians and (theoretical) computer scientists and will also be of interest to mathematical physicists, biologists and economists. |
| Beschreibung: | 1 online resource (xvi, 477 pages) |
| Bibliographie: | Includes bibliographical references (pages 440-465) and indexes. |
| ISBN: | 9781316838563 1316838560 9781316837030 1316837033 |
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| 490 | 1 | |a Cambridge tracts in theoretical computer science ; |v 59 | |
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| contents | Motivation -- Coalgebras of polynomial functors -- Bisimulations -- Logic, lifting and finality -- Monads, comonads and distributive laws -- Invariants and assertions. |
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| indexdate | 2024-11-27T13:27:31Z |
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| isbn | 9781316838563 1316838560 9781316837030 1316837033 |
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| spelling | Jacobs, Bart, author. Introduction to coalgebra : towards mathematics of states and observation / Bart Jacobs, Radboud University Nijmegen. Cambridge, United Kingdom : Cambridge University Press, 2017. ©2017 1 online resource (xvi, 477 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier Cambridge tracts in theoretical computer science ; 59 The area of coalgebra has emerged within theoretical computer science with a unifying claim: to be the mathematics of computational dynamics. It combines ideas from the theory of dynamical systems and from the theory of state-based computation. Although still in its infancy, it is an active area of research that generates wide interest. Written by one of the founders of the field, this book acts as the first mature and accessible introduction to coalgebra. It provides clear mathematical explanations, with many examples and exercises involving deterministic and non-deterministic automata, transition systems, streams, Markov chains and weighted automata. The theory is expressed in the language of category theory, which provides the right abstraction to make the similarity and duality between algebra and coalgebra explicit, and which the reader is introduced to in a hands-on manner. The book will be useful to mathematicians and (theoretical) computer scientists and will also be of interest to mathematical physicists, biologists and economists. Includes bibliographical references (pages 440-465) and indexes. Motivation -- Coalgebras of polynomial functors -- Bisimulations -- Logic, lifting and finality -- Monads, comonads and distributive laws -- Invariants and assertions. Print version record. Associative algebras. http://id.loc.gov/authorities/subjects/sh85008821 Universal enveloping algebras. http://id.loc.gov/authorities/subjects/sh85141070 Algebra, Universal. http://id.loc.gov/authorities/subjects/sh85003433 Algèbres associatives. Algèbres enveloppantes universelles. Algèbre universelle. MATHEMATICS Algebra Intermediate. bisacsh Álgebra universal embne Algebra, Universal fast Associative algebras fast Universal enveloping algebras fast Assoziative Algebra gnd http://d-nb.info/gnd/4293934-3 Theoretische Informatik gnd http://d-nb.info/gnd/4196735-5 has work: Introduction to coalgebra (Text) https://id.oclc.org/worldcat/entity/E39PCFxyYcGwTGpMb6vGc3rqjP https://id.oclc.org/worldcat/ontology/hasWork Print version: Jacobs, Bart. Introduction to coalgebra. Cambridge, United Kingdom : Cambridge University Press, 2017 9781107177895 (DLC) 2016023664 (OCoLC)950519615 Cambridge tracts in theoretical computer science ; 59. http://id.loc.gov/authorities/names/n86714937 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=1413741 Volltext |
| spellingShingle | Jacobs, Bart Introduction to coalgebra : towards mathematics of states and observation / Cambridge tracts in theoretical computer science ; Motivation -- Coalgebras of polynomial functors -- Bisimulations -- Logic, lifting and finality -- Monads, comonads and distributive laws -- Invariants and assertions. Associative algebras. http://id.loc.gov/authorities/subjects/sh85008821 Universal enveloping algebras. http://id.loc.gov/authorities/subjects/sh85141070 Algebra, Universal. http://id.loc.gov/authorities/subjects/sh85003433 Algèbres associatives. Algèbres enveloppantes universelles. Algèbre universelle. MATHEMATICS Algebra Intermediate. bisacsh Álgebra universal embne Algebra, Universal fast Associative algebras fast Universal enveloping algebras fast Assoziative Algebra gnd http://d-nb.info/gnd/4293934-3 Theoretische Informatik gnd http://d-nb.info/gnd/4196735-5 |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85008821 http://id.loc.gov/authorities/subjects/sh85141070 http://id.loc.gov/authorities/subjects/sh85003433 http://d-nb.info/gnd/4293934-3 http://d-nb.info/gnd/4196735-5 |
| 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. http://id.loc.gov/authorities/subjects/sh85008821 Universal enveloping algebras. http://id.loc.gov/authorities/subjects/sh85141070 Algebra, Universal. http://id.loc.gov/authorities/subjects/sh85003433 Algèbres associatives. Algèbres enveloppantes universelles. Algèbre universelle. MATHEMATICS Algebra Intermediate. bisacsh Álgebra universal embne Algebra, Universal fast Associative algebras fast Universal enveloping algebras fast Assoziative Algebra gnd http://d-nb.info/gnd/4293934-3 Theoretische Informatik gnd http://d-nb.info/gnd/4196735-5 |
| topic_facet | Associative algebras. Universal enveloping algebras. Algebra, Universal. Algèbres associatives. Algèbres enveloppantes universelles. Algèbre universelle. MATHEMATICS Algebra Intermediate. Álgebra universal Algebra, Universal Associative algebras Universal enveloping algebras Assoziative Algebra Theoretische Informatik |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=1413741 |
| work_keys_str_mv | AT jacobsbart introductiontocoalgebratowardsmathematicsofstatesandobservation |