https://direct.mit.edu/books/oa-monograph/5460/Sheaf-Theory-through-Examples Skip to Main Content MIT Press Direct, home MIT Press Direct, home Close * Books + Books Home + Browse Books * Journals + Journals Home + Browse Journals * CogNet * About MIT Press Direct * Customer Support * Librarians Search Dropdown Menu header search search input [ ] Search input auto suggest [ ] filter your search [All Books ] Search Advanced Search User Tools Dropdown Register Sign In Books Gateway Toggle MenuMenu * Browse Books * About * Librarians * Customer Support Skip Nav Destination Sheaf Theory through Examples Sheaf Theory through Examples By Daniel Rosiak Daniel Rosiak Daniel Rosiak is a Research Associate at the Inamori International Center for Ethics and Excellence at Case Western Reserve University. Search for other works by this author on: This Site Google Scholar The MIT Press DOI: https://doi.org/10.7551/mitpress/12581.001.0001 ISBN electronic: 9780262370424 Publication date: 2022 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. The open access edition of this book was made possible by generous funding from Arcadia - a charitable fund of Lisbet Rausing and Peter Baldwin. * Open the Book PDF for in another window * Share Icon Share + Facebook + Twitter + LinkedIn + Email * Tools Icon Tools + Permissions + Cite Icon Cite * Reader Sheaf Theory through Examples By: Daniel Rosiak https://doi.org/10.7551/mitpress/12581.001.0001 ISBN (electronic): 9780262370424 Publisher: The MIT Press Published: 2022 Download citation file: * Ris (Zotero) * Reference Manager * EasyBib * Bookends * Mendeley * Papers * EndNote * RefWorks * BibTex Table of Contents * [ Front Matter ] Doi: https://doi.org/10.7551/mitpress/12581.003.0001 Open the PDF Link PDF for [ Front Matter ] in another window * Acknowledgments Doi: https://doi.org/10.7551/mitpress/12581.003.0002 Open the PDF Link PDF for Acknowledgments in another window * Introduction Doi: https://doi.org/10.7551/mitpress/12581.003.0003 Open the PDF Link PDF for Introduction in another window * 1: Categories Doi: https://doi.org/10.7551/mitpress/12581.003.0004 Open the PDF Link PDF for 1: Categories in another window * 2: Prelude to Sheaves: Presheaves Doi: https://doi.org/10.7551/mitpress/12581.003.0005 Open the PDF Link PDF for 2: Prelude to Sheaves: Presheaves in another window * 3: Universal Constructions Doi: https://doi.org/10.7551/mitpress/12581.003.0006 Open the PDF Link PDF for 3: Universal Constructions in another window * 4: Topology: A First Pass at Space Doi: https://doi.org/10.7551/mitpress/12581.003.0007 Open the PDF Link PDF for 4: Topology: A First Pass at Space in another window * 5: First Look at Sheaves Doi: https://doi.org/10.7551/mitpress/12581.003.0008 Open the PDF Link PDF for 5: First Look at Sheaves in another window * 6: There's a Yoneda Lemma for That Doi: https://doi.org/10.7551/mitpress/12581.003.0009 Open the PDF Link PDF for 6: There's a Yoneda Lemma for That in another window * 7: Adjunctions Doi: https://doi.org/10.7551/mitpress/12581.003.0010 Open the PDF Link PDF for 7: Adjunctions in another window * 8: Sheaves Revisited Doi: https://doi.org/10.7551/mitpress/12581.003.0011 Open the PDF Link PDF for 8: Sheaves Revisited in another window * 9: Cellular Sheaf Cohomology through Examples Doi: https://doi.org/10.7551/mitpress/12581.003.0012 Open the PDF Link PDF for 9: Cellular Sheaf Cohomology through Examples in another window * 10: Sheaves on a Site Doi: https://doi.org/10.7551/mitpress/12581.003.0013 Open the PDF Link PDF for 10: Sheaves on a Site in another window * 11: Elementary Toposes Doi: https://doi.org/10.7551/mitpress/12581.003.0014 Open the PDF Link PDF for 11: Elementary Toposes in another window * A: Appendix (Revisiting Topology) Doi: https://doi.org/10.7551/mitpress/12581.003.0015 Open the PDF Link PDF for A: Appendix (Revisiting Topology) in another window * References Doi: https://doi.org/10.7551/mitpress/12581.003.0016 Open the PDF Link PDF for References in another window * Index Doi: https://doi.org/10.7551/mitpress/12581.003.0017 Open the PDF Link PDF for Index in another window Availability Key * Open Access * Free * Available * No Access Copyright (c) 2022 MIT Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International Public License The open access edition of this book was made possible by generous funding and support from Arcadia - a charitable fund of Lisbet Rausing and Peter Baldwin, and MIT Press Direct to Open This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License . 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