Sheaf Theory through Examples
An approachable introduction to elementary sheaf theory and its applications beyond pure math. Sheaves are mathematical constructions concerned with passages from local properties to global ones. They have played a fundamental role in the development of many areas of modern mathematics, yet the broa...
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| Format: | Online |
| Language: | English |
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The MIT Press
2022
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| Online Access: | ONIX_20221118_9780262370424_5 |
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| _version_ | 1869516625413144576 |
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| author | Rosiak, Daniel |
| author_browse | Rosiak, Daniel |
| author_facet | Rosiak, Daniel |
| author_sort | Rosiak, Daniel |
| collection | Directory of Open Access Books |
| description | An approachable introduction to elementary sheaf theory and its applications beyond pure math. Sheaves are mathematical constructions concerned with passages from local properties to global ones. They have played a fundamental role in the development of many areas of modern mathematics, yet the broad conceptual power of sheaf theory and its wide applicability to areas beyond pure math have only recently begun to be appreciated. Taking an applied category theory perspective, Sheaf Theory through Examples provides an approachable introduction to elementary sheaf theory and examines applications including n-colorings of graphs, satellite data, chess problems, Bayesian networks, self-similar groups, musical performance, complexes, and much more. With an emphasis on developing the theory via a wealth of well-motivated and vividly illustrated examples, Sheaf Theory through Examples supplements the formal development of concepts with philosophical reflections on topology, category theory, and sheaf theory, alongside a selection of advanced topics and examples that illustrate ideas like cellular sheaf cohomology, toposes, and geometric morphisms. Sheaf Theory through Examples seeks to bridge the powerful results of sheaf theory as used by mathematicians and real-world applications, while also supplementing the technical matters with a unique philosophical perspective attuned to the broader development of ideas. |
| format | Online |
| id | doab-20.500.12854ir-93884 |
| institution | Directory of Open Access Books |
| language | eng |
| publishDate | 2022 |
| publishDateRange | 2022 |
| publishDateSort | 2022 |
| publisher | The MIT Press |
| publisherStr | The MIT Press |
| record_format | ojs |
| spelling | doab-20.500.12854ir-938842024-04-04T14:41:06Z Sheaf Theory through Examples Rosiak, Daniel Sheaf theory sheaves category theory categories applied category theory topology geometry logic mathematics thema EDItEUR::P Mathematics and Science::PB Mathematics::PBC Mathematical foundations::PBCD Mathematical logic thema EDItEUR::P Mathematics and Science::PB Mathematics::PBP Topology::PBPH Analytic topology thema EDItEUR::P Mathematics and Science::PB Mathematics::PBF Algebra An approachable introduction to elementary sheaf theory and its applications beyond pure math. Sheaves are mathematical constructions concerned with passages from local properties to global ones. They have played a fundamental role in the development of many areas of modern mathematics, yet the broad conceptual power of sheaf theory and its wide applicability to areas beyond pure math have only recently begun to be appreciated. Taking an applied category theory perspective, Sheaf Theory through Examples provides an approachable introduction to elementary sheaf theory and examines applications including n-colorings of graphs, satellite data, chess problems, Bayesian networks, self-similar groups, musical performance, complexes, and much more. With an emphasis on developing the theory via a wealth of well-motivated and vividly illustrated examples, Sheaf Theory through Examples supplements the formal development of concepts with philosophical reflections on topology, category theory, and sheaf theory, alongside a selection of advanced topics and examples that illustrate ideas like cellular sheaf cohomology, toposes, and geometric morphisms. Sheaf Theory through Examples seeks to bridge the powerful results of sheaf theory as used by mathematicians and real-world applications, while also supplementing the technical matters with a unique philosophical perspective attuned to the broader development of ideas. 2022-11-18T11:05:12Z 2022-11-18T11:05:12Z 2022 book ONIX_20221118_9780262370424_5 9780262370424 9780262542159 https://directory.doabooks.org/handle/20.500.12854/93884 eng The MIT Press image/jpeg Attribution-NonCommercial-NoDerivatives 4.0 International https://doi.org/10.7551/mitpress/12581.001.0001 The MIT Press The MIT Press 10.7551/mitpress/12581.001.0001 10.7551/mitpress/12581.001.0001 ae0cf962-f685-4933-93d1-916defa5123d 9780262370424 9780262542159 The MIT Press 454 Cambridge open access |
| spellingShingle | Sheaf theory sheaves category theory categories applied category theory topology geometry logic mathematics thema EDItEUR::P Mathematics and Science::PB Mathematics::PBC Mathematical foundations::PBCD Mathematical logic thema EDItEUR::P Mathematics and Science::PB Mathematics::PBP Topology::PBPH Analytic topology thema EDItEUR::P Mathematics and Science::PB Mathematics::PBF Algebra Rosiak, Daniel Sheaf Theory through Examples |
| title | Sheaf Theory through Examples |
| title_full | Sheaf Theory through Examples |
| title_fullStr | Sheaf Theory through Examples |
| title_full_unstemmed | Sheaf Theory through Examples |
| title_short | Sheaf Theory through Examples |
| title_sort | sheaf theory through examples |
| topic | Sheaf theory sheaves category theory categories applied category theory topology geometry logic mathematics thema EDItEUR::P Mathematics and Science::PB Mathematics::PBC Mathematical foundations::PBCD Mathematical logic thema EDItEUR::P Mathematics and Science::PB Mathematics::PBP Topology::PBPH Analytic topology thema EDItEUR::P Mathematics and Science::PB Mathematics::PBF Algebra |
| topic_facet | Sheaf theory sheaves category theory categories applied category theory topology geometry logic mathematics thema EDItEUR::P Mathematics and Science::PB Mathematics::PBC Mathematical foundations::PBCD Mathematical logic thema EDItEUR::P Mathematics and Science::PB Mathematics::PBP Topology::PBPH Analytic topology thema EDItEUR::P Mathematics and Science::PB Mathematics::PBF Algebra |
| url | ONIX_20221118_9780262370424_5 |
| work_keys_str_mv | AT rosiakdaniel sheaftheorythroughexamples |