Category theory and applications: a textbook for beginners
"Category Theory now permeates most of Mathematics, large parts of theoretical Computer Science and parts of theoretical Physics. Its unifying power brings together different branches, and leads to a better understanding of their roots. This book is addressed to students and researchers of thes...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai ; Tokyo
World Scientific
[2021]
|
| Ausgabe: | Second edition |
| Schlagworte: | |
| Online-Zugang: | TUM01 |
| Zusammenfassung: | "Category Theory now permeates most of Mathematics, large parts of theoretical Computer Science and parts of theoretical Physics. Its unifying power brings together different branches, and leads to a better understanding of their roots. This book is addressed to students and researchers of these fields and can be used as a text for a first course in Category Theory. It covers the basic tools, like universal properties, limits, adjoint functors and monads. These are presented in a concrete way, starting from examples and exercises taken from elementary Algebra, Lattice Theory and Topology, then developing the theory together with new exercises and applications. A reader should have some elementary knowledge of these three subjects, or at least two of them, in order to be able to follow the main examples, appreciate the unifying power of the categorical approach, and discover the subterranean links brought to light and formalised by this perspective. Applications of Category Theory form a vast and differentiated domain. This book wants to present the basic applications in Algebra and Topology, with a choice of more advanced ones, based on the interests of the author. References are given for applications in many other fields. In this second edition, the book has been entirely reviewed, adding many applications and exercises. All non-obvious exercises have now a solution (or a reference, in the case of an advanced topic); solutions are now collected in the last chapter"-- |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | 1 Online-Ressource Illustrationen |
| ISBN: | 9789811236099 9789811236105 |
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| 245 | 1 | 0 | |a Category theory and applications |b a textbook for beginners |c Marco Grandis, Università di Genova, Italy |
| 250 | |a Second edition | ||
| 264 | 1 | |a New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai ; Tokyo |b World Scientific |c [2021] | |
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| 520 | 3 | |a "Category Theory now permeates most of Mathematics, large parts of theoretical Computer Science and parts of theoretical Physics. Its unifying power brings together different branches, and leads to a better understanding of their roots. This book is addressed to students and researchers of these fields and can be used as a text for a first course in Category Theory. It covers the basic tools, like universal properties, limits, adjoint functors and monads. These are presented in a concrete way, starting from examples and exercises taken from elementary Algebra, Lattice Theory and Topology, then developing the theory together with new exercises and applications. A reader should have some elementary knowledge of these three subjects, or at least two of them, in order to be able to follow the main examples, appreciate the unifying power of the categorical approach, and discover the subterranean links brought to light and formalised by this perspective. Applications of Category Theory form a vast and differentiated domain. This book wants to present the basic applications in Algebra and Topology, with a choice of more advanced ones, based on the interests of the author. References are given for applications in many other fields. In this second edition, the book has been entirely reviewed, adding many applications and exercises. All non-obvious exercises have now a solution (or a reference, in the case of an advanced topic); solutions are now collected in the last chapter"-- | |
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| discipline | Mathematik |
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| spelling | Grandis, Marco (DE-588)139362908 aut Category theory and applications a textbook for beginners Marco Grandis, Università di Genova, Italy Second edition New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai ; Tokyo World Scientific [2021] 1 Online-Ressource Illustrationen txt rdacontent c rdamedia cr rdacarrier Includes bibliographical references and index "Category Theory now permeates most of Mathematics, large parts of theoretical Computer Science and parts of theoretical Physics. Its unifying power brings together different branches, and leads to a better understanding of their roots. This book is addressed to students and researchers of these fields and can be used as a text for a first course in Category Theory. It covers the basic tools, like universal properties, limits, adjoint functors and monads. These are presented in a concrete way, starting from examples and exercises taken from elementary Algebra, Lattice Theory and Topology, then developing the theory together with new exercises and applications. A reader should have some elementary knowledge of these three subjects, or at least two of them, in order to be able to follow the main examples, appreciate the unifying power of the categorical approach, and discover the subterranean links brought to light and formalised by this perspective. Applications of Category Theory form a vast and differentiated domain. This book wants to present the basic applications in Algebra and Topology, with a choice of more advanced ones, based on the interests of the author. References are given for applications in many other fields. In this second edition, the book has been entirely reviewed, adding many applications and exercises. All non-obvious exercises have now a solution (or a reference, in the case of an advanced topic); solutions are now collected in the last chapter"-- Kategorie Mathematik (DE-588)4129930-9 gnd rswk-swf Categories (Mathematics) Mathematical analysis Morphisms (Mathematics) Homology theory (DE-588)4123623-3 Lehrbuch gnd-content Kategorie Mathematik (DE-588)4129930-9 s DE-604 Erscheint auch als Druck-Ausgabe, Hardcover 978-981-12-3608-2 |
| spellingShingle | Grandis, Marco Category theory and applications a textbook for beginners Kategorie Mathematik (DE-588)4129930-9 gnd |
| subject_GND | (DE-588)4129930-9 (DE-588)4123623-3 |
| title | Category theory and applications a textbook for beginners |
| title_auth | Category theory and applications a textbook for beginners |
| title_exact_search | Category theory and applications a textbook for beginners |
| title_exact_search_txtP | Category theory and applications a textbook for beginners |
| title_full | Category theory and applications a textbook for beginners Marco Grandis, Università di Genova, Italy |
| title_fullStr | Category theory and applications a textbook for beginners Marco Grandis, Università di Genova, Italy |
| title_full_unstemmed | Category theory and applications a textbook for beginners Marco Grandis, Università di Genova, Italy |
| title_short | Category theory and applications |
| title_sort | category theory and applications a textbook for beginners |
| title_sub | a textbook for beginners |
| topic | Kategorie Mathematik (DE-588)4129930-9 gnd |
| topic_facet | Kategorie Mathematik Lehrbuch |
| work_keys_str_mv | AT grandismarco categorytheoryandapplicationsatextbookforbeginners |