Categorical foundations: special topics in order, topology, algebra, and Sheaf theory
The book offers categorical introductions to order, topology, algebra and sheaf theory, suitable for graduate students, teachers and researchers of pure mathematics. Readers familiar with the very basic notions of category theory will learn about the main tools that are used in modern categorical ma...
Gespeichert in:
| Weitere Verfasser: | , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2004
|
| Schriftenreihe: | Encyclopedia of mathematics and its applications
volume 97 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 Volltext |
| Zusammenfassung: | The book offers categorical introductions to order, topology, algebra and sheaf theory, suitable for graduate students, teachers and researchers of pure mathematics. Readers familiar with the very basic notions of category theory will learn about the main tools that are used in modern categorical mathematics but are not readily available in the literature. Hence, in eight rather independent chapters the reader will encounter various ways of how to study 'spaces': order-theoretically via their open-set lattices, as objects of a fairly abstract category merely via their interaction with other objects, or via their topoi of set-valued sheaves. Likewise, 'algebras' are treated both as models for Lawvere's algebraic theories and as Eilenberg-Moore algebras for monads, but they appear also as the objects of an abstract category with various levels of 'exactness' conditions. The abstract methods are illustrated by applications which, in many cases, lead to results not yet found in more traditional presentations of the various subjects, for instance on the exponentiability of spaces and embeddability of algebras |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 online resource (xii, 417 pages) |
| ISBN: | 9781107340985 |
| DOI: | 10.1017/CBO9781107340985 |
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| 245 | 1 | 0 | |a Categorical foundations |b special topics in order, topology, algebra, and Sheaf theory |c edited by Maria Cristina Pedicchio, Walter Tholen |
| 264 | 1 | |a Cambridge |b Cambridge University Press |c 2004 | |
| 300 | |a 1 online resource (xii, 417 pages) | ||
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| 490 | 0 | |a Encyclopedia of mathematics and its applications |v volume 97 | |
| 500 | |a Title from publisher's bibliographic system (viewed on 05 Oct 2015) | ||
| 505 | 8 | 0 | |t Ordered sets via adjunction |r R.J. Wood |t Locales |r Jorge Picado, Ale�s Pultr, and Anna Tozzi |t Functional approach to general topology |r Maria Manuel Clementino, Eraldo Giuli, and Walter Tholen |t Regular, protomodular, and Abelian categories |r Dominique Bourn and Marino Gran |t Aspects of monads |r John MacDonald and Manuela Sobral |t Algebraic categories |r Maria Cristina Pedicchio and Fabrizio Rovatti |t Sheaf theory |r Claudia Centazzo and Enrico M. Vitale |t Beyond Barr exactness |r George Janelidze, Manuela Sobral, and Walter Tholen |
| 520 | |a The book offers categorical introductions to order, topology, algebra and sheaf theory, suitable for graduate students, teachers and researchers of pure mathematics. Readers familiar with the very basic notions of category theory will learn about the main tools that are used in modern categorical mathematics but are not readily available in the literature. Hence, in eight rather independent chapters the reader will encounter various ways of how to study 'spaces': order-theoretically via their open-set lattices, as objects of a fairly abstract category merely via their interaction with other objects, or via their topoi of set-valued sheaves. Likewise, 'algebras' are treated both as models for Lawvere's algebraic theories and as Eilenberg-Moore algebras for monads, but they appear also as the objects of an abstract category with various levels of 'exactness' conditions. The abstract methods are illustrated by applications which, in many cases, lead to results not yet found in more traditional presentations of the various subjects, for instance on the exponentiability of spaces and embeddability of algebras | ||
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| 700 | 1 | |a Pedicchio, M. C. |d 1953- |4 edt | |
| 700 | 1 | |a Tholen, W. |d 1947- |4 edt | |
| 776 | 0 | 8 | |i Erscheint auch als |n Druckausgabe |z 978-0-521-83414-8 |
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Datensatz im Suchindex
| _version_ | 1804176882290130944 |
|---|---|
| any_adam_object | |
| author2 | Pedicchio, M. C. 1953- Tholen, W. 1947- |
| author2_role | edt edt |
| author2_variant | m c p mc mcp w t wt |
| author_additional | R.J. Wood Jorge Picado, Ale�s Pultr, and Anna Tozzi Maria Manuel Clementino, Eraldo Giuli, and Walter Tholen Dominique Bourn and Marino Gran John MacDonald and Manuela Sobral Maria Cristina Pedicchio and Fabrizio Rovatti Claudia Centazzo and Enrico M. Vitale George Janelidze, Manuela Sobral, and Walter Tholen |
| author_facet | Pedicchio, M. C. 1953- Tholen, W. 1947- |
| building | Verbundindex |
| bvnumber | BV043941061 |
| classification_rvk | SK 320 |
| collection | ZDB-20-CBO |
| contents | Ordered sets via adjunction Locales Functional approach to general topology Regular, protomodular, and Abelian categories Aspects of monads Algebraic categories Sheaf theory Beyond Barr exactness |
| ctrlnum | (ZDB-20-CBO)CR9781107340985 (OCoLC)967601345 (DE-599)BVBBV043941061 |
| dewey-full | 511.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3 |
| dewey-search | 511.3 |
| dewey-sort | 3511.3 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9781107340985 |
| format | Electronic eBook |
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| id | DE-604.BV043941061 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:14Z |
| institution | BVB |
| isbn | 9781107340985 |
| language | English |
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| physical | 1 online resource (xii, 417 pages) |
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| publisher | Cambridge University Press |
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| series2 | Encyclopedia of mathematics and its applications |
| spelling | Categorical foundations special topics in order, topology, algebra, and Sheaf theory edited by Maria Cristina Pedicchio, Walter Tholen Cambridge Cambridge University Press 2004 1 online resource (xii, 417 pages) txt rdacontent c rdamedia cr rdacarrier Encyclopedia of mathematics and its applications volume 97 Title from publisher's bibliographic system (viewed on 05 Oct 2015) Ordered sets via adjunction R.J. Wood Locales Jorge Picado, Ale�s Pultr, and Anna Tozzi Functional approach to general topology Maria Manuel Clementino, Eraldo Giuli, and Walter Tholen Regular, protomodular, and Abelian categories Dominique Bourn and Marino Gran Aspects of monads John MacDonald and Manuela Sobral Algebraic categories Maria Cristina Pedicchio and Fabrizio Rovatti Sheaf theory Claudia Centazzo and Enrico M. Vitale Beyond Barr exactness George Janelidze, Manuela Sobral, and Walter Tholen The book offers categorical introductions to order, topology, algebra and sheaf theory, suitable for graduate students, teachers and researchers of pure mathematics. Readers familiar with the very basic notions of category theory will learn about the main tools that are used in modern categorical mathematics but are not readily available in the literature. Hence, in eight rather independent chapters the reader will encounter various ways of how to study 'spaces': order-theoretically via their open-set lattices, as objects of a fairly abstract category merely via their interaction with other objects, or via their topoi of set-valued sheaves. Likewise, 'algebras' are treated both as models for Lawvere's algebraic theories and as Eilenberg-Moore algebras for monads, but they appear also as the objects of an abstract category with various levels of 'exactness' conditions. The abstract methods are illustrated by applications which, in many cases, lead to results not yet found in more traditional presentations of the various subjects, for instance on the exponentiability of spaces and embeddability of algebras Categories (Mathematics) Kategorie Mathematik (DE-588)4129930-9 gnd rswk-swf Kategorie Mathematik (DE-588)4129930-9 s 1\p DE-604 Pedicchio, M. C. 1953- edt Tholen, W. 1947- edt Erscheint auch als Druckausgabe 978-0-521-83414-8 https://doi.org/10.1017/CBO9781107340985 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Categorical foundations special topics in order, topology, algebra, and Sheaf theory Ordered sets via adjunction Locales Functional approach to general topology Regular, protomodular, and Abelian categories Aspects of monads Algebraic categories Sheaf theory Beyond Barr exactness Categories (Mathematics) Kategorie Mathematik (DE-588)4129930-9 gnd |
| subject_GND | (DE-588)4129930-9 |
| title | Categorical foundations special topics in order, topology, algebra, and Sheaf theory |
| title_alt | Ordered sets via adjunction Locales Functional approach to general topology Regular, protomodular, and Abelian categories Aspects of monads Algebraic categories Sheaf theory Beyond Barr exactness |
| title_auth | Categorical foundations special topics in order, topology, algebra, and Sheaf theory |
| title_exact_search | Categorical foundations special topics in order, topology, algebra, and Sheaf theory |
| title_full | Categorical foundations special topics in order, topology, algebra, and Sheaf theory edited by Maria Cristina Pedicchio, Walter Tholen |
| title_fullStr | Categorical foundations special topics in order, topology, algebra, and Sheaf theory edited by Maria Cristina Pedicchio, Walter Tholen |
| title_full_unstemmed | Categorical foundations special topics in order, topology, algebra, and Sheaf theory edited by Maria Cristina Pedicchio, Walter Tholen |
| title_short | Categorical foundations |
| title_sort | categorical foundations special topics in order topology algebra and sheaf theory |
| title_sub | special topics in order, topology, algebra, and Sheaf theory |
| topic | Categories (Mathematics) Kategorie Mathematik (DE-588)4129930-9 gnd |
| topic_facet | Categories (Mathematics) Kategorie Mathematik |
| url | https://doi.org/10.1017/CBO9781107340985 |
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