Categories for the Working Mathematician:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1978
|
| Ausgabe: | Second Edition |
| Schriftenreihe: | Graduate Texts in Mathematics
5 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Categories for the Working Mathematician provides an array of general ideas useful in a wide variety of fields. Starting from the foundations, this book illuminates the concepts of category, functor, natural transformation, and duality. The book then turns to adjoint functors, which provide a description of universal constructions, an analysis of the representations of functors by sets of morphisms, and a means of manipulating direct and inverse limits. These categorical concepts are extensively illustrated in the remaining chapters, which include many applications of the basic existence theorem for adjoint functors. The categories of algebraic systems are constructed from certain adjoint-like data and characterized by Beck's theorem. After considering a variety of applications, the book continues with the construction and exploitation of Kan extensions. This second edition includes a number of revisions and additions, including two new chapters on topics of active interest. One is on symmetric monoidal categories and braided monoidal categories and the coherence theorems for them. The second describes 2-categories and the higher dimensional categories which have recently come into prominence. The bibliography has also been expanded to cover some of the many other recent advances concerning categories |
| Beschreibung: | 1 Online-Ressource (XII, 317 p) |
| ISBN: | 9781475747218 9781441931238 |
| ISSN: | 0072-5285 |
| DOI: | 10.1007/978-1-4757-4721-8 |
Internformat
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| 650 | 4 | |a Mathematics | |
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Datensatz im Suchindex
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| any_adam_object | |
| author | Mac Lane, Saunders |
| author_facet | Mac Lane, Saunders |
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| bvnumber | BV042421631 |
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| ctrlnum | (OCoLC)864061481 (DE-599)BVBBV042421631 |
| dewey-full | 512.66 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.66 |
| dewey-search | 512.66 |
| dewey-sort | 3512.66 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4757-4721-8 |
| edition | Second Edition |
| format | Electronic eBook |
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| id | DE-604.BV042421631 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:09Z |
| institution | BVB |
| isbn | 9781475747218 9781441931238 |
| issn | 0072-5285 |
| language | English |
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| physical | 1 Online-Ressource (XII, 317 p) |
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| publishDate | 1978 |
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| publisher | Springer New York |
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| series2 | Graduate Texts in Mathematics |
| spelling | Mac Lane, Saunders Verfasser aut Categories for the Working Mathematician by Saunders Mac Lane Second Edition New York, NY Springer New York 1978 1 Online-Ressource (XII, 317 p) txt rdacontent c rdamedia cr rdacarrier Graduate Texts in Mathematics 5 0072-5285 Categories for the Working Mathematician provides an array of general ideas useful in a wide variety of fields. Starting from the foundations, this book illuminates the concepts of category, functor, natural transformation, and duality. The book then turns to adjoint functors, which provide a description of universal constructions, an analysis of the representations of functors by sets of morphisms, and a means of manipulating direct and inverse limits. These categorical concepts are extensively illustrated in the remaining chapters, which include many applications of the basic existence theorem for adjoint functors. The categories of algebraic systems are constructed from certain adjoint-like data and characterized by Beck's theorem. After considering a variety of applications, the book continues with the construction and exploitation of Kan extensions. This second edition includes a number of revisions and additions, including two new chapters on topics of active interest. One is on symmetric monoidal categories and braided monoidal categories and the coherence theorems for them. The second describes 2-categories and the higher dimensional categories which have recently come into prominence. The bibliography has also been expanded to cover some of the many other recent advances concerning categories Mathematics K-theory K-Theory Mathematik Algebra (DE-588)4001156-2 gnd rswk-swf Mathematiker (DE-588)4037945-0 gnd rswk-swf Kategorie Mathematik (DE-588)4129930-9 gnd rswk-swf Kategorie Mathematik (DE-588)4129930-9 s Mathematiker (DE-588)4037945-0 s 1\p DE-604 Algebra (DE-588)4001156-2 s 2\p DE-604 https://doi.org/10.1007/978-1-4757-4721-8 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Mac Lane, Saunders Categories for the Working Mathematician Mathematics K-theory K-Theory Mathematik Algebra (DE-588)4001156-2 gnd Mathematiker (DE-588)4037945-0 gnd Kategorie Mathematik (DE-588)4129930-9 gnd |
| subject_GND | (DE-588)4001156-2 (DE-588)4037945-0 (DE-588)4129930-9 |
| title | Categories for the Working Mathematician |
| title_auth | Categories for the Working Mathematician |
| title_exact_search | Categories for the Working Mathematician |
| title_full | Categories for the Working Mathematician by Saunders Mac Lane |
| title_fullStr | Categories for the Working Mathematician by Saunders Mac Lane |
| title_full_unstemmed | Categories for the Working Mathematician by Saunders Mac Lane |
| title_short | Categories for the Working Mathematician |
| title_sort | categories for the working mathematician |
| topic | Mathematics K-theory K-Theory Mathematik Algebra (DE-588)4001156-2 gnd Mathematiker (DE-588)4037945-0 gnd Kategorie Mathematik (DE-588)4129930-9 gnd |
| topic_facet | Mathematics K-theory K-Theory Mathematik Algebra Mathematiker Kategorie Mathematik |
| url | https://doi.org/10.1007/978-1-4757-4721-8 |
| work_keys_str_mv | AT maclanesaunders categoriesfortheworkingmathematician |