Category theory: invariances and symmetries in computer science
This book analyzes the generation of the arrow-categories of a given category, which is a foundational and distinguishable Category Theory phenomena, in analogy to the foundational role of sets in the traditional set-based Mathematics, for defi nition of natural numbers as well. This inductive trans...
Gespeichert in:
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; Boston
De Gruyter
[2023]
|
| Schlagworte: | |
| Online-Zugang: | DE-1043 DE-1046 DE-858 DE-Aug4 DE-92 DE-859 DE-860 DE-863 DE-862 DE-91 DE-706 DE-29 DE-739 URL des Erstveröffentlichers |
| Zusammenfassung: | This book analyzes the generation of the arrow-categories of a given category, which is a foundational and distinguishable Category Theory phenomena, in analogy to the foundational role of sets in the traditional set-based Mathematics, for defi nition of natural numbers as well. This inductive transformation of a category into the infinite hierarchy of the arrowcategories is extended to the functors and natural transformations. The author considers invariant categorial properties (the symmetries) under such inductive transformations. The book focuses in particular on Global symmetry (invariance of adjunctions) and Internal symmetries between arrows and objects in a category (in analogy to Field Theories like Quantum Mechanics and General Relativity). The second part of the book is dedicated to more advanced applications of Internal symmetry to Computer Science: for Intuitionistic Logic, Untyped Lambda Calculus with Fixpoint Operators, Labeled Transition Systems in Process Algebras and Modal logics as well as Data Integration Theory. |
| Beschreibung: | 1 Online-Ressource (XXXI, 404 Seiten) |
| ISBN: | 9783111081670 9783111082011 |
| DOI: | 10.1515/9783111081670 |
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| 520 | |a This book analyzes the generation of the arrow-categories of a given category, which is a foundational and distinguishable Category Theory phenomena, in analogy to the foundational role of sets in the traditional set-based Mathematics, for defi nition of natural numbers as well. This inductive transformation of a category into the infinite hierarchy of the arrowcategories is extended to the functors and natural transformations. The author considers invariant categorial properties (the symmetries) under such inductive transformations. The book focuses in particular on Global symmetry (invariance of adjunctions) and Internal symmetries between arrows and objects in a category (in analogy to Field Theories like Quantum Mechanics and General Relativity). The second part of the book is dedicated to more advanced applications of Internal symmetry to Computer Science: for Intuitionistic Logic, Untyped Lambda Calculus with Fixpoint Operators, Labeled Transition Systems in Process Algebras and Modal logics as well as Data Integration Theory. | ||
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| 650 | 4 | |a Kategorientheorie | |
| 650 | 4 | |a Lambda-Kalkül | |
| 650 | 4 | |a Natürliches Schließen | |
| 650 | 7 | |a COMPUTERS / Information Theory |2 bisacsh | |
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Datensatz im Suchindex
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| author | Majkić, Zoran 19XX- |
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| bvnumber | BV048854246 |
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| discipline | Technik Informatik Mathematik |
| discipline_str_mv | Technik Informatik |
| doi_str_mv | 10.1515/9783111081670 |
| format | Electronic eBook |
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| id | DE-604.BV048854246 |
| illustrated | Not Illustrated |
| index_date | 2024-07-03T21:40:53Z |
| indexdate | 2025-01-11T04:01:48Z |
| institution | BVB |
| isbn | 9783111081670 9783111082011 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-034119471 |
| oclc_num | 1372482629 |
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| physical | 1 Online-Ressource (XXXI, 404 Seiten) |
| psigel | ZDB-23-DGG ZDB-23-DEI ZDB-23-DGG FAB_PDA_DGG ZDB-23-DGG FAW_PDA_DGG ZDB-23-DGG FCO_PDA_DGG ZDB-23-DGG FHA_PDA_DGG ZDB-23-DGG FKE_PDA_DGG ZDB-23-DGG FLA_PDA_DGG ZDB-23-DEI TUM_Paketkauf_2023 ZDB-23-DGG UER_Einzelkauf ZDB-23-DGG UPA_PDA_DGG |
| publishDate | 2023 |
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| publishDateSort | 2023 |
| publisher | De Gruyter |
| record_format | marc |
| spellingShingle | Majkić, Zoran 19XX- Category theory invariances and symmetries in computer science Data Integration Theory Kategorientheorie Lambda-Kalkül Natürliches Schließen COMPUTERS / Information Theory bisacsh |
| title | Category theory invariances and symmetries in computer science |
| title_auth | Category theory invariances and symmetries in computer science |
| title_exact_search | Category theory invariances and symmetries in computer science |
| title_exact_search_txtP | Category theory invariances and symmetries in computer science |
| title_full | Category theory invariances and symmetries in computer science Zoran Majkić |
| title_fullStr | Category theory invariances and symmetries in computer science Zoran Majkić |
| title_full_unstemmed | Category theory invariances and symmetries in computer science Zoran Majkić |
| title_short | Category theory |
| title_sort | category theory invariances and symmetries in computer science |
| title_sub | invariances and symmetries in computer science |
| topic | Data Integration Theory Kategorientheorie Lambda-Kalkül Natürliches Schließen COMPUTERS / Information Theory bisacsh |
| topic_facet | Data Integration Theory Kategorientheorie Lambda-Kalkül Natürliches Schließen COMPUTERS / Information Theory |
| url | https://doi.org/10.1515/9783111081670 |
| work_keys_str_mv | AT majkiczoran categorytheoryinvariancesandsymmetriesincomputerscience |