Algebraic Theories:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1976
|
| Schriftenreihe: | Graduate Texts in Mathematics
26 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | In the past decade, category theory has widened its scope and now interacts with many areas of mathematics. This book develops some of the interactions between universal algebra and category theory as well as some of the resulting applications. We begin with an exposition of equationally defineable classes from the point of view of "algebraic theories," but without the use of category theory. This serves to motivate the general treatment of algebraic theories in a category, which is the central concern of the book. (No category theory is presumed; rather, an independent treatment is provided by the second chapter.) Applications abound throughout the text and exercises and in the final chapter in which we pursue problems originating in topological dynamics and in automata theory. This book is a natural outgrowth of the ideas of a small group of mathematicians, many of whom were in residence at the Forschungsinstitut für Mathematik of the Eidgenössische Technische Hochschule in Zürich, Switzerland during the academic year 1966-67. It was in this stimulating atmosphere that the author wrote his doctoral dissertation. The "Zürich School," then, was Michael Barr, Jon Beck, John Gray, Bill Lawvere, Fred Linton, and Myles Tierney (who were there) and (at least) Harry Appelgate, Sammy Eilenberg, John Isbell, and Saunders Mac Lane (whose spiritual presence was tangible.) I am grateful to the National Science Foundation who provided support, under grants GJ 35759 and OCR 72-03733 A01, while I wrote this book |
| Beschreibung: | 1 Online-Ressource (X, 356 p) |
| ISBN: | 9781461298601 9781461298625 |
| ISSN: | 0072-5285 |
| DOI: | 10.1007/978-1-4612-9860-1 |
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Datensatz im Suchindex
| _version_ | 1804153092439015424 |
|---|---|
| any_adam_object | |
| author | Manes, Ernest G. |
| author_facet | Manes, Ernest G. |
| author_role | aut |
| author_sort | Manes, Ernest G. |
| author_variant | e g m eg egm |
| building | Verbundindex |
| bvnumber | BV042420491 |
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| ctrlnum | (OCoLC)863788914 (DE-599)BVBBV042420491 |
| dewey-full | 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-9860-1 |
| format | Electronic eBook |
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| id | DE-604.BV042420491 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:07Z |
| institution | BVB |
| isbn | 9781461298601 9781461298625 |
| issn | 0072-5285 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027855908 |
| oclc_num | 863788914 |
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| physical | 1 Online-Ressource (X, 356 p) |
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| publishDate | 1976 |
| publishDateSearch | 1976 |
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| publisher | Springer New York |
| record_format | marc |
| series | Graduate Texts in Mathematics |
| series2 | Graduate Texts in Mathematics |
| spelling | Manes, Ernest G. Verfasser aut Algebraic Theories by Ernest G. Manes New York, NY Springer New York 1976 1 Online-Ressource (X, 356 p) txt rdacontent c rdamedia cr rdacarrier Graduate Texts in Mathematics 26 0072-5285 In the past decade, category theory has widened its scope and now interacts with many areas of mathematics. This book develops some of the interactions between universal algebra and category theory as well as some of the resulting applications. We begin with an exposition of equationally defineable classes from the point of view of "algebraic theories," but without the use of category theory. This serves to motivate the general treatment of algebraic theories in a category, which is the central concern of the book. (No category theory is presumed; rather, an independent treatment is provided by the second chapter.) Applications abound throughout the text and exercises and in the final chapter in which we pursue problems originating in topological dynamics and in automata theory. This book is a natural outgrowth of the ideas of a small group of mathematicians, many of whom were in residence at the Forschungsinstitut für Mathematik of the Eidgenössische Technische Hochschule in Zürich, Switzerland during the academic year 1966-67. It was in this stimulating atmosphere that the author wrote his doctoral dissertation. The "Zürich School," then, was Michael Barr, Jon Beck, John Gray, Bill Lawvere, Fred Linton, and Myles Tierney (who were there) and (at least) Harry Appelgate, Sammy Eilenberg, John Isbell, and Saunders Mac Lane (whose spiritual presence was tangible.) I am grateful to the National Science Foundation who provided support, under grants GJ 35759 and OCR 72-03733 A01, while I wrote this book Mathematics Mathematics, general Mathematik Kategorie Mathematik (DE-588)4129930-9 gnd rswk-swf Algebra (DE-588)4001156-2 gnd rswk-swf Theorie (DE-588)4059787-8 gnd rswk-swf Algebraische Struktur (DE-588)4001166-5 gnd rswk-swf Kategorientheorie (DE-588)4120552-2 gnd rswk-swf Algebra (DE-588)4001156-2 s Theorie (DE-588)4059787-8 s 1\p DE-604 Kategorie Mathematik (DE-588)4129930-9 s 2\p DE-604 Kategorientheorie (DE-588)4120552-2 s 3\p DE-604 Algebraische Struktur (DE-588)4001166-5 s 4\p DE-604 Graduate Texts in Mathematics 26 (DE-604)BV000000067 26 https://doi.org/10.1007/978-1-4612-9860-1 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 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Manes, Ernest G. Algebraic Theories Graduate Texts in Mathematics Mathematics Mathematics, general Mathematik Kategorie Mathematik (DE-588)4129930-9 gnd Algebra (DE-588)4001156-2 gnd Theorie (DE-588)4059787-8 gnd Algebraische Struktur (DE-588)4001166-5 gnd Kategorientheorie (DE-588)4120552-2 gnd |
| subject_GND | (DE-588)4129930-9 (DE-588)4001156-2 (DE-588)4059787-8 (DE-588)4001166-5 (DE-588)4120552-2 |
| title | Algebraic Theories |
| title_auth | Algebraic Theories |
| title_exact_search | Algebraic Theories |
| title_full | Algebraic Theories by Ernest G. Manes |
| title_fullStr | Algebraic Theories by Ernest G. Manes |
| title_full_unstemmed | Algebraic Theories by Ernest G. Manes |
| title_short | Algebraic Theories |
| title_sort | algebraic theories |
| topic | Mathematics Mathematics, general Mathematik Kategorie Mathematik (DE-588)4129930-9 gnd Algebra (DE-588)4001156-2 gnd Theorie (DE-588)4059787-8 gnd Algebraische Struktur (DE-588)4001166-5 gnd Kategorientheorie (DE-588)4120552-2 gnd |
| topic_facet | Mathematics Mathematics, general Mathematik Kategorie Mathematik Algebra Theorie Algebraische Struktur Kategorientheorie |
| url | https://doi.org/10.1007/978-1-4612-9860-1 |
| volume_link | (DE-604)BV000000067 |
| work_keys_str_mv | AT manesernestg algebraictheories |